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Self-organising processes of task allocationZoethout, K.

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Self-Organising Processes of Task Allocation

A Multi-Agent Simulation Study

Kees Zoethout

Publisher: Labyrinth Publications

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ISBN-10: 90-5335-096-9

ISBN-13: 978-90-5335-096-6

© 2006, K. Zoethout

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RIJKSUNIVERSITEIT GRONINGEN

Self-Organising Processes of Task Allocation A Multi-Agent Simulation Study

Proefschrift

ter verkrijging van het doctoraat in de

Bedrijfskunde

aan de Rijksuniversiteit Groningen

op gezag van de

Rector Magnificus, dr. F. Zwarts,

in het openbaar te verdedigen op

donderdag 30 november 2006

om 14.45 uur

door

Kornelis Zoethout

geboren op 7 januari 1968

te Rauwerderhem

Promotor: Prof. Dr. H.B.M. Molleman

Copromotor: Dr. W. Jager

Beoordelingscommissie: Prof. Dr. N. Gilbert

Prof. Dr. R.J.J.M. Jorna

Prof. Dr. K.G. Troitzsch

Dit proefschrift beschrijft gedrag van gesimuleerde mensen. Waar gesproken wordt van ‘hij’ of ‘hem’ kan niet gelezen worden ‘zij’ of ‘haar’. De agents die de mensen representeren hebben namelijk geen geslachtskenmerken. Hoewel dit betekent dat ik strikt genomen de agents zou moeten aanduiden met ‘het’ heb ik dit niet gedaan vanwege de rare zinnen die dit oplevert.

Voorwoord

Gemakkelijk aanvaarden we de werkelijkheid, misschien omdat we bij intuïtie voelen dat niets werkelijk is (Jorge Luis Borges).

Een origineel voorwoord van een proefschrift schrijven is lastig. De inhoud, een korte schets hoe het toch zover heeft kunnen komen, een korte beschrijving van de hindernissen op de weg er naartoe en de dankwoorden richting de mensen die tot het eindproduct hebben bijgedragen ligt min of meer vast. In sommige gevallen leidt dit tot een verhaal over een lange zoektocht vol ontberingen waarbij besloten wordt de partner te bedanken zonder wiens steun dit alles nooit mogelijk zou zijn geweest. Soms wordt een proefschrift vergeleken met het baren van een kind, een vergelijking die overigens vooral door mannen wordt gemaakt, maar waar ik zelf als vader helemaal niet achter sta. Veel dank wordt verschuldigd aan mensen die een soort mentorpositie hebben vervuld, de meester die zijn kennis heeft overgedragen aan zijn leerling. Ook al is de bezetting steeds weer anders, het proces is min of meer hetzelfde. Hoe kan iets dat al zo vaak is beschreven dan toch nog op een oorspronkelijke manier worden verwoord? Een standaardverhaaltje schrijven is te gemakkelijk maar ik wil ook niet in de valkuil trappen originaliteit te willen maar gekunsteld te eindigen. Het enige dat me daarom nog rest is het voorwoord gewoon vanuit mijn eigen beleving te schrijven.

Het idee voor het onderzoek dat ik in dit proefschrift beschrijf stamt uit de tijd dat ik psychologie studeerde. Tijdens mijn studie werd ik gegrepen door het concept zelforganisatie, orde die vanzelf ontstaat, zonder bemoeienis van buitenaf, en allerlei vragen die daaraan zijn verbonden. Hoe ontstaan structuren? Hoe organiseren de hersenen zichzelf, zonder centraal besturingssysteem dat kennis ordent en indrukken categoriseert? Hoe kan het dat een mierenhoop zo’n ingewikkelde structuur heeft en tegelijkertijd in staat is zich op een flexibele wijze op zijn omgeving af te stemmen zonder dat daar enig management of ontwerp aan te pas is gekomen? Door de fascinatie voor dergelijke vragen en het onvermogen ze te beantwoorden werd zelforganisatie een soort mythisch concept voor me. Dit leidde ertoe dat ik me tijdens mijn studie eerst begon te verdiepen in zelforganiserende neurale netwerken om van daaruit een overstap te maken naar zelforganiserende sociale netwerken. Destijds wilde ik een beschrijving maken, gebaseerd op algemene zelforganiserende mechanismen en kennis van zelforganiserend gedrag van verschillende sociale dieren, zoals apen, wolven en mieren. Deze beschrijving zou ik vervolgens gebruiken om sociaal gedrag van mensen te beschrijven om zo vragen te beantwoorden als: ‘hoe ontstaan groepen? of ‘hoe werpt een leider zich op?’ Naast sociale kenmerken zou ik veel aandacht moeten besteden aan cognitieve en affectieve kenmerken. Dit zou ik dan allemaal onderzoeken met behulp van computersimulatie. De reden voor zo’n ingewikkelde omweg om menselijk gedrag te bestuderen kwam voort uit mijn overtuiging dat een samenleving als de onze te geordend en daardoor te weinig ruimte bood om spontane orde te kunnen waarnemen, enkele kunstenaarskolonies uitgezonderd. Ik wilde mensen beschrijven zoals ze oorspronkelijk waren, zonder de structuur van een Westerse samenleving, maar als dieren.

Een aantal jaren later –ik was inmiddels allang afgestudeerd maar had deze droom nog steeds niet verwezenlijkt- kwam ik op het spoor van een Aio-plaats met als titel: ‘Variatie en de noodzaak tot zelforganisatie’. Nadat ik het onderzoeksvoorstel had doorgelezen kwam ik tot de conclusie dat dit project voldoende aanknopingspunten bood om mijn hoogdravende ideeën in kwijt te kunnen, solliciteerde en werd aangenomen. Het eindproduct ligt voor u, geenszins een direct gevolg van het uitwerken van het oorspronkelijke onderzoeksvoorstel, zeker niet de verwezenlijking van mijn droom, maar iets dat ertussen in zit, met eigenschappen van beide en toch met een eigen identiteit. Toch een kind?

Mijn Aio-tijd betekende een tijd vol veranderingen. Ik was weer terug op de universiteit, met een mogelijke wetenschappelijke carrière in het verschiet, maar het belangrijkste was dat ik ging ik trouwen met Karin en vader werd. We kregen twee kinderen, Hanne en Mindra en zoals dat zo hoort te gaan zette het ouderschap mijn leven een tijdje op zijn kop. Gelukkig bleef er altijd tijd voor acteren en zeilen.

Maar ik zal u mijn al te persoonlijke bespiegelingen besparen en verder gaan met het bedanken van de mensen zonder wie ik dit proefschrift nooit geschreven zou kunnen hebben. Mijn dank gaat ten eerste uit naar Eric Molleman, wiens nuchterheid me steeds weer op aarde terugzette wanneer ik weer eens een poging tot hemelbestormen had ingezet. Verder dank ik natuurlijk Wander Jager die me niet alleen introduceerde binnen ESSA, de Europese Sociale Simulatie Associatie, maar me ook met zijn altijd optimistische houding steeds weer op wist te beuren wanneer ik me weer eens vertwijfeld afvroeg wat er voor anderen toch zo boeiend was aan hetgeen ik deed. Binnen deze bipolariteit had ik geen betere combinatie van begeleiders kunnen treffen. Daarnaast ben ik Gerhard Dalenoort veel dank verschuldigd, omdat hij me tijdens mijn studie psychologie op het huidige onderzoeksspoor heeft gezet waarvan dit proefschrift overigens geenszins een eindstation is. De leden van het cluster Human Resource Management and Organizational Behaviour wil ik bedanken voor de prettige sfeer waarbinnen ik heb kunnen werken en de Aio’s voor de gezellige lunches en de leuke gesprekken. Mijn dank gaat ook uit naar de mensen binnen en buiten de faculteit Bedrijfskunde voor de tijd die ze hebben genomen om met mij van gedachten te wisselen over mijn onderzoek en aanverwante zaken. Verder wil ik de leden van mijn leescommissie, Klaus Troitzsch, Nigel Gilbert en René Jorna bedanken voor hun opbouwende commentaar en nuttige aanvullingen. Hierbij wil ik René Jorna extra bedanken omdat hij vooral tijdens de afrondende fase van mijn proefschrift zich erg betrokken toonde bij mijn toekomstmogelijkheden.

Daarnaast bedank ik mijn goede vrienden en tevens paranimfen Jan Hein, die me dankzij de vele mailtjes die we elkaar tijdens mijn Aio-tijd stuurden zeker een half jaar tijd heeft gekost en Mathijs, die af en toe belangstellend vroeg of ik met mijn onderzoek nu eindelijk al eens iets nieuws had ontdekt en me zo fijntjes op de relativiteit van dit soort arbeid wist te wijzen. Maar ik bedank ook al mijn andere vrienden en vriendinnen omdat vriendschappen het leven nu eenmaal meer kleur bieden dan een proefschrift, zelfs al is het paars met roze gekaft. Zonder hen had ik onmogelijk de motivatie kunnen opbrengen om zo lang aan een project te werken. Verder bedank ik ook mijn ouders en schoonouders voor de vele keren dat ze als oppas fungeerde zodat ik weer verder kon met mijn proefschrift. Ik wil ook alle spelers bedanken waarmee ik tijdens de afgelopen jaren toneelproducties heb gemaakt. Zonder

hen had ik beslist het risico gelopen een workaholic te worden en van verslavingen zijn mensen nog nooit beter geworden. Bedankt ook Meta en Keimpe, die me steeds weer wisten op te kalefateren wanneer ik weer eens teveel hooi op mijn vork had genomen en me met mijn voeten op aarde zetten wanneer ik te bevlogen was. Tenslotte wil ik Karin nog het meest bedanken, voor het dragen van mijn humeurigheid wanneer ik me weer eens had vastgebeten in de diverse programmeerproblemen, voor het meedenken met de verschillende fasen van mijn proefschrift, maar vooral omdat ze is wie ze is, als collega, medetoneelspeelster en regisseur, maar vooral als mijn vrouw en moeder van onze kinderen. En als allerlaatste wil ik Hanne en Mindra bedanken voor het inzicht dat de naïeve blik van een kind soms meer ziet dan de geschoolde blik van een wetenschapper.

Kees Zoethout

Groningen, November 2006

Table of Contents

Chapter 1 Introduction 1 1.1 Self-organisation in a socio-managerial context 2 1.2 A comparison with the brain 5 1.3 The whole and its parts 6 1.4 Self-managing teams and task allocation 7 1.5 Multi agent simulation 9 1.6 The chapters 11

Chapter 2 Modelling 13 2.1 Introduction 13 2.2 Neural Networks and Social Processes 15

2.2.1 From a Brain Metaphor to Self-Organising Neural Networks 15 2.2.2 A Neural-Network Model: Properties and principles 16 2.2.3 Social Processes of Task Allocation 17

2.3 Task Components 17 2.4 Psychological Components 18

2.4.1 The Cognitive Architecture of the Agent 19 2.4.2 Interaction at the Skill Level 21 2.4.3 The Individual Level: Social Interaction 22

2.5 Concluding Remarks 23

Chapter 3 Formalisation and Verification 25 3.1 Introduction 25 3.2 A theoretical framework 27

3.2.1 The task 27 3.2.2 A task performing system 28

3.3 Formalisation and Description of WORKMATE 31 3.3.1 The task 32

3.3.2 Initial choice 32 3.3.3 Excitation and inhibition 34 3.3.4 Learning 36 3.3.5 Performance 37

3.4 Results 37 3.4.1 Experiment 1: Expertise differences and coordination time 38 3.4.2 Experiment 2: Task variety, coordination time, and specialisation 42 3.4.3 Experiment 3: Boredom 45

3.5 Discussion 47

Chapter 4 Simulating the emergence of task rotation 49 4.1 Introduction 49 4.2 The model 50

4.2.1 The task 50 4.2.2 The agents 50 4.2.3 The model 51 4.2.4 The Allocation Process 52 4.2.5 Performance, learning and boredom 54

4.3 Experiments 55 4.4 Results 58

4.4.1 Organisation type 58 4.4.2 Boredom 60 4.4.3 Rotation frequency 62

4.5 Conclusions and Discussion 65 4.5.1 Conclusions 65 4.5.2 Discussion 66

Chapter 5 Task Dynamics in Self-Organising Task Groups 68 5.1 Introduction 68 5.2 The model 70

5.2.1 Tasks and task dynamics 70 5.2.2 The multi agent system 71 5.2.3 Specialisation and generalisation 73 5.2.4 Model and hypotheses 74

5.3 Experimental Design 76 5.3.1 Variables and Design 76 5.3.2 parameter values and initial settings of the agents 77

5.4 Results 78

5.4.1 Total performance time 78 5.4.2 Acceptance of the hypotheses 80 5.4.3 Underlying processes 81

5.5 Conclusion and discussion 88

Chapter 6 Newcomers in Self-Organising Task Groups 91 6.1 Introduction 91 6.2 The model 93

6.2.1 The multi agent system 93 6.2.2 Task and task performance 94 6.2.3 Model and hypotheses 96

6.3 Experimental design 98 6.3.1 Variables and design 98 6.3.2 Agent values and parameter settings 99

6.4 Results 101 6.4.1 Total performance time 102 6.4.2 Underlying processes 103 6.4.3 Acceptance of the hypotheses 106

6.5 Conclusion and discussion 106

Chapter 7 Conclusion 109 7.1 Modelling self-organising social processes of task allocation 109 7.2 Verification of the model and the program 111 7.3 Task rotation and minimal critical specification 112 7.4 Task dynamics and requisite variety 112 7.5 Task rotation, flexibility and redundancy of functions. 113 7.6 Expertise and motivation processes and learning 114 7.7 Final Conclusion 115

Chapter 8 Discussion 117 8.1 Scientific contribution 117 8.2 Managerial contribution 118 8.3 Validation of the model 120

8.4 Strength, Weaknesses and Future Research 121 8.5 Finally 123

References 125 URLs: 137

Appendix I. Computer Code 139

Samenvatting 146

1

Chapter 1 Introduction

The group escaped from the crash site after nearly three months. But the group that came down from Andes was not the same group that began the chartered flight; the pattern of relationships among the group members, or the group’s structure, had been altered.

(cited from Forsyth, 1983)

This quote describes some of the dramatic consequences of the air crash of a rugby team in the Andes in 1972. Many were severely injured, many were dead. The survivors had no radio, only some candy bars, wearing only ruby equipment. From the twenty six survivors only sixteen finally survived. The story of all the horrible things the survivors had to endure (Read, 1974) serves as an important example that describes different aspects of group dynamical processes and structures (see Forsyth, 1983). For instance, it describes how people organise without the context of an organisation. Although the rugby-team already had some organised structure, the horrible circumstances in the Andes forced them to coordinate their actions in a whole different manner than what they were used to do on the field. Without the daily structure of an organisation, in circumstances that differ largely from normal life, people must create new structures by organising their own behaviour. But how do they do that? Cases such as the Andes group describe that roles, status patterns, and communication networks emerge, but how do the underlying processes take place? How do people organise their own behaviour?

Unlike other animal behaviour, human behaviour is embedded in an institutionalised context (Zoethout, Jager, and Molleman, 2004). This implies that human behaviour in organisations is not only determined by individual characteristics and interactions emerging from it, but mostly by the organisational structure this behaviour is embedded in. In this way, components that determine human behaviour can be split up in top-down processes that indicate how our behaviour is enforced by the institutionalised context that we are working in and in bottom-up processes, that describe how we organise ourselves. The first question as stated above can be answered just by studying human behaviour in organisations. The second question however, cannot be answered by just looking at the daily world around us. By definition societal structures hinder the study of bottom-up processes. It is just because of that that scientists use cases such as the Andes group for building theories: only without the cover of institutions the human ability to organise becomes visible. Thus it is important to know how human beings organise their own behaviour because we could only be able to answer the question to


2

what extent we need these institutions if we would know what our behaviour is like without them. Therefore, the main question I would like to answer is:

How does a group of human beings organises its own behaviour?

Another fundamental question that precedes this question is why human beings organise themselves. With regards to the Andes case the answer would be quite easy to give: in order to survive. In other cases the answer might be less easy to give and refers to ‘improving performance’ or ‘to accomplish something that cannot be done without organising’. However, in this thesis I will not focus on this. To answer the question that I stated above, in this chapter first I will focus on the concept of self-organisation and relate this to a socio-managerial context. On the basis of this, I will describe a basic self-organising principle by means of a comparison between organisations and the brain. I further will clarify some concepts from General Systems Theory (GST) that are related to the different aggregation levels of the study of self-organising social systems. Then I will restrict the broad question as stated above down to the study of self-organising processes of task allocation. Next, I will describe the research method that I used and position this thesis within the tradition of this method. I will finish this chapter by giving an overview of the different chapter this thesis consists of.

1.1 Self-organisation in a Socio-Managerial Context Self-organisation refers to the process in a system leading to the emergence of global order within this system without the presence of another system dictating this order (e.g. Dalenoort, 1989; 1995; Heylighen, 1997). Self-organising systems have been object of study in a wide variety of disciplines, such as chemistry (Prigogine & Stengers, 1984), biology (Maturana & Varela, 1980) and cognitive psychology (Dalenoort, 1982; 1995). Self-organising principles of social systems have been formulated as well (for an overview, see Ulrich & Probst, 1984) but those principles are formulated in an abstract system-theoretical way and are not related to behavioural theory.

The aforementioned definition of self-organisation is the most widely used definition that I will use in this thesis as well. However, some scholars in management literature use the concept of self-organisation to refer to local autonomy instead of an emergent ordering process (e.g. Kuipers, 1989; Molleman & Van der Zwaan, 1994; Molleman, 1998; 2000). As the title of the paper ‘self-organisation as design principle’(Kuipers, 1989) demonstrates, here the concept refers to the result of an externally dictated design-approach. But according to the first definition, self-organisation cannot be designed, nor externally dictated: ‘self-organisation as design principle’ is a contradiction in terms (see also Zoethout & Molleman, 2000).

It looks as if the different use of the concept of self-organisation in management science seems to express a difference between top-down design and bottom-up development. In a sense, this difference can be related to two contrasting views: The classic view states that there must be some kind of entity that brings order into chaos, a

Chapter 1: Introduction

3

God that creates life and structures nature. In contrast to this, nowadays we know that the emergence of life as well as the ordering principles of nature can be described by using self-organising mechanisms (e.g. Kauffmann, 1995). Therefore, it can be questioned whether or not an organisation needs a designer to bring order out of chaos at all! (Zoethout, 2002; see also Rutges, 2002). For instance, social insects such as bees and ants, that are both simple creatures compared to us, are able to form complex organisations that are able to adapt flexibly to a changing environment (Hemelrijk, 2005; Gordon, 2001; Camazine, Deneubourg, Franks, Sneyd, Theraulaz, & Bonabeau, 2001; Hemelrijk, 2002; see also Rutges, 2002). If they do not need an organisational design or managers, why do we?

But human beings are not bees, for instance because we have the cognitive capacity of self-consciousness which enables us to anticipate all kinds of possible future scenarios. And although by principle we cannot know whether our self-consciousness really manages our actions or makes us just an observer of it, it is a necessary condition to create functions related to management and organisation design. Furthermore, because human beings have a need for leadership or control (De Vries, Roe, & Taillieu, 1999), a manager could very well function as someone to fulfil this need. Moreover, as the empirical studies of Burns & Stalker (1961) have indicated, in stable environments a top-down approach, which they call a mechanistic approach, may function the best, whereas a bottom-up organic approach fits best in dynamic environments (Burns & Stalker, 1961).

Nevertheless, nature shows that highly complex adaptive organisations survive without any top-down management or design, but just by means of self-organisation. This evokes the question whether or not management science uses principles of self-organisation to describe organisational processes. But, as we stated, the confusion of concepts related to self-organisation and design makes it difficult to describe how the concept of self-organisation is integrated into management science. For instance Morgan (1986) formulated four principles of holographic design1 that must facilitate the process of self-organisation. These principles indicate under which conditions self-organisation may or may not occur. Therefore, I would rather speak of conditions instead of principles. These conditions are: requisite variety, minimum critical specification, double loop learning, and the redundancy of functions (see also Zoethout & Molleman, 2000). To describe the integration of the concept of self-organisation in management science I will shortly discuss each of these conditions.

The first condition, ‘requisite variety’, is often referred to as ‘Ashby’s law’ (1956). This condition describes that the internal diversity of any self-organising system should match at least the diversity of its environment. This condition implies that a stable

1 The notion of holographic design is based on the false assumption that the brain is somehow structured as a hologram, i.e. information about the whole is stored in every part. For instance, if you could break a hologram of a brain in 1000 pieces, you would end up with 1000 little holograms of a complete brain. Unfortunately, a real brain is organised differently (e.g. Rumelhart, 1998).


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environment matches the best with a mechanistic centralised organisation, a turbulent environment demands an organic organisation with high individual autonomy, and somewhere in between, autonomous teams would match the demands of the environment the best (Molleman, 1998). The empirical studies of Burns & Stalker (1961) indicated this condition to be valid. The implications of this condition are worked out further in chapter five of this thesis.

In addition to the first condition, the second condition of minimal critical specification states that only critical issues should be fixed (Herbst, 1974). This condition is related to the tension between top-down structures and bottom-up processes. Too much structure leads to a rigid system with no self-organising processes at all but not enough structure may lead to performance loss (Burns & Stalker, 1961). Some consequences of this condition, such as the relation between the freedom to self-organise and performance are described in chapter four of this thesis.

Whereas the first and second condition describe the relation of a self-organising system with its environment, the other two conditions describe the consequences within the system (Zoethout & Molleman, 2000). The third condition, double loop learning is also referred to as learning to learn (Argyris & Schön, 1978). Whereas single loop learning implies to skill improvement, double loop learning refers to monitoring the tasks (including its goal) itself and constantly looking for better alternatives. In all the studies I describe in this thesis, I use the concept of task as an independent variable. This means that a group cannot choose or change its own task. Therefore, the concept of double loop learning does not apply to the self-organising processes I describe in this thesis.

The last condition is aimed at the redundancy of functions, which refers to the multi-availability of team members, with regards to knowledge, skills and abilities (Morgan, 1984; Kuipers, 1989). Without redundancy of functions a team lacks the flexibility to re-organise itself in case of external changes or personnel loss. In theory redundancy of functions does not necessarily imply multi-functionality of team members: two team members, one with function A and B and one with function B and C have as much redundancy of functions as four team members, one with A, two with B and one with C. However, in organisational practice, workers are not hired to just sit and wait. Therefore, redundancy of functions does refer to multi-functionality. Although not used as a variable or parameter, all chapters in this thesis refer to it.

Although these conditions are necessary for the process of self-organisation to take place in the first place, they do not offer a description of the process itself. For describing self-organising social process, some scholars compare a human organisation with the human brain (e.g. Beer, 1981; Morgan, 1986; Minsky, 1986; Zoethout, 1994) because the human brain is self-organising, able to learn, and a complex system that can be described by means of simple interconnecting element, i.e. neurons. To understand why such a comparison is useful and to create a framework to describe self-organising processes, I will now shortly describe this comparison.


5

1.2 A Comparison with the Brain Varela (1981;1984) states that the autonomy of a system is defined by its organisation. Autonomous systems are characterised by organisational closure which is defined by two properties that are based on the assumption that a system can be described as a network of interactions. These properties hold that: a) the interactions regenerate the system i.e. the system is able to maintain itself. b) by means of these interactions, the system distinguishes itself from its environment. The definition of Beer (1981), i.e. a system that is responsible for its own regulation, agrees with this.

Since a self-organising system is able to regulate itself by definition, every self-organising system functions autonomously. To describe the internal processes that maintains the autonomy of the system, some scholars used a cybernetic description with the help of operators, feedback loops and the like (e.g. Beer, 1981; Von Foerster, 1984; Geyer & Van der Zouwen, 2001) and relate this to human behaviour. However, a description of self-organising social processes that is based on psychological theory has - as far as I know- never been made.

As I stated, a comparison with the brain could be useful to describe self-organising social processes. To do so, we must know first how to describe self-organising processes in the brain. These processes are described by making use of neural network models (see Rumelhart, Hinton, and Williams, 1986). They are based on the notion that the brain consists of a large network of interconnected neurons. Self-organisation is described in terms of changes of the connections between the neurons (e.g. Dalenoort, 1982). The only principle that describes these changes, i.e. Hebb’s learning rule, states that simultaneous activity of two elements increases the likelihood for the emergence of an new - or strengthening of an existing- connection between those elements (Hebb, 1949). The application of Hebb’s learning rule as a general principle to describe social processes is first formulated by Zoethout (1994) and is worked out later by Nowak, Vallacher, & Burnstein (1998) and Kitts, Macy & Flache (1999). With respect to this, Kitt’s et al. (1999) refer to structural learning that refers to changes in the structure of the social network. This type of learning exists next to individual learning in the classic sense, i.e. individual changes such as skill improvement. An elaborate description of this can be found in chapter two. The distinction between structural learning and individual learning must not be confused with the distinction between single loop and double loop learning. The first refers to the difference between learning at the individual and the social aggregation level whereas the second refers to the difference between improving skills and improving tasks. This means for instance that a single individual has the capability for double loop learning but not for structural learning. Furthermore, within a group that cannot change its own task (as in the experiments in my thesis) there is both individual learning and structural learning but only single loop learning.

Thus, a comparison with the brain brought us to the application of Hebb’s learning rule to describe self-organising social processes. This rule enables the possibility for describing self-organising social processes in terms of individual interactions by means of a network metaphor. In chapter two I relate these processes to behavioural theory.


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On the basis of these interactions, a social structure, i.e. a group, may emerge. This may imply that individual behaviour cannot only be described in terms of local interactions, but is also as a function of the group as a whole. For instance, the influence of reputation (Conte & Paolucci, 2002) describes how a group influences its members. In the next section I will discuss the reciprocal action between individual and group in relation to the concepts of emergence, i.e. the influence of the lower individual level to the higher group level and downward causation, the influence of the higher group level to the lower individual level.

1.3 The Whole and its Parts When a group is formed as a result of self-organising processes, some properties of the group can be considered as emergent. Emergent properties refer to higher level properties, i.e. from the group, that cannot be reduced to lower level properties, i.e. the individuals (Heylighen, 1997; Klein & Kozlowski, 2000a). The notion of emergence originates from the GST approach that states, using Aristotle’s words, that the whole is more than the sum of its parts. This approach contradicts with a reductionist approach that states that the whole equals the sum of its parts. According to the latter approach, the whole could be studied just by studying its parts. For instance, a crowd could be studied just by describing the properties of each individual, the brain of an individual could be understood just by studying each neuron separately, etc. However, it seems to be equally impossible to know the parts without knowing the whole than to know the whole without knowing the parts in detail (cited from Pascal, 1995b). Therefore, according to GST, we must study our subjects of research on different aggregation levels and relate these levels to another. This implies that, by studying a crowd, we must focus at the behaviour of both the individual and the crowd level, and by studying the brain, we must relate a description of the brain to the properties of a neuron.

Whereas the notion of emergence describes how lower level properties influence higher level properties, the notion of downward causation describes the opposite. Originally formulated by Campbell (Campbell, 1974; see also Heylighen, 1995), downward causation refers to the notion that all processes at a the lower level of a hierarchy are restrained by and act in conformity to the laws of the higher level. In shorten this means that a group determines the behaviour of its members (e.g. Zeggelink, 1993). The condition of minimal critical specifications of Herbst (1974) that I stated in the former section addresses to this notion because it states that there should only be minimal restriction from the higher level to the lower level.

On the basis of this I may state that self-organising processes in a social system, i.e. a group, can be described as a combination of horizontal and vertical processes. The horizontal processes refer to the interactions between the members of the group that can be described with the use of a network analogy. Vertical processes indicate to processes between the higher (group) and the lower (individual) aggregation level. The horizontal processes affect the higher level properties and, therefore, the vertical processes. At the same time the vertical processes influence the horizontal processes. Therefore, to answer the question: ‘What makes the whole more than the sum of its


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parts’, from a Systems Theoretical point of view one could answer that the difference between the whole and its parts is determined by the relations among the parts (see also Klein & Kozlowski, 2000a; 2000b).

1.4 Self-Managing Teams and Task Allocation Now that I have described some general properties and principles of a self-organising system, I will focus on the research subject of this thesis: self-managing teams. A self-managing team can be defined as a group of workers being responsible for the performance of a task, whereas each worker possesses a variety of skills relevant to that task (e.g. Manz, 1992). In theory, a self-managing team has the freedom to allocate and perform the task any way the team likes. Therefore, apart from all difficulties of implementing and maintaining them, within self-managing teams, there must be self-organising processes. Moreover, since the start of the popularity of the concept of self-managing teams, there has not been given a description of the self-organising processes within these teams yet.

Since a self-managing team consists of a group of people that must perform a task, it is likely that we study the processes of task allocation. Self-organising processes of task allocation have been studied within biology, for instance how ants allocate tasks on the basis of local interactions (e.g. Gordon, 2001). However, they have not been studied within the area of management science. Although there has been research on the behavioural and motivational consequences of task characteristics, primarily based on the Job Characteristics Model (Hackman & Oldham, 1980), the behavioural and motivational consequences of self-organising processes of task allocation have not been studied so far.

Components that determine the process of task allocation can be divided in task components and team components. Task components refer to the complexity of the task, i.e. the number of skills that are necessary to perform the task (skill variety), the interdependence between the different parts of the task, and the way in which the task changes over time (task variety) (Wood, 1986). Team components can be divided in attributes of the individual team members such as expertise and motivation (Wilke & Meertens, 1994) and social components, such as power, attraction (Leary, 1957; Kiesler, 1983) and coordination (Wilke & Meertens, 1994). These components influence the performance of the team (e.g. Wilke & Meertens, 1994). Figure A describes all these components:


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Figure A The model

An elaborate description of this model is given in chapter two, which forms the basis of the study this thesis is about.

A systematic study that includes all these components would easily lead to incomprehensible results. As Bonini’s Paradox states: The more realistic and detailed one’s model, the more the model resembles the modelled organisation, including resemblance in the directions of incomprehensibility and indescribability’ (Starbuck, 1976, p. 1101, cited in Weick, 1979). Therefore choose to study these components in a stepwise manner. I started studying the influence of task variety, and the individual components on the task allocation process in relation to performance (see the bold components in Figure A). I will describe this in chapter two. On the basis of these findings, I explore the group dynamical processes in more detail, especially by focusing on the conditions under which task rotation emerges, the process in which workers mutually changed what they were doing. This will be described in chapter three. On the basis of this study I am able to describe the processes within the system as a function of the variables that are marked bold in Figure A. However, these processes are only tested in stable conditions. A description of self-organising processes should certainly incorporate processes related to the flexibility of the system in case the conditions change. On the one hand, the work to be done might change (‘the demand side’). On the other, changes may come from the human resource side of the system (‘supply side’) Therefore, I will conduct two series of experiments. The first series focuses on the behaviour of the system as a function of task changes. Starting from the basis I formulate in chapter two, using a design that incorporates groups of generalists and groups of specialists, I conduct experiments about the relation between team performance and task dynamics. This will be described in chapter four. Whereas these experiments focus on the demand side, the second series describe how the system would adapt to changes in the supply side of the system, or, more specifically, adapt to the entrance of newcomers in the team. This will be described in chapter five.


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Simply due to a limited time horizon for writing this thesis, I primarily focus on task variety as a factor that affects the task allocation process. I do not study the social components of power and attraction, although these may lead to fascinating dynamics regarding group and subgroup formation and possible leadership dynamics. However, I do study the related component of coordination, but only in some pilot experiments (see Chapter 3).

1.5 Multi Agent Simulation Now that I have described what I study, I will proceed with specifying how I am going to study it. I have stated that the study of self-organising behaviour is hard because humans mainly operate in an institutionalised context. We can only answer the question to what extent we need organisational structures if we know what our behaviour would be like without them. Moreover, in theory, self-organising processes occur in self-managing teams, while in practice such self-managing teams are not purely self-managing because of management practice and organisational constraints (Manz, 1992). Therefore, a study of self-organising processes of task allocation should take place in an artificially context, such as team building sessions or experimental settings. However, for a number of reasons these real-life-contexts will not be sufficient.

First, experimentation with human beings is limited because of its limited possibilities to control for the large number of variables involved and its possible threats to the internal validity (Arrow, McGrath, & Berdahl, 2000). Within a laboratory setting, it is almost impossible to control for variables related to age, sex and gender, status, or social abilities. In field settings there are even less possibilities to control, because of the institutional environment of the research subject. Furthermore, is impossible to elaborately manipulate all kinds of relevant variables and parameters, just to describe their relation. Cook & Campbell (1979) mention a number of threats to the internal validity. For instance, human beings learn or get bored during the experiments which may affect their performance in the next task. This effect is called maturation. The effect of testing, i.e., familiarity of a test which may increase performance, is related to this. All such threats make it difficult to study self-organising processes.

Second, social psychological observations or experiments are not sufficient to describe the complexity and dynamics of social systems (Arrow et al. 2000; Vallacher & Nowak, 1994; Jager & Mosler, subm.). The relation between the different aggregation levels involves variables and parameters that interact in a complex way. Because of this, slight variation in initial conditions may cause large outcome differences. For instance, a dispute of two team members just before they start with a task could easily affect the allocation process.

Third, the study of many intra team processes would need such a time span that experiments with real subjects would be unrealistic (Jager, 2000) or unethical. Furthermore, sometimes it is hard to know in advance what valid time periods would be (Arrow et al. 2000; Vallacher & Nowak, 1994). How much time does it takes before workers are adjusted to each other? An hour? A day? A month? A year?


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Thus, since a real-life context is not sufficient to study self-organising processes of task allocation, another method is necessary. Due to the advent of advanced information systems and the use of computational models, the last decade the bottom-up approach, which makes use of computer simulation, has become increasingly popular (Carley, Prietula, and Lin, 1998; Gilbert & Troitzsch, 1999; Axelrod & Cohen, 2000; For an historical overview of the development of different simulation approaches, see Gilbert & Troitzsch, 1999). For instance when guided by empirically validated theory or empirical observations, simulation seems to be a scientifically sound method to study self-organising processes. In particular situations computer simulation is even the only way of studying a certain phenomenon (Vallacher & Nowak, 1994; Harrison, 2002). The methodology of computer simulation introduces the possibility of a new way of studying social processes, based on ideas about the emergence of complex behaviour from relatively simple activities (Gilbert & Troitzsch, 1999).

Besides the benefits of experimentation without the validity threats I mentioned above, and the possibility to cope with the complexity and the time horizon of social systems, computer simulation yields at least three other profits (see Arrow et al. 2000). First, it does not tolerate vague ambiguous theories because it forces the researcher to explicitly formalise theory into computational algorithms. Second, it offers a possibility to integrate all kinds of theories and models related to the same phenomenon (see also Vallacher & Nowak, 1994). Third, because of the possibility to generate systematic descriptions of process variables and parameters, it may help to build and evaluate theories for empirical studies.

A specific way of using computer simulation is by means of multi-agent simulation (MAS). MAS can describe complex behaviour at the macro level by using a set of simple interacting agents at the micro-level (see also Gilbert & Troitzsch, 1999). In general, multi agent models are based on formalised descriptions of empirical phenomena (e.g. Edmonds & Hales, 2004), with or without the help of empirically validated theories. Holland (1995) defines agents as rule-based input-output elements where rules can be based either on simple economic rationality or complex psychological processes. With regards to my study, agents refer to psychological models of humans beings. The behaviour at the macro level refers to the group they are a member of.

With regards to this study, MAS offers a number of advantages that real-life studies lack It enables the possibility to model interaction processes within a social group, and to conduct a variety of experiments with elaborate designs. In this way it offers a method to systematically describe the relevant variables and parameters with regards to the processes I want to study.

By looking at studies that simulate social phenomena, I see a number of theories that are formalised into simulation programs (e.g. Troitzsch, 2005; see also the journals JASSS, SIMPAT, CMOT or AAMAS). Within the field of social simulation studies we can distinguish two different approaches. The first approach involves the study of sociological systems, social networks, and social interaction (Axelrod, 1984; Zeggelink, 1993; Kitts et al, 1999; Back & Flache, 2006). The second approach involves the study of the behaviour of cognitive plausible agents (Carley & Prietula,


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1994a; Van den Broek, 2001; Helmhout, Gazendam & Jorna, 2004). Whereas the first approach does not concern about a plausible description of the cognitive properties of the agents, the second approach does not apply sociological or social-psychological theories to its models. Only a very few scholars focus on both the individual and the social level (e.g. Conte & Paolucci, 2001). Therefore, for me this thesis was a challenge to develop a model that links both approaches.

Simulation studies concerning organisational processes encompass a wide range of topics, including organisational learning (Carley, 1992), computation organisational theory (Carley & Prietula, 1994b), organisational semiotics (Helmhout et al. 2004), the co-evolution of social networks and behavioural norms (Kitts, 2005), and teams (Pynadath & Tambe, 2002; Coen, 2006). Up to now, studies of self-organising processes of task allocation have not been conducted. Furthermore, most studies focus only on cognitive or network components, while neglecting the influence of motivation on the internal processes and performance. Therefore, my study may contribute to this line of research.

1.6 The Chapters All experiments that I will describe in this thesis are based on the same model. The chapters of this thesis consist of papers that either have been published or have been submitted to journals within the field of computer simulation. This implies that in each paper, although adapted to the specific experiments described in that chapter, I shortly highlight the general model on which the experiments are based.

In chapter two of this thesis I describe the basics of my conceptual model on which my simulation experiments are based. This conceptual model is partly based on a comparison of self-organising teams with the brain. I combine general self-organising principles and mechanism with psychological theory of task performance and organising behaviour. The conceptual model describes self-organising processes of task allocation both at the individual level, i.e. changes of skills, and at the social level, i.e. changes of power and attraction. This conceptual model is partly formalised into a computer simulation program, called WORKMATE. Chapter three focuses on this formalisation. I only formalised the individual level of the model, being only a first step but already leading to interesting behaviour. In this chapter I describe the results of three experiments: First, I describe how differences in expertise affect the duration of the task-allocation process. Second I describe how task variety and coordination time are related. Finally, I describe the relation between boredom, performance and task allocation. By conduction these experiments, I was able to simulate the phenomenon of the emergence of task rotation. In chapter four, I describe when task rotation may or may not emerge under different conditions of organisational constraints, which is called ‘level of self-organisation’. This chapter can be related to the condition of ‘minimal critical specification’. Further, I conducted experiments that focus on the flexibility of work groups. I have made a distinction between external and internal changes that force a work group to adapt to a changing situation. In chapter five, I focus on external changes. I describe a series of experiments to test the influence of


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task dynamics (variety in demand) on groups of specialists and generalists. Chapter six focuses on internal changes of the team, i.e. the influence of turnover (variety in supply) on performance. I especially indicate the adaptation processes concerning different kinds of newcomers (specialists and generalists with various levels of expertise) in teams. The internal and external changes that these two chapters describe can be related to the condition of ‘requisite variety’. The influence of the differences between specialists and generalists on the adaptation process can be related to the condition of ‘redundancy of functions’. In all experiments I focus on individual processes related to expertise and motivation. In chapter seven I propose the conclusions based on all the previous chapters in relation to the conditions for self-organisation. Finally, in chapter eight I reflect on the research itself, by discussion the validity of the model and the experiments, by proposing some suggestions for future applications and further research.

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Chapter 2 Modelling2 Abstract In literature, self-organising social behaviour is often described by means of a brain metaphor. These descriptions either discuss some general principles or propose a systems-theoretical analysis, but have not been related to existing psychological theory. In this chapter we propose a way of describing self-organising social processes of task allocation by using principles derived from a neural-network model and from theories of cognitive- and social psychology.

2.1 Introduction Unlike other animal behaviour, human behaviour is embedded in an institutionalised context. If we want food, we do not hunt, but go to a store, pay money that we earned doing a job we once applied for in an organisation. In our spare time we are part of another structure, playing sports, taking some courses, or watching television. Even our holidays may take a pre-structured shape, e.g., visiting a holiday-bungalow or trailer vacation park we are visiting for the 25th time. In some cases, humans can be considered as institutionalised animals. Usually the institutionalisation of human behaviour seems an efficient way of organising large groups of people. It is safe and it is easy. But in some cases, safe and easy may become boring and rigid. In these cases the human animal becomes a caged pet of the society that once emerged from his own behaviour. In a ‘healthy’ society, institution and individual freedom should be well balanced. Life without structure leads to chaos and structure without freedom implies inhuman conditions. This balance does not only yield for society but reflects a general principle regarding order and chaos in living systems (Ashby, 1956; see also Kauffman, 1995).

In this chapter, we will not present some general considerations about order and chaos in relation to living systems. We do not even want to discuss the implications for society. We only shall deal with the question how organisational behaviour is related to the principle we just mentioned. This means that we want to answer questions

2 This chapter is published as: Zoethout, K., Jager., W, & Molleman, E., (2004), Self-organising social processes of task allocation, , Cognitive Systems, vol 6-2,3, pp. 189-203 special issue on Multidisciplinary Aspects of Learning


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regarding the relation between the order of an organisation and the chaos of its environment. According to Ashby’s law of requisite variety, the internal diversity of any self-regulating system must match the variety and complexity of its environment if it is to deal with the challenges posed by that environment. (Morgan, 1986, p. 100, after Ashby, 1956). One of the questions this law may answer is whether employees should specialise in one particular skill or perform all of the necessary skills to perform a task. This particular type of question, which refers to principles regarding specialisation versus generalisation, should be considered the main issue of this chapter. One of the implications of Ashby’s law is that there is an optimal organisation for every task. Molleman (1998) discussed the implication of Ashby’s law for organisational design more elaborately. He states that if the level of task variety is low, standardisation will be the most efficient and effective. If the level of variety is high, the assignment of control tasks to the individual worker will fit in best. If the level of variety is moderate, autonomous teams will give the best result.

However, the proposed relation between task variety and need for organisational structure is merely static and design-based. In practice the environment is constantly changing, task variety itself being an altering component. This suggests that, for a complete understanding of the relation between task and organisation we should study the processes of organising and learning as well. This means we have to answer the question: how do people organise themselves according to a task they must perform? This question refers to human behaviour as self-organising instead of simply following an existing institution. The study of self-organising social processes has two main purposes. First, insight in adaptation processes regarding task alterations may provide a practical use in organisational settings. Second, studying the relation between tasks and organising behaviour does not refer to human behaviour as an institutionalised animal, but as an animal that can create institutions. We can only answer the question to what extent we need organisational structures if we know what our behaviour is like without them.

This brings us to the question of the best approach to follow. The study of self-organising behaviour without an organisational context may need an experimental setting, such as at team-building sessions and the like. However, for a number of theoretical and methodological reasons, within social psychology, experimental studies of organising behaviour in particular and social dynamics in general cannot build on an extensive tradition (Vallacher & Nowak, 1994). Computer simulation introduces the possibility of a new way of thinking about social processes, based on ideas about the emergence of complex behaviour from relatively simple activities (Gilbert & Troitzsch, 1999). The idea of the emergence of complex behaviour from simple activities can be found in the area of cognitive psychology as well, such as Searle’s description of consciousness as the final result of properties that emerged from simple neural activities (Searle, 1992). But this is not the only similarity between studies of social dynamics and of the brain. Both can be described as self-organising systems. This notion is not new. Some scholars used the metaphor of the brain, being the most widespread known self-organising system, to describe social behaviour as well (e.g. Beer, 1981; Morgan, 1986). However, these descriptions do not reflect common theories of social psychology.

Chapter 2: Modelling

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Both similarities, the notion of emergent properties and the notion of self-organisation, form the basis for the model we propose. In the first part of the chapter we will discuss the use of a brain metaphor for describing self-organising social processes. As we shall point out, by using a self-organising neural network model, being a particular model of the brain, we shall integrate different social psychological theories and models into a theoretical framework. The theoretical framework itself is a multi-agent architecture. We shall describe this architecture at two levels, the skill-level and the individual level. At the skill level, we shall describe the cognitive architecture of the single agent. The social level deals with the interaction between agents.

2.2 Neural Networks and Social Processes In this section we describe some general principles of self-organising neural network models. A self-organising system can be considered as a system that can change its own structure. A neural network is a set of interconnected nodes with an excitation level that serves as a model of the structural architecture of the brain (for an overview, see Rumelhart, Hinton, & Williams, 1986; Smolensky, 1986). Principles of neural networks will be related to existing psychological theories and models to describe social processes of task allocation.

2.2.1 From a brain metaphor to self-organising neural networks Self-organisation refers to the process in a system leading to the emergence of global order within this system without the presence of another system dictating this order (e.g. Dalenoort, 1989; 1995; Heylighen, 1997). Self-organising systems have been object of study in a wide variety of disciplines, such as chemistry (Prigogine & Stengers, 1984), biology (Maturana & Varela, 1980) and cognitive psychology (Dalenoort, 1982; 1995). Self-organising principles of social systems have been formulated as well (for an overview, see Ulrich & Probst, 1984) but those principles are formulated in an abstract system-theoretical way and are not related to social psychological theory. Some scholars use a ‘brain metaphor’ for describing self-organising social behaviour (e.g. Beer, 1981; Morgan 1986), or discuss the use of neural networks for describing social processes (Ritschard, 1991; Zoethout, 1994).

Indeed, we could mention at least three arguments to use a brain-metaphor for describing social behaviour with respect to learning. First, in the area of artificial intelligence, neural networks are widely used because of their ability to learn. A model that describes social behaviour based on neural-network-like properties should also be capable to describe learning processes in social systems. Second, the brain is the most commonly known self-organising system. The use of a brain-like description opens the possibility of using knowledge regarding self-organising behaviour to describe social systems. Third, neural networks are used to describe complex behaviour by means of simple interconnected elements. On the basis of the interaction between these elements, properties are likely to emerge that cannot be attributed to the individual elements (Dalenoort, 1982; Heylighen, 1997). The notion of ‘emergent properties’ can be used to


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describe complex social processes resulting from individual behaviour as well (Gilbert & Troitzsch, 1999).

Some of these arguments concern with the use of the brain-metaphor in general; others regard the self-organising neural-network model in particular. Self-organising neural-network models are biologically plausible models of the brain. The brain is able to adapt to the environment autonomously by changing its own structure accordingly. Therefore the brain can be considered as a self-organising system. Furthermore, these self-organising processes may lead to more efficiency, which indicates that in fact the brain is a learning system (Krippendorf, 1986).

2.2.2 A neural-network model: properties and principles The main scope of the chapter is self-organising social processes of task allocation. Therefore we shall only mention the neural network properties that we will use to describe these processes.

A neural network consists of a set of interconnected cells with an excitation level and a threshold. Within these cells the excitation level is built up until it exceeds the threshold. If the excitation level exceeds the threshold, the cell fires to the cells connected. The excitation level of these connected cells changes as a result of this (Dalenoort, 1982). We may discern two types of connections: excitatory and inhibitory: an excitatory connection increases the tension of the connected cells and an inhibitory connection decreases the tension. Connections may vary in strength: if a connection is stronger, the proportion of excitation or inhibition is larger.

Since the brain is self-organising, there is not a mind that dictates its order. The brain creates its own order and changes its own structure autonomously. This implies that a description of the way the brain changes its own structure should be based on interaction principles of the elements (i.e. neurons) the brain consists of. In the literature a mechanism that describes this interaction is ‘Hebb’s learning rule’. It implies that for the emergence of a new connection between two neurons, or for strengthening an existing connection, these neurons must be active simultaneously (Hebb, 1949). This mechanism is not only the only mechanism that describes processes of self-organisation and learning within the brain, it can be considered as a general learning mechanism as well, that can be used to describe learning processes in other self-organising systems. Therefore Hebb’s learning rule can also be used for social systems (Zoethout, 1994; Nowak, Vallacher, & Burnstein, 1998; Kitts, Macy, & Flache, 1999).

Another obvious but nonetheless important similarity between the brain and social groups is that both are living systems. Living systems can grow tired: in a neural network model neural fatigue might be due to an overall ability to reach sufficiently high levels of excitation (e.g. can be described as a tension decrease of afferent cells after a longer period of firing. We can experience this in a train: in a travelling train, the constant input of the rails passing by leads to a decrease of the excitation level of the neurons. At the railway station this results in the experience that, as soon as the train has stopped, we notice that we are going backwards instead of standing still.


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2.2.3 Social processes of task allocation Now we relate the properties we discussed above to the self-organising social processes of task allocation. Social processes of task allocation refer to the way people allocate tasks they should perform together. For instance, a group hiring a sailing boat should perform (at least) the following tasks: handling the helm, the jib, the sail, the swords, looking at the weather, watching the environment, and monitoring the rest of the crew. The crew should decide who does what. This decision may depend on the skills of the individual crew-members, their willingness of performing either one of these skills, the power and experience of the captain, and the ‘degrees of freedom’, the space in which the process of allocation may take place: if the boat is small and consists of only one crew-member we do not have to think of social processes of task allocation. Furthermore the captain of a professional sailing ship that is participating in a contest may have carefully selected his crew of highly skilled specialists. In neither of these cases we speak of self-organising social processes of task allocation. In the first case there are no social processes and in the second case there is no self-organisation. We stated that a self-organising system refers to a system that can change its own structure. This means that we want to describe situations in which the process of allocation occurs inside the system. On board, a crew of three people should autonomously decide how to use their skills in a smart way. This may finally result in a crew of well-trained sailors, balancing between specialisation and multi-functionality. What yields for the sailing boat may also apply to daily working life: a group of people plucking apples, making cars, performing surgery, doing their jobs is somehow involved in allocation processes. This brings us to the question which components influence processes of task allocation. In order to answer this question we should distinguish between task components and psychological components.

2.3 Task Components Much research has been devoted to the area of tasks, task allocation, and designing organisations to perform tasks as effectively and efficiently as possible (for an overview, see Hunt, 1976; Steiner, 1972; see also Tschan & von Cranach, 1996). Wood (1986) describes three dimensions of task complexity: Component complexity describes the number of different actions necessary to perform a task. This resembles the dimension of skill variety of the Job Characteristics Model, a model that is widely used in work and organisational psychology (Hackman & Oldham, 1980). Every task can be split up into actions in such a way that every action needs exactly one skill. Co-ordinate complexity refers to the extent to which the different actions are connected. This is also called task interdependence (Thompson, 1967; Van der Vegt, Emans & Van der Vliert 1998). Dynamic complexity refers to the task changing in time (Tschan & von Cranach, 1996). This is also called task variety. As task variety increases, the task itself becomes less familiar, which implies that the information about the task decreases. In literature, the information about the task is often referred to as task uncertainty (Manz, 1992; Molleman, 2000). According to this description, a task can be defined as a set of actions, in such a way that every action requires one skill to perform it (see Figure 1):


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Figure 1: Components of task complexity

In the figure, the actions required to perform a task are represented as a grey box. The component of task variety (e.g. dynamic complexity) indicates the variety of actions. Every action sends out information about what must be done. This information activates the skill that is necessary to perform the action. In the figure the activated skills are represented by the grey dots. High task variety implies low information (e.g. high task uncertainty) about the actions. As the actions a task consists of increases, more skills are necessary to perform the task. This is called skill variety (e.g. component complexity). Interdependence being a task characteristic refers to the relations between the different actions a task consists of. Some actions may be conditional for others; some actions may be inseparably connected. These relations imply relations between skills as well. This refers to the situation in which the agents are forced to co-operate because individually they can only contribute partly to the performance of the task. In the next section we shall describe people as agents with a set of skills. This description indicates that if this set of skills is not sufficient to perform a task on its own the agents should work together.

2.4 Psychological Components In psychological literature, human behaviour is often described as using two dimensions, for instance: task-directed and social-emotional, goal-directed and sensation-seeking (Apter, 1987), the need for certainty and the need for pleasure (Veen & Wilke, 1986), or love-hate and dominance-submission (Leary, 1957). These dimensions can be found in studies on task performance in groups as well. Wilke and Meertens (1994) state that the most important components that determine performance are: expertise, motivation, and co-ordination costs. Expertise and motivation can be considered as characteristics of skills: some skills are performed better than others (expertise) whereas some skills are more preferable than others (motivation). Co-ordination costs can be considered to be dependent on the interaction between individuals, i.e. social interaction. Social interaction can be described in two dimensions as well, for instance power-submission and love-hate (e.g. Leary, 1957).


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Thus task performance can be described at the skill level by means of two components, expertise and motivation. At the individual level, we use the components power and attraction.

The components Wilke & Meertens (1994) proposed, as well as the use of two dimensions to describe human behaviour, will form the basis notion of a multi–agent architecture. This architecture relates psychological theory as well as the neural-network model to both the skill-level and the individual level.

2.4.1 The cognitive architecture of the agent We have defined a task as a set of actions, and a skill as the ability that is required to perform one action. This means that every action of a task requires the matching skill to be performed. We describe a skill by using two components, motivation and expertise (derived from Wilke & Meertens, 1994). In analogy to the neurons in a neural network, every skill can be active or passive. A skill is activated if it is necessary for performing a task. In order words, a task will activate the accompanying skills. Information about the necessity of the skill will determine the level of the activity.

The activity of the skill represents the motivation of using this skill. Some skills, such as handling the helm in a sailing boat, are nice to do. Others, such as pulling the swords, or the jib are less motivating. On the one hand our motivation to use a skill increases if we would receive more information regarding the necessity of this skill: it is nice to know why we must do something. On the other hand, if the same skill should be used over and over again, we eventually would know the skill so well that it could be boring to use it. This inverse relation between motivation and information is the most important reason for the failure of Taylor’s scientific management (Taylor, 1911). Using the neural-network analogy, we describe motivational decrease as a result of ‘neural fatigue’.

Motivation is one of the components a skill consists of and by itself insufficient to perform a task. We may know that we should handle the helm and we even may be very motivated to prevent the ship from colliding with the shore. But this will not necessarily imply we know how to handle it properly. Expertise refers to knowing how to use a skill. Expertise increases the more often a skill is used, and it will decrease if it is not used for a longer period of time. In analogy to the neural network model we shall represent the expertise of a skill as a connection between ‘skill’ and ‘use of skill’. In this way we are able to describe changes in expertise by means of Hebb’s learning rule: expertise increases as the activation of a skill and the use of a skill occur together frequently.


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Figure 2: The representation of the relation between a task, skills, motivation, and expertise

Figure 2 explicates what we have described so far. In this example a task consists of three actions. Here we will use the example of John and his sailing ship. The task is ‘sailing’, action a is ‘handling the helm’, action b is ‘handling the sails’, and action c is ‘watching the other ships’. John has low expertise in handling the helm ( in Figure 2 represented by the thin arrow between skill a and ‘ use of skill a’) but he is very motivated to use this expertise (skill a is completely grey, i.e. highly activated). Furthermore John has high expertise in handling the sails (in the figure represented by the thicker arrow connecting skill b with ‘use of skill b’), but he not very motivated to do it (in the figure represented as the dot that is 'half-grey'). However, until now, John has never sailed alone before. This means that he knows something about the other ships and traffic rules, but he does not know how to use these rules, and he does not feel motivated to apply them either! Thus, John decides not to go sailing by himself.

The skills to perform a task, and the components a skill consists of, i.e. expertise and motivation, are embedded in a cognitive architecture. Every agent has a set of skills. The activity of skills can be described in the same way we can describe memory. Memory consists of Long-Term Memory (LTM) and Short-Term Memory (STM). LTM is the part in which all of the skills and accompanying components exist passively. As we stated, as soon as a task is presented, skills that are necessary to perform this task become active. The set of activated skills is a representation of the STM. The relation between skills can be described according to the architecture of memory: memory can be represented as a set of concepts that are connected by means of links that correspond to associations at the functional level (Dalenoort, 1985; Minsky, 1986). In analogy to a neural network, these links are represented by connections that can change in strength according to Hebb’s learning rule. All of the skills present in a single agent can be represented in a similar way: skills that are likely to be used together will have a stronger connection. We can illustrate this by using the example of the handyman and his toolbox (adapted from Minsky, 1986). For every job, before grasping his tools, the handyman paints his hands in a colour. For instance, blue is for repairing bikes, green is for making furniture, yellow is for repairing a roof. As a result of this the next time the handyman should repair a bike he simply picks the blue tools. Some tools may have more than one colour, because they are used for different tasks. The underlying principle: simultaneous activity causes a relation (same colour) which causes simultaneous activity, that can invoke Hebb’s learning rule.


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2.4.2 Interaction at the skill level On the basis of the cognitive architecture we discussed above, we shall now describe how agents interact. We stated that the actual use of a skill depends on motivation and expertise (see Figure 2). What would somebody do to perform a task if he lacks the skill or motivation to do it on his own? Ask for help! In the case of a single agent, e.g. John, we have represented the actual use of skills as active nodes (handling the helm and the sails) or passive nodes (watching the environment). In a multi-agent context, the agent may perform some skills individually, while other skills demand help. We may reformulate this as the choice: ‘I will do it’ or ‘You will do it’. This choice will be made for every skill in every agent. In the case of John, who wants to sail by himself, these choices result in a: I, b: I, c: You (see Figure 2). This choice is solely based on the expertise and the motivation of a single agent, i.e. John. On the basis of this choice, he will influence another agent, but the final allocation has not been made yet. Therefore, we call this choice ‘initial choice’.

John needs another crewman in his boat that knows how to interpret the motions of the other ships (e.g. to watch). Both Peter and Achmed know how to do this, but John knows that Peter likes to take the helm as well, which may result in a potential conflict whereas Achmed only likes watching other ships. Therefore John decides to ask Achmed to join him (see Figure 3):

Figure 3: Complementarity of John and Achmed

John’s decision is based on what is called ‘complementarity of needs‘ (Kerckhoff & Davis, 1962): agents with initial choices that do not conflict are attracted to each other.

But how do these ‘initial choices’ affect each other? Again we will use the analogy to a neural-network model by using excitatory and inhibitory connections. The I-or-You- choice can be represented as two nodes of which one is activated. This node affects the I- and You-nodes of the other agents in the following way (see Figure 4a):

Figure 4a: influence between agents from one skill to another

If an I -node of an agent is activated, this node excitates the You-node of the other agent and inhibits the I-node of the other agent. An activated You-node excitates the I-


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node of the other agents and inhibits the You-node of the other agent. Hence, every skill that is activated within an agent may influence other agents by means of four possible connections (I-I, I-You, You-I and You-You).

The same obtains for the other agent: both agents will influence each other simultaneously (see Figure 4b):

Figure 4b: Mutual influence between agents from one skill to another

This leads to the ‘final allocation’: if a skill must be actually used, it remains active until the task is finished. If a skill is not used after all, it becomes passive again.

2.4.3 The individual level: social interaction In the previous section, we have described how expertise and motivation within a single agent lead to an ‘initial choice’, and how agents influence the choices of each other by making use of excitatory and inhibitory connections. After influencing and being influenced, the task is finally allocated to the agents. But how are these processes of allocation related to actual social behaviour? We have chosen to describe social behaviour by using two components, power and attraction. Consistent with our prior description of influence at the skill-level, we will use a neural network analogy to describe influence at the social level as well. But first, we shall give an overview of social psychological theories and models that describe processes of power and attraction in terms of social interaction.

Power can be described as the difference between the influence of A on B and the influence of B on A (e.g. Cartwright, 1959). Both Berger et al. (1974) and Latané (1981) stated that influence increases as status increases and status increases as expertise increases (Berger, Conner & Fisek, 1974; Latané, 1981). Within the context of task performance, processes of attraction are related to the preferences of co-workers. People will only be attracted to each other if they are aware of each other. Awareness increases as proximity increases (Festinger, Schachter, & Back, 1950). Since we discuss behaviour in a task-performing situation, attraction between agents can only increase if they work on the same task. This may be considered as a specific example of the similarity-attraction effect (Newcomb, 1960), which implies that attraction will increase as a function of the frequency of agents working together on the same task. The mere- exposure effect suggests that we like people whom we have been exposed to repeatedly (Zajonc, 1968). Each for its own specific condition, both the ‘similarity attraction effect’ and the ‘mere-exposure effect’ are analogous to Hebb’s


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learning rule. Both approaches describe the emergence of a new connection and the strengthening of an existing one as a consequence of mutual activity (Zoethout, 1994; Nowak et al., 1998). Kitts et al. (1999) refer to this as ‘structural learning’.

In analogy to a neural network, connection strength between agents represents the amount of influence. Influence only takes place as a part of allocation processes. This implies that agents are only temporarily connected, i.e. if they are performing the same task. The property of ‘temporal connectivity’ is specific for social behaviour and does not apply to neural behaviour. An important component of social behaviour is distance (e.g. Festinger et al., 1950; Latané, 1981). This component does not play a significant role in neural networks because cognitive structures do not appear to be spatially localised in the brain (e.g. Dalenoort, 1982). However, for describing social behaviour, we use the concept of functional distance to describe the possibility of working together: as distance between agents increases, the possibility that they will work together on the same task decreases. Both agents are able to change the distance between them. If agent P becomes more motivated when he works together with agent Q, he will decrease the distance. However, if agent P becomes less motivated when he works together with agent Q, he will increase the distance. If P and Q are actually working together, they will influence each other. The power of P over Q is represented as the influence of P on Q minus the influence of Q over P (Cartwright, 1959). We stated that power increases as status increases and status increases as expertise increases. Only expertise that is actually used to perform a task will affect power, because expertise that has not been used is not socially present. At the skill level we stated that growth of expertise is represented as an increase of connection strength of the accompanying skill (see Figure 2). At the individual level, influence can be represented as the mean of all connection strengths.

2.5 Concluding Remarks We have proposed a multi-agent architecture, which incorporates different psychological theories and models at different levels of aggregation. This makes the chapter susceptible to different disadvantages that arise from multi-disciplinary research. First we have the problem of different disciplines speaking different languages: the explanation of a multi-disciplinary model implies a carefully stepwise description to prevent misunderstanding (see also Klein & Kozlowski, 2000). Second we have the problem called ‘Bonini’s paradox’: ‘the more realistic and detailed one’s model, the more the model resembles the modelled organisation, including resemblance in the directions of incomprehensibility and indescribability’ (Starbuck, 1976, p 1101, cited in Weick, 1979). This refers to both multi-disciplinary research, and to the development of computer simulation models. In this chapter we have tried to overcome these disadvantages by describing both cognitive and social principles in terms of active and passive nodes and variable connections. This approach has forced us to look at the general principles behind a variety of existing theories and models. By using these principles we have simplified these theories and models and related them. In this way we think we have overcome the disadvantage of ‘ speaking different languages’ by making use of general principles the different theories and models have


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in common. The simplification of these theories and models should overcome the disadvantage of ‘Bonini’s paradox’.

A contribution to science refers to the need for integration of different theories and models into a meta-theory (e.g. Vallacher & Nowak, 1994; Jager, 2000). Moreover, both the studies of self-organising social systems and of social processes may make promising additions to existing social science. The contribution to society refers to the insights into group-dynamics of self-managing teams that may be used to enhance efficiency and effectiveness. Furthermore, the simulation model we described so far can be implemented within an organisational context, with organisational constraints such as fixed relations, limited space and time. Moreover, it is suited for conducting experiments regarding performance-criteria or learning. In short, the description of the hypothetical need for organisation in a task-performing context based on knowledge of human nature, will provide insight into social processes. This insight will be beneficial to both social sciences and management issues.

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Chapter 3 Formalisation and Verification3 Abstract In this chapter multi-agent simulation is applied to explore how people organise themselves when they have to perform a task. The multi agent model that we used is based on the formalisation of psychological and organisational theories. Three experiments are presented in which multi-agent simulation is being used to study processes of self-organisation. This chapter is structured as follows. First, we describe how expertise differences and coordination time affect the duration of the task allocation process. Second, we demonstrate how task variety and coordination time are related. Finally, we depict the relation between boredom, performance and task allocation.

3.1 Introduction How do people organise themselves when they have to perform a task? Before attempting to answer this question, let us start with an observation we made in the Dutch Postal Company about students who had signed up for holiday-jobs. The work they had to do was quite easy. Every day the incoming mail had to be sorted, collected, put together into bundles, and thrown into mailbags. These bags were loaded into transport vans that distributed the mail to the different locations. Although all students were initially assigned to all the different tasks, they had some freedom in interchanging them among each other. And that was precisely what happened. Sorting mail all day appeared to be boring, just as collecting it and putting it into bundles. Therefore, after a period of sorting, most of the holiday-workers left their sorting closets and started collecting and bundling the mail. This switching of tasks eliminated the boredom caused by the sorting work, and so the workers kept on bundling until either there was no more mail left to bundle or they became bored again. Then they returned to their sorting closets and the whole process started all over again. However, not only boredom determined the process of switching tasks. While performing either the sorting task or the bundling task, the workers experienced a certain degree of improvement in their skills. As opposed to the boredom effect, this degree of improvement caused the workers to stick to their tasks for a little longer before they

3 This chapter is published as: Zoethout, K., Jager., W, & Molleman, E., (2006), Formalizing Self-Organizing Processes of Task Allocation, Simulation Modelling Theory and Practice, 14, 342-359, special issue on simulating organisational processes


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decided to start a new one. Furthermore, some workers appeared to be better sorters whereas others turned out to be better bundlers. This also affected the process. All in all, the workers somehow managed all by themselves to find a balance between improvement of skills and monotony of the task.

This example shows three findings: first of all, the allocation process is determined by the expertise and the motivation of the individual workers. Second, since some tasks are more boring or difficult than others, the allocation process may also be determined by task characteristics. Finally, rotating tasks does not necessarily needs to be implemented by an external designer but may emerge from the behaviour of the individual workers as well. This latter finding is related to two approaches in management science: the top-down approach and the bottom-up approach. The top-down approach redesigns organisations in order to meet the altered demands of their environments on the basis of empirical research and organisational theories (Daft, 2004). However, due to the advent of the information age and the use of computational models, the past years the bottom-up approach, which makes use of computer simulation, has become increasingly popular (Carley, Prietula, and Lin, 1998; Carley, 2002; see also Axelrod & Cohen, 2000). Moreover, this approach does not only seem to be a scientifically sound method to study the processes we described in our example above, it might be the only way. In particular cases computer simulation is indeed the only way of studying a certain phenomenon (Vallacher & Nowak, 1994; Harrison, 2002).

This chapter deals with the study of self-organising processes similar to those described in the example. These processes are self-organising because the workers themselves re-allocate the tasks rather than some system, i.e. manager or designer, dictating this re-allocation. We modelled these processes by means of a multi-agent system, i.e., a system consisting of simple agents, workers in our case, who are able to influence each other. We will start this chapter by proposing a theoretical framework that describes the properties of the agents and the self-organising processes of task allocation. Then we will describe how this framework is formalised into the computer simulation program WORKMATE I. The theoretical framework and the formalisation of WORKMATE I will be the main issue of this chapter. To test the model and the dynamics it describes, we conducted three experiments. These experiments were very simple and the results are quite evident, because they mainly show what the model predicts. However, the importance of these experiments lies in the insight in the dynamics that the model generates. The empirical relation is less emphasised.

We conducted three experiments. First, we tested how expertise differences and coordination time affect the duration of the task-allocation process. This relation shows the dynamics of specialisation. Second, we tested how task variety affects coordination time. This relation indicates the dynamics regarding specialisation and task changes. Finally, we tested the relation between boredom, performance and job rotation. This relation shows the dynamics of motivational changes and task allocation.

Chapter 3: Formalisation and Verification

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3.2 A Theoretical Framework To understand how a system organises itself when it has to perform a task, we will first distinguish between a task and the system that has to perform the task. Then, we will describe how changes in the task will affect the behaviour of the system.

3.2.1 The task Despite all the different definitions and perceptions regarding tasks, it is quite clear that a task requires one or more skills to be performed. These skills are related to task actions, i.e., the parts which a task consists of. Theories on tasks indicate that a task can be split up into task actions. Tasks can be related to skills in a large number of ways (Hunt, 1976; Weick, 1979; Tschan & von Cranach, 1996). This chapter focuses on the effects of task variety on self-organisational processes by using computer simulation. To do so, the task concept has to be formalised in such a way that it can be subjected to a definition of task variety as well as a way of splitting the task into task actions. This has led us to use the following definition of a task:

A task consists of actions in such a way that for every action exactly one skill is required to perform this action.

This definition can be related to the description of Wood on task variety, which he calls dynamic complexity. Dynamic complexity refers to the task that is changing over time (Wood, 1986; see also Tschan & von Cranach, 1996) and is considered one of the most important dimensions of task complexity. In Figure 5, the actions which the task consists of are depicted by a grey box. The component of task variety (e.g. dynamic complexity) indicates the variety of actions. Every action activates the skill that is necessary to perform the action. In Figure 5 the activated skills are represented by the grey dots. High task variety implies a high degree of changes in the task over time. For example, at t1, the task consists of action 2,3, and 4, which activate skills 2,3, and 4. In case of a high task variety at t2, the task consists of actions 4,5, and 6, whereas in case of a low task variety, the task consists of actions 3,4, and 5.

Figure 5: task variety

For instance, at t1, the task is ‘running an apple orchard’. This task consists of three actions: plucking the apples, putting them in a box, and selling them. However, after the apples have been plucked, it appears that some buyers prefer apple-juice to apples.


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This implies that at t2, the task of running an apple orchard remains, but the actions have changed to: putting the apples in a box, juicing some of them, and selling the juice.

An important characteristic of the actions which a task consists of with respect to task performance is repetitivity (Hackman & Oldham, 1980). Taylor-like organisations where workers have to perform tasks of a highly repetitive nature generate highly specialised, but very de-motivated workers. The repetitivity of the actions can be described by cutting the actions which a task consists of into cycles. We define a cycle as the smallest part of a task that still requires the same skills to be performed as are needed for the whole task. For example, a single cycle of running the apple orchard would consist of: plucking a single apple, putting a single apple in the box, and selling it.

Figure 6: Tasks consisting of actions and cycles

Schematically, we can describe a task as a matrix of actions and cycles (see Figure 6). Splitting up a task into cycles may seem a somewhat artificial approach. Moreover, the number of cycles which the different actions consist of differs for each action. Nevertheless, this schematic description is a useful way of dealing with the different aspects of tasks.

3.2.2 A task performing system Since the discovery of the ‘Hawthorne effect’ in the 1940s, scholars became more focused at social-psychological components of group performance (Scott, 1981). This lead to numerous psychological and sociological studies on group processes in organisational settings (e.g. Thompson, 1967; Hulin & Blood, 1968; Steiner, 1972; Hunt, 1976; Hackman & Oldham, 1980, for an elaborate overview, see Arrow, McGrath, & Berdahl, 2000). Wilke and Meertens state that the most important components that determine group performance are: expertise, motivation, and coordination costs (Wilke & Meertens, 1994; see also Steiner, 1972). Expertise and motivation are individual components that can be considered as characteristics of skills: agents perform some skills better or worse than others (expertise) and prefer some skills more or less than others (motivation). Coordination costs are considered to depend on social interaction. We will describe these components by using a multi-agent model Zoethout, Jager, & Molleman, 2004). A multi-agent model can describe


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complex behaviour at the macro level by using a set of simple interacting agents at the micro-level (see also Gilbert & Troitzsch, 1999). This way of modelling may clarify how task characteristics, individual properties and social interaction may affect the processes of task allocation.

3.2.2.1 Agent properties According to our description an agent is a simple model of a human being with properties that are necessary to perform tasks. The individual properties are represented as a set of skills, each skill consisting of two variable components: expertise and motivation. Analogous to human memory, skills can be passive or active (Newell, Rosenbloom, & Laird, 1989). The long-term memory store (LTM) consists of a large set of passive skills. Once an agent starts to perform a task, a subset of these skills corresponding to the actions which the task consists of, is activated. The set of active skills corresponds to the short-term memory store (STM). This means that the motivation of the agent is a function of the motivation of the active skills and the expertise of the agent is a function of the expertise of the active skills.

Figure 7: the agent

Figure 7 summarises what we just described. The task, which is indicated by the grey box, activates the skills that are necessary to perform it, for instance, (1) plucking apples, (2) putting them in a box, and (3) selling them. As a result of this activation these skills go from LTM (white dots) to STM (grey dots). Now let us assume that the task changes in time, i.e. there is task variety, for example because some buyers want apple juice. In Figure 3, the box behind the grey box represents the ‘new task’. This task also consists of three actions, corresponding to skill (2): putting apples in a box, (3): selling them, and (4): juicing them. This means that as soon as the task changes, skill (1): plucking apples, goes from STM to LTM and skill (4): juicing the apples, goes from LTM to STM. Both the LTM and the STM are subject to different processes regarding changes in expertise and motivation.

3.2.2.2 Interaction between agents To every skill applies that the values of the expertise and motivation determine whether or not that skill will be used to perform the corresponding action. We can represent this


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choice by using thresholds. If the expertise exceeds its threshold a skill is ‘good enough’ and if the motivation exceeds its threshold a skill is ‘nice enough’. If a skill is both good enough and nice enough, the agent can decide to actually use it. If neither expertise nor motivation is high enough, the agent decides not to use it. Because at this point, this decision is solely based on individual properties and has not been affected by social interaction, we will call this decision initial choice. Because this choice is made for every skill, the initial choice is a representation of what every agent would like to contribute to a task individually.

On the basis of the initial choice the allocation process starts. This implies that the agents themselves allocate the tasks, which means that the final allocation of the tasks is carried out by means of a self-organising process. Self-organisation refers to the process in a system leading to the emergence of global order within this system without the presence of another system dictating this order (Dalenoort, 1989; Heylighen, 1997). The process of allocation takes place by mutual influence on the basis of initial choice. This influence causes the agents to try to reach a complementary situation in which every agent has to perform different actions (Kerckhoff & Davis, 1962). This means that in our model every action can only be performed by one agent at the same time, and that every action which a task consists of has to be performed. We have based the process of influencing on a neural network analogy by using excitatory and inhibitory connections. Excitatory connections increase the tension of the node that is affected and inhibitory connections decrease its tension. The choice whether or not to use a skill can be represented by two nodes, an I-node and a You-node of which only one is activated. An activated I-node excitates the You-nodes of other agents and inhibits the I-nodes of other agents:

Figure 8: Excitation (+) and inhibition (-) of two agents

Figure 8 only shows the influence of agent 1 on agent 2. Agent 1 wants to put the apples in a box and therefore tries to influence agent 2 no to do so. The same happens the other way around. Both agents influence each other simultaneously until a complementary state is reached, for instance, agent 1 puts the apples in a box and agent 2 sells them. This is called the final allocation. As soon as this state is reached, the unused skills will become passive again and as a result return to the LTM. At this stage the tasks have been allocated and the agents can start performing them.


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3.2.2.3 Learning processes and performance During the process of performing their tasks, within the agents two potential changes may occur: changes in expertise and changes in motivation. Changes in expertise refer to processes of individual learning and forgetting. Individual learning refers to improving a skill by using it and forgetting refers to deteriorating a skill by not using it (Nembhard, 2000). This means that the expertise regarding the skills of the agents will change during the performance of the task. Motivation may also change during the performance of the task, for instance due to effects of boredom, especially in the case of tasks that are highly repetitive (Hulin & Blood, 1968; Hackman & Oldham, 1980). Moreover, the motivation of the agent not only changes during the task performance but also as a consequence of the discrepancy between the initial choice and the final allocation. The motivation of the agent is a function of the motivation regarding the active skills. If there is a discrepancy between the initial choice and the final allocation, the active skills change. Therefore, the motivation of the agent changes. If there is no discrepancy, the agent simply ‘gets what he wants’ and therefore his motivation is maintained (see also Hirst, 1988).

Learning can be considered as a process of increasing success in a fixed environment (Krippendorf, 1986). This definition not only applies to increase in expertise, but also refers to the increase in motivation, since motivation and performance are positively correlated (Hackman and Oldham, 1980). In a setting consisting of three or more agents, agents may be able to choose their co-worker. This indicates that their mutual relations may change as a result of task performance or task allocation. If these changes lead to higher performance, we may speak of learning as well. Kitts et al. call this type of learning structural learning (Kitts, Macy, & Flache, 1999). The term structural refers to changes in the social-network-structure, which is based on Zoethout’s notion of applying learning principles in neural networks to describe structural changes of social networks (Zoethout, 1994; Zoethout, Jager, & Molleman, 2004).

Since we stated that learning refers to a process of increasing success, we have to define what success really is. A system that performs successfully can be considered as a system of high performance. Expertise, motivation, and coordination are the most important components that determine performance (Wilke & Meertens, 1994). This means that a highly performing system should score high on expertise and motivation, and low on coordination costs. In our model, the concept of coordination costs refers to the time it takes to allocate a task. The total performance time is defined as the sum of the performance time of the single agents plus the coordination time.

3.3 Formalisation and Description of WORKMATE WORKMATE I is a deterministic discrete event-based simulation program for simulation self-organising processes of task allocation, which we developed in DELPHI6. The event is the task that triggers the allocation processes of a multi-agent system. Once the task has been allocated, this system performs it and stops until another event starts. Discrete means that all events are treated separately. Discrete event simulation is often used for queuing models, but is also appropriate for a larger


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class of problems related to social and management science (Gilbert & Troitzsch, 1999). In this section we will describe the formalisation of the theoretical framework as depicted in the former section, based on a setting consisting of two agents. The description will follow the actual process, starting with the task and finishing with its performance.

3.3.1 The task A task can be manipulated by using four parameters: the number of cycles, which refers to the number of times that the same skills are needed, the number of actions, which refers to the minimal number of skills that the system needs to perform the task, the variety of actions, which refers to the extent to which a task changes over time. A variety of 1 means that every next task differs 1 action from the former task. The variety value cannot exceed the number of actions that a task consists of because a variety equal to the number of actions already indicates that every new task is completely different from the former. The fourth parameter is the task unit duration. A task unit is defined as a single cell within the 2-dimensional matrix of actions and cycles (see Figure 6). The task duration is the product of task unit duration, the number of actions and the number of cycles. Task duration is defined as the minimal required time to perform a task. The significance of this parameter will be explained later on in this section.

3.3.2 Initial choice Once the parameters of the task and the agents have been set, we can start the system. First, all the actions which the task consists of activate the skills of the agents that are necessary to perform the task. Activation of skills means that for every skill the value of expertise and motivation goes from LTM to STM where they are compared to the thresholds according to the following decision rule:

IF Expertise > ExpertiseThreshold AND Motivation > MotivationThreshold THEN I DO ELSE YOU DO

This decision rule means that an agent wants to perform a particular action (I DO) if both the expertise and the motivation related to the skill to perform that action are sufficient. The logical reverse of this rule is that, if either the expertise or the motivation is insufficient, the agent does not want to perform that particular action (YOU DO).

The decision whether or not to perform an action is depicted by means of two nodes, an I-node and a You-node, each having values between 0 and 1. The values of these nodes are functions of expertise, motivation, their thresholds, their maxima, and a parameter λ that determines the balance of expertise and motivation. The initial choice depends on these nodes according to the rule that I DO means that the value of the I-node is bigger than the value of the You-node, and You DO means the other way around.

The I- and You-nodes are calculated as follows: expertise and motivation have values (x) between 0 and a maximum with a threshold somewhere in between. A value of x between 0 and the threshold refers to the You-node and a value between the threshold


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and the maximum refers to the I-node. The I-node will be 1 if the x is maximal, and will approach 0 if the x reaches the threshold. The You-node will be 1 if x is 0, and will approach 1 if x reaches the threshold. Therefore, for the I-node, the height of the threshold is subtracted from x. For the You-node, x is subtracted from the threshold. Then, these values are divided by their maxima to make up the I- and You-values between 0 and 1.

We can distinguish three situations. In the first situation there is insufficient expertise, which will consequently lead to a YOU DO choice. In this situation, no matter how high the motivation is, the skill will not be influenced since the agent cannot perform that particular action anyway. The values of I and You can simply be described as:

0=I (1a)

1=You (1b)

The second situation refers to expertise and motivation both exceeding their thresholds, which leads to the initial choice of I DO. In this situation the I-node is a function of the expertise (e) and motivation (m), their thresholds (the, thm), their maxima (emax, mmax), and a parameter λ [0,1] that indicates the balance between expertise and motivation.

m

m

e

e

thmthm

thetheI

−−

−+−−

=maxmax

*)1(* λλ

(2a)

0=You (2b)

The third situation refers to sufficient expertise and insufficient motivation. According to the decision rule, this situation would lead to an initial choice of YOU DO, whereas the I-node =0 and the You-node are determined by motivation, their thresholds and the balance parameter λ [0,1]. However, this situation may not provide a sound basis to start the allocation process. If we look at the initial choice of the other agent, again, we may distinguish three situations: insufficient expertise leading to YOU DO, sufficient expertise and motivation leading to I DO, and sufficient expertise and insufficient motivation. In the first and second situation the choice is clear. In the third situation both agents have insufficient motivation and sufficient expertise. It will not be plausible to determine the choice of these agents solely by their motivation, as rule 1 suggests. Therefore, we have defined the I-node as a function of expertise rather than labelling it zero, and the You-node as a function of motivation:


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e

e

thetheI−−

=max

*λ

(3a)

m

m

thmthYou −

−= *)1( λ

(3b)

3.3.3 Excitation and inhibition Figure 8 indicates the way in which an agent influences another agent by means of excitatory and inhibitory connections. As a result of this influence, the values of the I-and You nodes change. These changes depend on the values of the I-and You nodes of both agents: the higher the value of the sending agent, the higher the potential influence. This potential influence is limited by the values of the I-and You node of the receiving agent. Excitation will decrease as the values approach their maxima and inhibition will decrease as the values approach 0. Therefore, excitation can be described as follows:

)1( 0001 yxyy −+= (4a)

y0 represents the old value of the receiving node, y1 the new value, and x0 the old value of the ‘sending’ node. x0 is multiplied by (1-y0) to make sure that the value of y1 does not exceed the maximum value of 1. Inhibition can be described as:

0001 yxyy −= (4b)

x0 is multiplied by y0 to make sure that the value of y0 does not exceed the minimum of 0.

The agents simultaneously influence each other. If two nodes with the exact same value influence each other, it is likely that nothing will happen. This means that the difference between two nodes should be included into the excitatory as well as the inhibitory functions:

)( 21 IIAbsDiffII −= (4c)

)( 21 YouYouAbsDiffYouYou −= (4d)


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I1, I2, You1, and You2 correspond to Figure 8. DiffII equals the absolute value of (I1 - I2) and DiffYouYou equals the absolute value of (You1 – You2). We combine the equations (4a) to (4d) to describe all excitatory and inhibitory connections as shown in Figure 8:

IIDiffIIII 2122 : ι−= I1 inhibits I2 (5a)

YouYouDiffYouYouYouYou 2122 : ι−= You1 inhibits You2 (5b)

IIDiffIYouYouYou 1222 )1(: −+= ε I1 excitates You2 (5c)

YouYouDiffIYouII )1(: 2122 −+= ε You1 excitates I2 (5d)

ε and ι [0,1] represent parameters that can set the height of the excitation (ε) and the inhibition (ι). Next, we will give an example how the influence actually works. In this example, we will use maximal excitation and inhibition, which means that ε =1 and ι=1.

An example: I1 = 0.6, You1=0, I2=0.2, You2=0. We see that both agents have an initial choice of I DO but I1 > I2, which means that agent 2 will change his choice from I to You. We will now describe the first step of the allocation process.

I1 inhibits I2: I2 = 0.2 – 0.6*0.2*0.4 *0.1= 0.152

I1 excitates You2: You2 = 0 + (1-0)*0.6*0.4 = 0.24

I2 inhibits I1: I1 = 0.6 – 0.2*0.6*0.4 = 0,552

I2 excitates You1: You1 = 0 + (1-0)*0.2*0.4 = 0.08

So, I1 = 0.552, You1 =0.08, I2=0.152, and You2=0.24. This means that the initial choice of agent 1 is still the same. Agent 2’s choice has been changed into You DO because You2 >I2.

These allocation processes take place for every action. The time it takes to allocate an action is called allocation time. According to the formulas (5a)-(5d), the allocation time is determined by two components. First, we mention the values of the sending and receiving nodes. As the I-and You nodes of the agents are more similar, the allocation time increases. Second, the allocation time is determined by the values of the excitation and inhibition parameters, ε and ι. As the value of these parameters increase, so will the allocation time. This explains the use of these parameters. If the allocation time of the different actions is too low, we cannot distinguish between them. If the allocation time is too high, the simulations will take too much time.

The total allocation time is the sum of the allocation time of the different actions which a task consists of. Since we stated that the coordination costs refer to the time it takes to


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allocate a task, we define the total allocation time as the coordination time, tcoord., which can be expressed as:

∑==

n

iicoord tt

1.

(6)

whereas ti is the allocation time of action i.

3.3.4 Learning After the task has been allocated, the agents start performing it. During the performance processes, learning and forgetting as well as boredom and motivation will occur. An important characteristic of most learning curves is that they reach a maximum asymptotically (Nembhard, 2000). Therefore, we define learning by means of: the relation between expertise at a certain time (t), expertise in the future (t+1), the maximum expertise, and a parameter that determines the learning speed:

maxmax

)1( eeeee t

tt−+=+ λ

(7)

e being expertise, t being the current time step, (t+1) being the next time step, emax being the maximum expertise, and λ being the parameter value between 0 and 1 that indicates the learning speed. In the program, parameter λ is called learning speed. Not only learning curves can be described as being asymptotic with a maximum, motivation curves can be described by using the same characteristics. This means that in case of boredom recovery we use the same formula for both learning and motivation. In the latter case parameter λ is replaced by a parameter that is called rest rate, which indicates the motivational recovery from boredom.

Studies on learning and forgetting suggest that the slope of the second is in fact the inverse of the slope of the first (Nembhard, 2000). Therefore, forgetting can be represented as the inverse of formula (7):

µµ−

−=+

max

max)1(

)(e

eee tt

(8)

µ being a parameter value between 0 and 1. In the program, parameter µ is called forget speed. Just as formula (7) expresses both learning speed and the rest rate, formula (8) expresses both forget speed and the boredom rate. Boredom rate refers to the decrease


37

in motivation as a result of boredom. In this case, parameter µ is replaced by a boredom rate parameter.

3.3.5 Performance The performance of the system is a function of expertise, motivation and coordination costs (Wilke & Meertens, 1994). The concept of coordination costs is defined as the time that it takes to allocate a task. Expertise and motivation are components of the skills of the agents. We define both expertise and motivation in terms of the time it takes to perform a task: the higher the degree of expertise or motivation, the sooner the task is finished. Furthermore, we define a minimal time to complete an action, taction, which is equal to the actual time it takes to perform the action at a maximal rate of expertise and motivation. The actual performance time of a single agent, tperf. , can therefore be expressed as:

∑=−+

=n

i ii

iactionperf

mm

ee

tt1

maxmax

.

)1(

_

λλ

(9)

In the program, the agents perform the actions simultaneously. This means that the time it takes to perform the total task, Tperf. , is determined by the slowest agent and the coordination time:

oncoordinatiperfnperfkperfperfperf tttttT += ),..,..,,max( 21. (10)

3.4 Results In this chapter, for two reasons we are especially interested in testing the dynamics of WORKMATE I. First, by testing its dynamics, we will observe if the agents behave according to the model we described in the former section. The results will show whether our model has correctly been implemented and whether it does not show any unpredictable behaviour. The second reason is related to the comprehensibility of the system. WORKMATE I is able to generate complex behaviour due to the deterministic interaction of simple elements, the agents. We will not be able to describe the complex behaviour of task allocation if we cannot build our studies on insights in the dynamics of the system. In that sense, the experiments we describe here only serve as a basis for more sophisticated experiments on the relation between tasks and groups.

The dynamics which WORKMATE I is able to generate refer to processes of learning and forgetting, boredom, and changes as a result of task variety. We are especially interested in the way in which these processes are related to task allocation and task


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performance. On this basis, we have conducted experiments to answer three questions. Our first research question is:

What is the relation between specialisation and coordination time?

On the basis of the model, we hypothesise that coordination time decreases as specialisation increases. We tested two conditions, small differences and large differences, and compared the performance time. Our second research question refers to the relation of task variety and coordination time:

What is the relation between task variety and coordination time?

Since the agents will specialise less whenever the task variety increases, we hypothesise that coordination time increases as task variety increases. We tested three conditions, no task variety, moderate task variety, and high task variety. The third question depicts the relation of boredom, task allocation, and task performance:

What are the consequences of boredom effects with respect to specialisation, task allocation, and task performance?

The consequences of boredom effects are more difficult to hypothesise. The relation between motivation and task performance is evident but the relation between motivation and task allocation is more difficult to predict. We tested three conditions, a low degree of boredom and recovery, a moderate degree of boredom and recovery, and a high degree of boredom and recovery.

We conducted all three experiments under the following constraints:

The task unit duration is 104

The system consists of two agents

The maximum of both motivation and expertise is set at 25

The motivation and expertise thresholds are set at 10

Expertise and motivation are equally balanced, i.e. λ=0.5

Within each skill, expertise and motivation have the same initial values

The height of the excitation (ε) and inhibition (ι) is set at 0.15

3.4.1 Experiment 1: expertise differences and coordination time Since the allocation process ends at the point when the agents have become complementary with respect to the performance of the task, we expect the coordination time to correlate positively with the resemblance of the agents. Here resemblance

4 Early testing indicated that this value would give a proper balance between performance time of the individual agents and coordination time. 5 Early testing indicated that this value would lead to a proper spread of the interaction time


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means: making the same initial choice, i.e. values of the I-and You nodes, with respect to one or more actions to be performed. This would imply that two identical agents are not able to allocate a task. Instead they would generate an infinite coordination time. Because this would not be a realistic assumption we defined an upper limit of the coordination time. Of course this upper limit should not be too low because if so it would disturb the processes. It should not be too high either because that would not be realistic. After some testing, we decided to set the upper limit at 1000 time steps. We tested two conditions. In the first condition we used agents with small differences in expertise. In the second condition the agents showed large differences. These conditions were tested under the following constraints:

Each agent has two skills

The agents have to perform one task consisting of two actions and 50 cycles

The task variety is 0 (no task variety)

The boredom rate is 0 (no boredom)

The learning speed is set at 100, the forget speed is set at 50

The agent has two skills because that is all we need to describe the process. The absence of task variety is trivial because the agents only have to perform one task. However, it is indicated here to make sure that task variety does not affect the process.

Table 1 shows the initial expertise of both agents in both conditions:

Table 1: Small and large expertise differences

Low Agent 1 Agent 2 High Agent 1 Agent 2

Exp. skill 1 16 14 Exp. skill 1 20 12

Exp. skill 2 14 16 Exp. skill 2 12 20

3.4.1.1 Results The results confirmed our expectations as derived from the conceptual model. In the first condition, the agents started off quite similarly, with an expertise difference of 2. But with every cycle the difference increased due to learning and forgetting effects. Figure 9a and 9b show only the active skills, i.e. skills that are necessary to perform the task. In Figure 9a, we see that agent 1 specialises in skill 1 (the upper curve, indicated by the dots) while forgetting skill 2 (the lower curve, indicated by the crosses).


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Figure 9a: First condition: small differences: expertise of agent 1

Figure 9b shows the same situation in reverse: agent 2 only uses skill 2 and therefore specialises in performing this skill. He does not use skill 1 and as a result loses it. Hence, agent 1 uses skill 1 and agent 2 uses skill 2.

Figure 9b: First condition: small differences: expertise of agent 2

Because of this specialisation, the coordination time gradually decreases, since coordination time is negatively correlated to agent differences. Figure 9c shows this decrease. It shows four curves of which the curve of agent 2 is covered by the curve of agent 1. The curve of agent 1 covers the curve of agent 2. These curves indicate the performance time of the single agents, which slightly decreases due to the increase in expertise. The crossed curve shows the coordination time, and the triangled curve shows the performance time of the entire system, i.e. the performance time of both agents + the coordination time. We see that the coordination time starts at 43, and then decreases until it reaches 0 during the 17th cycle. From that point on we see that the performance time of the whole system is only determined by the performance time of the individual agents.


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Figure 9c: First condition: performance

The second condition shows the same process starting with different values (see Table 1). As in the first condition, the agents specialise. The main difference with the other condition is the initial difference of the agents (8 vs. 2). The larger difference in the second condition does not affect the specialisation processes with respect to the expertise of the agent. As in figure 9a and 9b, the curves of skill 1 and skill 2 of agent 1 are identical to the curves of skill 2 and skill 1 of agent 2. Therefore, we will only show the expertise of agent 1:

Figure 10a: Second condition: large differences: expertise of agent 1

Furthermore, the larger difference in the second condition leads to a decrease in the interaction time that is much larger than it was in the first condition. The coordination time starts much lower (4) than in the first condition (43) and has turned to 0 in the 9th cycle.


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Figure 10b: Performance in the second condition

3.4.1.2 Conclusions These results confirm that WORKMATE1 generates dynamics that are in accordance with the expectations as derived from the conceptual model. No matter what the initial conditions are, under the constraints we described at the beginning of this section, the best becomes better and the worst becomes worse. This process indicates that the system will always end up in a stable state in which both agents specialise themselves in one or more skills. But again, this only happens in systems where there is no boredom, and in which the same skills are used over and over again.

3.4.2 Experiment 2: task variety, coordination time, and specialisation As task variety increases, we expect the agents to specialise less. Furthermore, less specialisation implies more coordination time because of the inverse relation between coordination time and specialisation. We tested three conditions: no task variety, moderate task variety (2), and high task variety (4). These conditions were tested under the following constraints:

The agents have to perform 10 tasks consisting of 4 actions and 5 cycles

Every agent has 40 skills

The boredom rate is 0 (no boredom)

The learning speed is set at 100, the forget speed is set at 5

The agents require minimally 40 skills to be able to perform 10 tasks consisting of 4 actions in the condition with a high task variety. High task variety is defined as maximal task variety, i.e. every new task only consists of new actions. We lowered the forget speed to 5 to prevent situations in which the agents forget their skills to perform the last tasks. Table 2 indicates that in all three conditions the agents started off with the same level of expertise.


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Table 2: initial expertise of both agents in all three conditions

Skill Agent 1 Agent 2

1 + 8*k 18 17

2 + 8*k 15 16

3 + 8*k 14 13

4 + 8*k 11 12

5 + 8*k 12 11

6 + 8*k 13 14

7 + 8*k 16 15

8 + 8*k 17 18

x + 8*k means that the value of skill x equals the value of skill x + 8*k, with k [0,4].

3.4.2.1 Results The first condition of no task variety leads to results that are quite similar to those of our first experiment. Since the expertise differences are 1 instead of 2, the coordination time starts at a higher level and decreases more slowly, but both slopes show the same process (see Figure 11a:).

Figure 11a: Performance with no task variety

As depicted in Figure 11b, in the second condition, we observe a decrease in the interaction time while the task is being performed. As soon as the task changes, the interaction time suddenly increases because the emerging new task has to be allocated. Furthermore, we see the performance time of the single agents decrease slightly, due to the specialisation effect within a single task. As soon as the agents start performing a new task, their performance time increases because they are not specialised yet in the new skills that are needed to perform this task. The peaks as shown in Figure 11b are somewhat arbitrary, which can be explained by the level of task variety. Moderate task variety implies that for every new task, only half of the actions change. The remaining half is subject to the specialisation effects we described in the first experiment. This


44

means that specialisation effects within a task will affect the allocation processes of the next task.

Figure 11b: Performance with moderate task variety

The third condition of high task variety shows that the peaks are quite equal, because the specialisation effect within a single task now does not affect the processes of the next task (see Figure 11c).

Figure 11c: Performance with high task variety

3.4.2.2 Conclusions In accordance with our expectations, the results show that in a setting with task variety the coordination time increases straight after the change in the task and decreases until the next change. The decrease is caused by the specialisation effect as described in the first experiment. The increase results from the time it takes to allocate the new actions. Furthermore, we see that in conditions with low and moderate task variety, there is some overlap between old actions and new actions, resulting in an erratic performance time. In the condition where there is a high task variety with no overlap, every change implies a task that is completely new, generating a performance time that is quite regular.


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3.4.3 Experiment 3: boredom Boredom implies a decrease in motivation, which leads to a decrease in task performance. Furthermore, a change in motivation may lead to a change in the initial choice, which could lead to a change in the allocation of the task. We tested three conditions, a high degree of boredom and recovery (100), a moderate degree of boredom and recovery (50), and a low degree of boredom and recovery (10). We tested the effects of boredom under the following constraints:

The agents have to perform tasks consisting of 100 cycles of 2 actions

Every agent has 2 skills

The learning speed and the forget speed are 0, i.e. no learning and forgetting

In the first setting, the initial values of the agents were set as follows:

Table 3: initial values of agents 1 and 2

Agent 1 Agent 2

Expertise skill 1 17 13

Motivation skill 1 17 13

Expertise skill 2 13 17

Motivation skill 2 13 17

3.4.3.1 Results Figure 12a shows the results of the first condition. We see a curve consisting of two phases. The first phase indicates the first 18 cycles. We see an increase in the coordination time because of the decrease in the motivation of both agents. The second phase starts during the 19th cycle, where the coordination time suddenly drops. Apparently the agents switched actions! After the switch, the coordination time increases again because of the motivational decrease of both agents and then the agents switch again. This continuous switching of actions demonstrates that a job rotation schedule emerges under this condition.


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Figure 12a: boredom and action rotation: boredom/recovery=100

Furthermore, in Figure 12b we see that, apart from the decrease in the first phase, the motivation of the agents does not further decrease in the second phase.

Figure 12b: motivation of agent 1

We only depicted the motivation of agent 1 because his motivation for skills 1 and 2 is equal to the motivation of agent 2 for skills 2 and 1.

The next condition, moderate boredom and recovery, shows that the first phase now ends in the 36th cycle. Because of the lower boredom rate, it takes longer before the agents reach a state in which they start switching actions. Furthermore, we see a fluctuation of the coordination time, indicating the same rotation process as in the former condition. We see that the fluctuations are somewhat smaller, i.e. between 190 and 240 instead of 150 and 240 as in the first condition. This can be explained by the lower boredom and recovery rates: because the processes of boredom and recovery are much slower, after the switch the initial choices of the agents remain more similar, resulting in higher coordination times.


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Figure 12c: boredom and action rotation: boredom/recovery=50

The third condition, a boredom/recovery rate of 10, indicates that the first phase shows an increase in the interaction time which is so small that the second phase of switching actions does not even occur in a task consisting of 100 cycles.

Figure 12d: boredom and action rotation: boredom/recovery=10

3.4.3.2 Conclusions The results show that boredom affects the performance time in two subsequent phases. In the first phase, we see an increase in the coordination time because of the decrease in the motivation of both agents. When the motivational decrease causes the initial choice to change, the second phase emerges, in which the agents rotate their actions. When we lower the boredom and recovery rates, it takes more time before the second phase starts because a lower degree of boredom implies less motivational decrease, which diminishes the effect on the change in the initial choice.

3.5 Discussion Not only do the results show that WORKMATE I generates dynamics in accordance with the expectations as derived from the conceptual model, they also reveal interesting behaviour, such as the emergence of job rotation. This type of behaviour is particularly interesting because it can be observed in daily life (Van den Beukel, 2003). This implies that WORKMATE I is able to produce emergent behaviour that shows a strong resemblance with daily-life phenomena. This resemblance does not apply to all the


48

behaviour which the results show. For instance, the negative correlation between coordination time and agent differences is plausible, but an increase in coordination time as part of the rotation process every time the action shifts is not. People invent standard rules to shift actions, which the agents in WORKMATE I cannot do. Furthermore, the model describes the task allocation of two agents. A setting consisting of more agents would be more realistic and could result in processes that are far more complex than the ones we have described here so far. Moreover, the allocation process we described is only based on expertise and motivation, which are individual components. It does not involve any social components. The relation between task duration and motivation is not involved either although this relation might influence the allocation process (see also Csickszentmihalyi, 1992). Therefore, an important subject for further research lies in the plausibility and the realism of the model (Zoethout et al., 2004). This does not only refer to the agents and their interaction but applies to the task as well. This study merely concerns dynamic complexity, but as the examples of the apple orchard suggest, interdependence is also an important task characteristic (Wood, 1986; Thompson, 1967). Although many scholars are in favour of the KISS-principle: Keep It Simple, Stupid, the principle of EROS: “Enhanced Realism Of Simulation”, as Conte stated in 1997 at the First International Conference on Computer Simulation and the Social Sciences (ICCS&SS), may well be used as long as we add complexity in a stepwise manner and only after a full understanding of the dynamics of the simpler model (Harrison, 2002). Nevertheless, we should be aware of what is called Bonini’s paradox: the more realistic and detailed one’s model, the more the model resembles the modelled organisation, including resemblance in the directions of incomprehensibility and indescribability (Starbuck, 1976, cited in Weick, 1979). Another subject for further research could be the relation of simulation experiments with empirical data. Although simulation may be the best method of studying self-organising processes of task allocation, we still wish to validate the results by comparing them with daily-life situations.

WORKMATE 1 may be useful in different scientific areas. Within the area of management science, it serves as a tool for studying self-organising social processes of task allocation. Moreover, computer simulation is a common method within the area of Operations Management (Law & Kelton, 2000). Within this area, physical infrastructures are modelled, but psychological theories are less emphasised. Applying WORKMATE 1 results in interesting outcomes regarding the simulation of production processes with agents, which are psychologically more realistic. Within the area of social sciences, the theoretical framework may contribute to the integration of the amount of fragmented theories and models (Jager, 2000; see also Vallacher & Nowak, 1994).

The field of computational social and organisational science is growing rapidly (Carley, 1998). Applications arising from this field lead to new perspectives and new approaches, such as for example, complexity theory. These approaches and applications will find their way into science and society, generating new ways of thinking as well as new combinations of existing views.

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Chapter 4 Simulating the Emergence of Task Rotation6 Abstract In work groups, task rotation may decrease the negative consequences of boredom and lead to a better task performance. In this chapter we use multi agent simulation to study several organisation types in which task rotation may or may not emerge. By looking at the development of expertise and motivation of the different agents and their performance as a function of self-organisation, boredom, and task rotation frequency, we describe the dynamics of task rotation. The results show that systems in which task rotation emerges perform better than systems in which the agents merely specialise in one skill. Furthermore, we found that under certain circumstances, a task that leads to a high degree of boredom was performed better than a task causing a low level of boredom.

4.1 Introduction According to the principle of minimal critical specification (Herbst 1974), an organisation should only offer constraints that are necessary to fix critical issues. For the rest, the workers should be free to self-organise their way of performing a task. Self-organisation refers to the process within a system in which a general order is created without the presence of another system dictating this order (e.g. Dalenoort 1989; 1995; Heylighen 1997). An important organising mechanism is the allocation of tasks. Task allocation refers to the way workers split up tasks into subtasks and divide them among each other. This process depends on task components, psychological components and the constraints the organisation has prescribed. These components not only have an impact on the self-organising process of task allocation, but also influence to what extend the task allocation can be maintained or should be changed. A change in task allocation can be considered as task rotation. In the literature the benefits of task rotation have been discussed extensively (for instance Emery & Trist 1960; Van den Beukel 2003). Workers become experienced in all of the skills that are required to perform a task, which creates multi-availability of team members and therefore leads to a redundancy of functions (Morgan 1986; Kuipers 1989; Van den Beukel 2003). This makes a team more flexible to adapt to changes, either within the team (e.g. illness,

6 This chapter is published as: Zoethout, K., Jager., W, & Molleman, E., (2006), Simulating the Emergence of Task Rotation, Journal of Artificial Societies and Social Simulation vol. 9-1, http://jasss.soc.surrey.ac.uk/9/1/5.html


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turnover), or within its environment (e.g. changes in product demand). Another benefit of task rotation is that it may prevent the individual worker to become physically or mentally overburdened due to the repetitivity of the performance of a single operation (Van den Beukel 2003). In addition, workers may start rotating a task as a consequence of boredom.

Because of its benefits, task rotation has been implemented in various settings, often related to self-managing teams (e.g. Atkinson 1984). However, although the outcome of task rotation has been studied intensively, studies on the emergence of task rotation have not been conducted. Emergent properties refer to properties of a system that cannot be reduced to the properties of the elements, i.e. the agents, which the system consists of (e.g. Heylighen 1997). In the case of a popular concept such as task rotation, research into its emergence will certainly contribute to a better understanding of the concept.

In this chapter, we describe three classes of components that could influence the process of task rotation: organisation components, referring to the constraints on the self-organising process, system components, referring to the psychological characteristics of the workers, and task components, referring to the characteristics of the task. On the basis of these components we conducted three series of experiments. First, we studied the performance and the development of the expertise of agents in a system where they were not allowed to rotate tasks. Second, we studied the performance and the expertise of agents who were free to rotate tasks whenever they liked to. Third, we studied task rotation in a setting in which the agents could only rotate at fixed points in time.

4.2 The model

4.2.1 The task Despite all the different definitions and perceptions of tasks, it is quite clear that a task requires one or more skills. These skills are related to task-actions, i.e., the parts a task consists of. Theories on tasks indicate that a task can be split up into task-actions that can be related to skills in a large number of ways (Hunt 1976; Weick 1979; Tschan & Von Cranach 1996). According to our definition, a task consists of actions in such a way that for every action exactly one skill is required to perform this action. In order to perform the whole task, all of the actions that a task consists of have to be performed one or more times. The number of times the actions have to be performed, we call cycles. In this way we describe a task as a two-dimensional matrix of actions and cycles.

4.2.2 The agents Important components that determine group performance are expertise and motivation (Wilke & Meertens 1994; see also Steiner 1972). These components can be considered as the characteristics of skills; workers, i.e. task performing humans, perform particular

Chapter 4: Simulating the Emergence of Task Rotation

51

skills better or worse than other skills (expertise), and prefer using some skills more or less to using other ones (motivation). Workers are formalised as agents with properties necessary to perform the tasks (for an elaborate description, see Zoethout, Jager, and Molleman 2004). These properties are represented as a set of skills, with each skill consisting of two variable components, expertise and motivation, and thresholds. These thresholds determine whether the expertise and motivation are sufficient to perform the task.

Skills can be considered as being either active or passive. Passive skills refer to the total range of skills of the agents. Active skills concern the skills that are actually required to perform a specific task. As soon as agents have to perform a task, a subset of the set of passive skills is activated, which corresponds to the actions the task requires. After the skill has been used and the task has been completed, the skill becomes passive again.

If the agents use the same skill over and over again, their expertise will improve, but their motivation may decrease (Hackman & Oldham 1980; see also Hackman & Morris 1975). This may affect the performance in a number of ways. First, an increase in expertise will lead to an increase in performance. Second, the decrease in motivation may lead to a decrease in performance. Third, the decrease in motivation may lead to re-allocation of the task, i.e. task rotation.

4.2.3 The model Figure 13a and 13b describe the different components of our model:

Figure 13 a: The system and its environment

The model is a simple input-process-output model (see Figure 13a). The input is a task. As we stated above, a task consists of a number of actions and a number of cycles. Some organisations offer a higher degree of freedom in the self-organising allocation process than others. For instance, in some organisations the agents are allowed to rotate tasks whenever they want, in others only once a day, or not at all. In the model this is represented as rotation frequency, i.e. the number of possible rotations of one task. The output of the system is the task that has been performed. The performance of the system, which is the dependent variables, indicates how well the agents have performed the task. The performance is based on expertise and motivation, the two


52

mediating variables, and the way in which the task has been allocated. It is expressed as the total time.

Figure 13b: The System

The system that has to perform the task consists of agents (see Figure 13b). Every agent has skills that correspond to the action that the task consists of. Each skill has two components, expertise (how good?) and motivation (how nice?). On the basis of these components, the agents allocate the task and subsequently perform it. The performance process influences the expertise of the agents: the agents learn by carrying out the task and forget by not carrying out the task. Motivation is subject to fluctuation because the agents can become bored and can again recover from that. When there is a change in an agent’s expertise and/or motivation, task rotation may emerge. Whether or not the process of task allocation is self-organising depends on the specifications of the organisation (see also Herbst 1974). Input, condition, and output refer to the concepts as proposed in Figure 13a.

4.2.4 The allocation process On the basis of the expertise and motivation components of the active skills, each agent determines individually what actions he does or does not want to perform by applying the following rule:

IF Expertise > ExpertiseThreshold AND Motivation > MotivationThreshold THEN I DO ELSE YOU DO

With every action the agents choose whether to perform it (I do) or leave it to others (You do). This choice is represented as two nodes, I and YOU, whereby there is a tension based on the values of the expertise and motivation. The choice forms the basis of influencing other agents. The influence process starts from the assumption that every agent persists in his choice and will try to influence other agents to make a choice complementary to it (see also Kerckhoff & Davis 1962). For example, five agents have


53

to sail a ship. Sailing a ship is a task consisting of five actions: handle the helm, the main sail, the jib, the swords, and watch the area. Based on his expertise and motivation, agent one only wants to handle the helm. Therefore, he tries to influence the other ship members not to handle the helm, but to handle the main sail, the jib, etc. instead. Simultaneously, the other agents will try to influence others in the same way. We represent the influence process by using excitatory, i.e. tension increasing, and inhibitory, i.e. tension decreasing connections (see Figure 14):

Figure 14: Excitation (+) and inhibition (-) of two agents

With every action, the I-node of one agent inhibits the I-node of the other(s) and excitates the You-node of the other(s). The You-node of one agent inhibits the You-node of the other(s) and excitates the I-node of the other(s). If the I-node of an agent is bigger than the You-node, the choice of the agent is ‘I Do’, otherwise it is ‘You-do’.

The excitation and inhibition functions are based on the values of I and You of both agents and the differences of their nodes. The differences of the nodes are included into the functions in order to prevent possible oscillations when the nodes have about the same value (see also Zoethout, Jager, and Molleman, 2006b):

IIDiffIIII 2122 : ι−= I1 inhibits I2 (11a)

YouYouDiffYouYouYouYou 2122 : ι−= You1 inhibits You2 (11b)

IIDiffIYouYouYou 1222 )1(: −+= ε I1 excitates You2 (11c)

YouYouDiffIYouII )1(: 2122 −+= ε You1 excitates I2 (11d)

I1, I2, You1, and You2 correspond to Figure 14. DiffII equals the absolute value of (I1 - I2) and DiffYouYou equals the absolute value of (You1 – You2).

This process ends as soon as the agents reach a complementary situation. This means that after the allocation process, with respect to a particular action, there is only one agent who finally chooses ‘I Do’. All the others choose ‘You Do’. Only when this complementary situation has been reached with all actions, the agents start performing the task.


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4.2.5 Performance, learning and boredom We consider the performance of the system as a function of expertise and motivation (see also Wilke & Meertens 1994). Both expertise and motivation are defined in terms of the time it takes to perform a task: the higher the degree of expertise or motivation, the sooner the task will be finished. Furthermore, we define a minimal time to complete an action, taction, which is equal to the actual time it takes to perform the action at a maximal rate of expertise and motivation. The actual performance time of a single agent, tperf., can therefore be expressed as:

∑=−+

=n

i ii

iactionperf

mm

ee

tt1

maxmax

.

)1(

_

λλ

(12a)

λ represents a parameter that determines the balance between expertise and motivation (0.5 in all of our experiments). In the present study, the agents perform the actions simultaneously. This means that the time it takes to perform the total task, tperf. , is determined by the slowest agent.

During the performance process, the expertise and the motivation of the agents change. When agents perform a task, their expertise increases, and when they do not, it decreases. According to Nembhart (2000), forgetting can be described as ‘following the way back’ on a learning curve. Therefore we use the inverse function of learning to describe forgetting. Furthermore, an important characteristic of most learning curves is that they reach a maximum asymptotically (Nembhart 2000). Therefore, we define learning by means of the relations among expertise (e) at a certain time (t), expertise in the future (t+1), the maximum expertise (emax), and a parameter (λ, [0,1]) that determines the learning speed:

maxmax

)1( eeeee t

tt−+=+ λ

(13a)

Forgetting is the inverse of learning, therefore:

µµ−

−=+

max

max)1(

)(e

eee tt

(13b)

whereby µ[0,1] determines the forget speed.


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Motivation curves can be described by applying the same characteristics: a maximum that is reached asymptotically, and recovery as the inverse of boredom. This means that formula (13b) describes the motivational decrease related to boredom and formula (13a) represents the motivational increase related to the recovery from boredom. In this case the parameters µ and ν respectively describe the recovery and the boredom speed.

By using the parameters λ and µ we can set the degree of boredom/recovery and learning/forgetting of different tasks. For instance, repetitive tasks, i.e. tasks with a large number of cycles, may lead to an increase in expertise and a decrease in motivation. As the failure of the Taylor-approach indicates, this may finally lead to a decrease in performance (see also Wilke & Meertens 1994). On the other hand, not using skills for a period of time may lead to a decrease in expertise. This suggests that there must be a balance between expertise and motivation. Task rotation may help to reach this balance.

4.3 Experiments All experiments were conducted with WORKMATE II, a computer simulation program that we developed in DELPHI67. We studied a task performing system using three types of organisations. In accordance with the first type, self-organisation, the organisation does not constrain the allocation process. This means that the agents are free to allocate tasks by themselves and change the task allocation whenever they want to. Here, the allocation process takes place in the way we described it in the former section. The second type we call semi-self-organisation. This type differs from the former type in three ways: first, the agents are still free to allocate the tasks by themselves, i.e. the task is not yet assigned by the organisation. However, agents are only allowed to re-allocate the task, i.e. rotate tasks, after a fixed number of cycles. Thus, during this fixed number of cycles, the agents have to maintain the same task allocation. Second, the agents are only allowed to use one skill per cycle. Third, the allocation process is not based on interaction between agents, but on the following rule:

IF

)()(kjkjkiki skillagentskillagentskillagentskillagent YouIYouI −>−

THEN

iagent performs

kskill

This rule implies that as regards a certain skill, the agents with the highest difference of the I- and You-node will perform that skill. For example: agent 1 has an I-node of 0.5 and a You-node of 0.2, and agent 2 has an I-node of 0.5 and a You-node of 0.4. The difference of the nodes of agent 1 is 0.5 - 0.2 = 0.3. To agent 2 applies: 0.5 - 0.4= 0.1. Therefore, agent 1 will perform the action. The use of this rule will make no difference in the actual allocation. The only difference is that here the outcome, i.e. the final allocation, is calculated on the basis of the initial choice of the agents rather than on the

7 The program can be downloaded at http://jasss.soc.surrey.ac.uk/9/1/5.html


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interaction among the agents8. In the third type of no self-organisation, the agents cannot rotate tasks at all, but have to keep performing the same action that they initially started with. The agents choose that particular action in the same way as they do in case of the former type.

For each of these organisation types we studied tasks with degrees of demotivation/recovery that were high, moderate and low. Regarding the semi-self-organisation types, we studied three settings of rotation frequency. Rotation frequency is defined as the inverse of the number of cycles in which the agents are forced to use the same skills consecutively. As regards the other types, the rotation frequency has not been manipulated: the ‘no self-organisation’ type does not involve task rotation and in case of self-organisation, the agents decide for themselves whether or not to rotate. Table 4 summarises the experimental design by showing the independent variables.

Table 4: Experimental design

Organisation type Boredom/Recovery Rotation Frequency

High (100/100)

Moderate (50/50)

No Self-organisation

Low (29/29)

NONE

High 1/5, 1/25, 1/50, 1/75

Moderate 1/5, 1/25, 1/50, 1/75

Semi Self-organisation

Low 1/5, 1/25, 1/50, 1/75

High

Moderate

Self-Organisation

Low

NOT MANIPULATED

A rotation frequency of 1/5 implies that the agents are allowed to rotate every 5 cycles. Expertise, motivation and performance are considered as the dependent variables.

We conducted the experiments by using the following parameter values:

A system consisted of 5 agents, each with 5 skills

The agents had to perform one task of 200 cycles and 5 actions

The maxima of both motivation and expertise were set at 25

The motivation –and expertise thresholds were set at 10

8 We maintained the interaction model to be able to conduct experiments by using the variable interaction time, which we did not use in the study we described in this paper.


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The learning speed was 100, the forget speed 10

After conducting numerous trials, we found out that these values appropriately marked the parameter space in which the processes occurred that we wanted to study (see also Zoethout et al, 2006b).

In all experiments, we used the following initial skill values of the agents (see Table 5).

Table 5: Initial setting of the agents in all experiments

Agent 1 Agent 2 Agent 3 Agent 4 Agent 5

Skill 1 11 12 13 14 15

Skill 2 12 13 14 15 11

Skill 3 13 14 15 11 12

Skill 4 14 15 11 12 13

Skill 5 15 11 12 13 14

We see that all the agents have the same pattern of values, but they are assigned to different skills. Initially, to each skill applied that the expertise value was the same as the motivation value. Therefore, in Figure 15, with each skill we mention only one value, representing both the initial expertise and the initial motivation. Although we start from these values, under the influence of expertise and motivational processes, the agents may decide to start rotating their tasks.

Figure 15: An example of task allocation

Figure 15 depicts an example of task allocation. The x-axis represents the cycles and the y-axis shows the skills. The numbers in the table refer to the agents using a particular skill. We see that the agents start in accordance with the initial values as described in table 5, i.e. agent 1 starts with skill 5, agent 2 starts with skill 4, etc. At the 12th cycle, the agents rotate for the first time, i.e. agent 1 rotates from skill 5 to skill 4, agent 2 rotates from skill 4 to skill 3, etc. This is represented by means of the small


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lines. During the next cycle, the agents rotate back, etc. This example depicts the actual task allocation as it occurs by using certain parameter values. Since we will give an elaborate description of expertise, motivation, and performance in the next section, in the actual allocation tables no information has been added. Therefore, we did not include them in the result section.

4.4 Results In this section we have chosen not to depict all the results in detail, but to focus on the most interesting phenomena instead. Therefore, we will only present the results that show the most important aspects of the allocation processes and their outcomes.

4.4.1 Organisation type In this section we will discuss the influence of the three organisation types, self-organisation, semi self-organisation, and no self-organisation, in a setting with a high degree of boredom/recovery. For the semi self-organisation type we used a rotation frequency of 1/5. We will discuss the expertise, motivation, and performance.

4.4.1.1 The influence of self-organisation on expertise development In accordance with the self-organisation type, the agents rotate between two skills (see Figure 16a).

Figure 16a: Expertise in case of self-organisation

Figure 16a shows the development of expertise with respect to the five skills of agent 1. The x-axis represents the cycles and the y-axis shows the expertise. Since the agents are similar in the sense that they will all become specialised in the two skills with the highest initial value, and will forget the other three, we only show the results of agent 1. We see that the expertise in the second best skill of the agents increases after they have started rotating their tasks at the 12th cycle. The first time the agents rotate is determined by boredom. After that, they rotate after every cycle. As a result, the agents do not have time to forget their skills, but are able to increase their expertise. The semi self-organisation type shows about the same development of the expertise. No self-


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organisation leads to a situation in which the agents specialise in one particular skill while forgetting the other skills.

4.4.1.2 The influence of self-organisation on motivation In all three organisation types, initially, the motivation of the agent for using the best skill, i.e. the skill that is initially used, decreases while their motivation for the other skills remains the same. In case of no self-organisation, the motivation of the best skill simply decreases to zero. In case of self-organisation, after the first rotation at the 12th cycle, the agents start using their second best skill. As a result, the motivation for the best skill increases, whereas the motivation for the second best skill decreases until the next rotation. After that, the whole process is repeated. In the long run, we see that the motivation for both skills stabilises at 12. In case of semi-self-organisation, we observe about the same periodic changes, although here the frequency is 10 cycles instead of 2, as is the case with the self-organisation type (see Figure 16b):

Figure 16b: Motivation in case of semi self-organisation

Figure 16b shows the motivation for all skills. The flat lines represent the motivation level of the skills that are not used. The motivation for the skill that was initially performed the best, skill 5, initially decreases and then starts fluctuating. At the 80th cycle, the agents did not rotate, although they had the opportunity. This led to a further recovery of the best skill, and a higher degree of boredom with respect to the second best. The reason for this anomaly can be found in the expertise development. The expertise levels regarding the skills used to perform the task are inclined to increase in a similar way, because both skills will eventually reach the same maximum (see also figure 16a). This means that as the task proceeds, expertise will have less influence on the decision what to do than motivation has. This implies that the agents will only rotate the task after the lowest and the highest motivation rates have been swapped. From the 85th cycle onward, we see that this is precisely what happens.

4.4.1.3 The influence of self-organisation on performance In the case of self-organisation, the agents rotate between two skills. Because of the initial increase in the boredom, the performance time initially increases until the first task rotation. After that, the agents rotate after every cycle. Therefore, the agents do not forget or get bored. However, they do learn. This implies that the performance time is


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solely determined by the increase in expertise. Finally, when the expertise reaches its maximum, the performance time ends in a flat line at the value of 14.

With respect to the performance time the semi self-organisation type shows about the same development (see Figure 16c).

Figure 16c: Performance time in case of semi-self-organisation

Because the agents work synchronously and start with the same initial values, their performance time is identical. This is why we only show the performance of one agent. Here the rotation frequency of 1/5 causes some small fluctuations because during the time period of 5 cycles there is some time to learn, to forget, to get bored and to recover from it. Apart from these fluctuations we see the same development as with the former type, including the final performance time of 14.

The type of no self-organisation shows about the same development. First, we see an increase in performance time due to boredom. However, this increase does not stop at the 12th cycle as in the former types, but continues until the agents have lost all of their motivation at the 22nd cycle. After that, the increase in expertise causes a small decrease in the performance time until it ends in a flat line at value 19. Thus, without self-organisation the performance is a great deal worse.

4.4.2 Boredom In this section we will discuss the influence of high, moderate and low levels of boredom in an organisation type with self-organisation. We will discuss the impact on expertise, motivation, and performance respectively.

4.4.2.1 The influence of boredom on expertise development The first setting in which there is a high degree of boredom is identical to the first organisation type we discussed in the former section: the agents rotate between two skills from the 12th cycle (see also Figure 16a). From that point on, both of these skills improve, whereas the other skills are forgotten. In case of a moderate boredom rate, the task rotation starts at the 34th cycle. This implies that the expertise of the skill that the agents use after the task rotation has already decreased somewhat before rotation. This


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effect is even more clearly visible in the setting in which there is a low level of boredom (see Figure 17a).

Figure 17a: Expertise development in a situation with a low degree of boredom

Here we see that, initially, the agents seem to specialise in one skill. However, at the 77th cycle, they develop expertise in the second skill. This is ‘right on time’, because the expertise in the second best skill has almost dropped below its threshold of 10. This explains why a boredom-recovery rate <29 will not result in a task rotation process.

4.4.2.2 The influence of boredom on motivation It is evident that at a high boredom rate the motivation decreases quicker than it does at a low rate. Figure 17b shows that the curve of the best skill decreases much slower than in the situation of a high boredom level.

Figure 17b: Motivation in the situation with a low boredom rate

After the first rotation at the 77th cycle, we see that the motivation for the skill that was initially performed the best increases again, whereas the motivation of the second best skill decreases.

4.4.2.3 The influence of boredom on performance As we discussed in 4.4.1.2, in the first setting of high boredom, the performance time first increased because of the boredom, and subsequently decreased from the first


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rotation at the 12th cycle to a flat line at a value of 14. In the second setting of moderate boredom we found that the initial increase in the performance time was less rapid. This implies that the performance time decreases later, i.e. from the first rotation at the 34th cycle, and also ends at the value of 14. The last setting of low boredom starts with a decrease in the performance time (see Figure 17c).

Figure 17c: Performance time in a situation with a low boredom rate

The initial decrease is caused by the increase in expertise, which has a stronger effect than the decrease in motivation. After 30 cycles the performance time increases until the first rotation at the 77th cycle, and then decreases to a value of 15. The value of 15 instead of 14 is caused by the recovery time: In the experiments the values of boredom and recovery were set at the same value. This implies that the setting of low boredom includes low recovery. Apparently the recovery process takes place slower than the learning process. With respect to the allocation process this means that, if the recovery rate decreases, the role of the expertise of the agents becomes more important. Figure 17c depicts only one agent because the performance time of all the agents is identical, apart from one exception which the figure does not depict: from the 78th cycle, the agents sometimes perform 2 actions in one cycle and none in the other. This indicates that the performance time either suddenly increases to twice as high or decreases to zero. We consider this phenomenon as an anomaly that does not contribute to an understanding of the process.

4.4.3 Rotation frequency In this section we will discuss the influence of four different rotation frequencies on the semi-self-organisation type. Rotation frequency only occurs with semi self-organisation: In case of self-organisation, the rotation frequency is determined by the agents themselves, and no self-organisation does not involve task rotation. We studied the rotation frequency in a high boredom setting.


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4.4.3.1 The influence of rotation frequency on expertise development In the first situation with a rotation frequency of one possible rotation occurring every 5th cycle, the agents develop two skills while forgetting the other skills. If we lower the frequency to once every 25 cycles, the effect remains the same, although the second skill is learned later (see Figure 18a).

Figure 18a: Expertise development at a rotation frequency of 25

This also applies when we lower the frequency further. Even at a frequency of once every 75 cycles, the agents are still capable of learning two skills (see Figure 18b).

Figure 18b: Expertise development at a rotation frequency of 75

Figure 18b shows a process comparable to the one depicted in Figure 17a. The decrease in the rotation frequency results in the same effect as the decrease in boredom/recovery does: because the first moment of task rotation occurs quite late, either because of a low boredom rate or a low rotation frequency, the agents have more time to specialise in one skill and forget the second. This implies that if we would lower the rotation frequency even further, the agents forget their second best skill at a level below the threshold of 10, and as a result end up specialising in only one skill. As Figure 17a indicates, a setting with a rotation frequency lower than 1/77 would actually lead to this outcome.


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4.4.3.2 The influence of rotation frequency on motivation As soon as an agent uses a skill, the motivation decreases until the skill is no longer used. After that, the motivation increases again, until the skill is used again. The periodicity of this in- and decrease is determined by the rotation frequency. A rotation frequency of 5 implies that it takes 10 cycles from the first use before the motivation has reached its original level again. Figure 18c shows a situation in which there is a rotation frequency of 25.

Figure 18c: Motivation at a rotation frequency of 25

We see that the skill with the highest motivation rate (green) starts decreasing, reaches zero at the 22nd cycle and maintains this level until the next rotation at the 26th cycle. Then, the motivation increases again until it reaches its original value at the 47th cycle. Simultaneously, the agent uses its second best skill, following the same periodicity as the highest skill.

4.4.3.3 The influence of rotation frequency on performance The first situation, in which the rotation frequency takes place once every 5 cycles, is described in section 4.4.1.3 (see also Figure 16c). During the time period of 5 cycles there is some time to learn, to forget, to get bored and to recover from it, which causes small fluctuations. Apart from these fluctuations the performance time slowly decreases due to the increase of the expertise and finally reaches a value of 14. In the second situation, in which there is a rotation frequency of 1/25, we see the development of a cyclic change (see Figure 18d).


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Figure 18d: Performance time at a rotation frequency of once every 25 cycles

During the first period of 25 cycles, expertise is build up in the best skill, but boredom will nevertheless cause an increase in the performance time. After the task rotation at the 25th cycle, the performance time starts at a lower level because now the agent uses its second best skill. During the first 25 cycles the expertise in this skill dropped resulting in a higher initial start level of the performance time and a higher level at the end of the second period at the 50th cycle (see also Figure 18a). Nevertheless, the expertise in both skills has increased over 20, causing the performance time in each period to start from value 14 from the 51st cycle, after which as a result of boredom it increases until it reaches the value of 21. Then the agents rotate, the performance time shifts back to its lowest level and the same process starts all over again. The differences in performance time at the start of every period (1st, 26th, 51st, etc,) decrease because the differences of the best and the second best skill will decrease once they have both reached their maxima (see also Figure 18a).

The figure shows that it takes about 50 cycles, i.e. two rotations, before this periodicity has been adjusted. If we lower the rotation frequency to 1/50, it again takes two rotations, to adjust this periodicity, in which the performance time now shifts from 11 to 19. If we lower the rotation frequency to 1/75, we again see that it takes two rotations, i.e. 150 cycles to adjust the periodicity. When studying the results of a task with more than 200 cycles, we found out that in the latter situation the periodicity of the performance time shifts from 10 to 19. If we compare the different situations, we see that the slowest performance time decreases slightly as a function of the rotation frequency. A lower frequency results in more time to recover from boredom, which leads to a higher motivation.

4.5 Conclusions and Discussion

4.5.1 Conclusions With regard to self-organisation, we conclude that the influence of self-organisation on expertise and performance shows that in the situations where task rotation emerged, the system delivered a better performance than in case of no self-organisation. This finding


66

suggests that, when performing a task, workers must have the freedom to rotate tasks whenever they feel bored. As regards boredom/recovery, we have arrived at two conclusions: First, if the boredom/recovery rate decreases, it takes more cycles before the agents start to rotate tasks. Consequently, it takes more time before they develop a second skill. If the boredom/recovery rate drops beneath a certain point, the agents will specialise in only one skill, because the time it takes to decrease the motivation enough to rotate tasks exceeds the time that it takes to forget the second best skill. Second, if the boredom/recovery rate decreases, at a certain point the motivational processes become slower than the expertise processes. This implies that, with respect to a particular skill, at the time the agents are bored, the level of their expertise has become quite high. This results in a situation in which the agents only rotate tasks when their level of motivation is very low and rotate back before they have fully recovered. As regards the task rotation frequency, we conclude that with respect to expertise, the decrease in the rotation frequency has the same effect as the decrease in boredom/recovery. We found no significant effects of the interaction of self-organisation and boredom or boredom and task rotation frequency, except in the situation with a low degree of boredom: This situation is ‘close to the edge’, which means that in the setting with a high task rotation frequency, which we used to manipulate by adjusting the boredom/recovery rate, the agents still rotated tasks. But as soon as we lowered the boredom/recovery rate from 29 to 28, the edge was crossed and task rotation did no longer emerge. The same happens if we lower the task rotation frequency. In the other situation, a frequency of once every 78 cycles still led to task rotation. However, in this particular setting the process of task rotation did no longer occur at a frequency lower than 1/25. Therefore, if an organisation or a work group needs workers that are capable of using multiple skills, for instance to create flexibility, the components described in this study should be taken into account. A low task rotation frequency and a task that is interesting (low level of boredom) more easily lead to the specialisation in one particular skill than a boring task or a high task rotation frequency does.

4.5.2 Discussion In the present study we used expertise and motivation as components that determine group performance. These components can be considered as elements within a broad range of factors that affect team performance, such as work-related attitudes, team composition, commitment, and team cohesion (e.g. Cohen, Ledford & Spreitzer 1996). Although motivation and expertise are important components that affect performance (Wilke & Meertens, 1994), it is obvious that they do not cover all the other factors. Moreover, we supposed that processes, such as getting bored, were solely influenced by the repetitiveness of tasks, whereas it is likely that several other factors might cause boredom, such as for example, the physical condition of an agent. Factors that we consider to be fruitful extensions of our model are, for example, coordination costs (e.g. Cohen et al., 1996), task interdependence (Van der Vegt & Van de Vliert 2005) team size and team composition (e.g. Molleman 2005). Regarding coordination costs, prior tests have indicated that simulation experiments could only produce plausible outcomes if the interactions among agents led to the emergence of rotation rules and


67

routines that decrease coordination costs (see Zoethout et al., 2006b). Task interdependence might seriously affect the possibilities to divide tasks among agents, and the composition of teams in terms of team size, the distribution of skills, demographic characteristics and personality traits has proven to influence team functioning (Molleman 2005). Inclusion of such factors will bring our model more close to reality, but will also make the results much more difficult to interpret.

Several studies have elucidated the benefits of job rotation within teams (e.g., Van den Beukel 2003). These studies have led to a so-called design-based view on organisations, i.e., since job rotation has proven to bring forth advantages, management should implement it. As a consequence, job rotation has been implemented by management in various settings, even in work designs that are considered as self-managing teams. This may raise the question whether job rotation that is designed for and implemented in a system by an external party has the same effect as job rotation that has spontaneously emerged from the part of the workers themselves. Of course, the discussion about designing job rotation externally versus spontaneous development within the organisation itself involves a lot more issues than dealt with in the present study. Nevertheless, our use of computer simulation has made it possible to start comparing both approaches. We therefore conclude that simulation studies of this kind contribute to the understanding and analysis of the social dynamics of work groups.

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Chapter 5 Task Dynamics in Self-Organising Task Groups9 abstract Multi-agent simulation is applied to explore how different types of task variety cause workgroups to change their task allocation accordingly. We studied two groups, generalists and specialists. We hypothesised that the performance of the specialists would decrease when task variety increases. The generalists, on the other hand, would perform better in a high task variety condition. The results show that these hypotheses were only partly supported because both learning and motivational effects changed the task allocation process in a much more complex way. We conclude that although no variety leads to specialisation and high variety leads to generalisation, in general, performance is better when variety is low. Further, in case of no variety, specialists clearly outperform generalists. In highly dynamic situations, since there is no space for any development, the behaviour of specialists and generalists becomes more similar, and, consequently also their performance.

5.1 Introduction Should one hire specialists of generalists to maximise group performance? This question still puzzles personnel managers and organisational scientists alike. Well known by practitioners and scientists is that group performance depends on many factors. Both task factors, such as the number of skills required, rotation schedules and variability in tasks, as well as personal factors such as expertise, learning, motivation and boredom have been found to affect group performance (for an overview see, for example, Yeatts & Hyten, 1998). Whereas the effects of separate variables – or limited combinations - have been empirically investigated by many researchers (e.g., Steiner, 1972; Hackman & Oldham, 1975; Wilke & Meertens, 1994; Tschan and von Cranach, 1996), it is difficult to derive empirical based conclusions on how the combination of these variables affects the performance of a team of experts versus generalists. Social simulation offers a methodology to systematically explore a large number of conditions, and thus may contribute to deriving such conclusions (e.g. Gilbert and

9 This chapter is submitted to Autonomous Agents and Multi Agent Systems as: Zoethout, K., Jager., W, & Molleman, E., Tasks Dynamics and Flexibility of Self-Organising Task Groups: Expertise, Motivational, and Performance Differences of Specialists and Generalists

Chapter 5: Task Dynamics in Self-Organising Task Groups

69

Troitzsch, 1999). In this chapter we explore how task and personnel factors jointly affect the performance of teams consisting of specialists or generalists.

The social simulation approach we follow here typically tries to explain group processes from a bottom-up perspective. This approach shows the influence of complexity theory and multi-agent simulation to describe higher order developmental and adaptation processes in terms of local interactions (Panait & Luke, 2005; Arrow, McGrath, and Berdahl, 2000; see also Axelrod and Cohen, 2000; Gilbert and Troitzsch, 1999). Although different disciplines meet in the broad area of group dynamics, there are still large differences between them. For instance, if we look at studies on self-organisation, some empirical work shows a solid theoretical basis (e.g. Arrow and Crosson, 2003). However, because of its methodology, these studies are often limited regarding their design. On the other hand, simulation studies may show an elaborate experimentally based description, but are limited with respect to the use of psychological theory regarding properties of individuals (e.g. Kitts, Macy, and Flache, 1999). In general most simulation models concerning processes within task groups or teams focus on abstract computational and mathematical descriptions (e.g. Pynadath and Tambe, 2002a; 2002b) or use a so-called bounded rationality approach (e.g. Carley, 1992). Psychological theory that for instance focuses on the influence of motivational related effects such as boredom, fatigue, etc. however, is less emphasised. Nevertheless, it is well known that motivation strongly influences processes within work groups (Hackman & Oldham, 1975; see also Wilke & Meertens, 1994).

In this chapter we will use a model that combines a multi-agent simulation approach with psychological theory on motivation. Our study deals with the question how a workgroup adapts to changes of the tasks it has to perform. There are a lot of approaches related to task descriptions and performance (Hunt, 1976; Weick, 1979; Tschan & Von Cranach, 1996). Our description is based on Wood (1986) who states that task changes are in fact a component of task complexity. The adaptation process of the group is described in terms of task allocation. Processes of task allocation are affected by task characteristics and group characteristics. With respect to the latter we focus on the expertise and the motivation of the individual team members. Following Ashby (1956) we studied the differences between groups of generalists and specialists, not only regarding the way in which they adapt to task changes, but also the implications for performance.

In the first section of the chapter we focus on the theories and models we use and their formalisation, which form the basis of WORKMATE, the simulation program that we developed to study self-organising processes of task allocation. WORKMATE is used to test a number of hypotheses concerning the relation between task dynamics and performance differences of groups of specialists and generalists. The second section describes the experimental design and the parameter settings. Next we will describe the results and we end up with conclusions and a discussion.


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5.2 The model WORKMATE III is a deterministic discrete event based simulation program for simulating self-organising processes of task allocation that is developed in DELPHI6. It is an elaborated version of the simulation program that we used for experiments on the emergence of job rotation (Zoethout, Jager, and Molleman, 2006a), and the relation between task variety and coordination time (Zoethout Jager, and Molleman, 2006b). In this section we shortly describe the theoretical framework WORKMATE III is based on.

5.2.1 Tasks and task dynamics A task is considered as a set of actions in such a way that each action is related to a single skill (Hunt, 1976; Weick, 1979; Tschan & von Cranach, 1996). Each action has to be performed a number of times, i.e. cycles, before the whole task is finished. In this way, a task can be represented as a matrix of actions (what) and cycles (how often) (see also Figures 19a and 19b). This chapter deals with the relation between flexibility and performance under conditions of task dynamics. Task dynamics refer to the speed in which tasks change over time (Wood, 1986; see also Tschan & von Cranach, 1996). In our study task dynamics consists of two components, task variety and number of tasks and cycles. Task variety refers to the differences between every next task in relation to the former one with respect to its actions. Number of tasks and cycles refers to the size, i.e. number of cycles, of a single task and the number of times this tasks has to be performed. For instance, given a task variety of 1, performing 2 tasks of 100 cycles implies lower task dynamics than performing 8 tasks of 25 cycles. In the first example after 200 cycles one new skill has been used whereas in the second example after 200 cycles the agents has used seven new skills.

In the Figures 19a and 19b we see a task consisting of 3 actions, a, b, c and 3 cycles, i.e., 1, 2 and 3. Thus, the 3 actions need to be performed 3 times before the complete task is finished. The agents may perform the task in a number of ways, for instance cycle by cycle, action by action, or something in between. The possible ways a task can be allocated are bounded by two general allocation types, generalisation and specialisation. We define generalisation as the multi-functionality of agents, i.e. the agents use all their skills. Specialisation is defined as a clear preference of the agents for a subset of the skills necessary to perform a task (see Figure 19a and 19b).


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Figure 19a (left) and 19b (right): Representation of generalisation and specialisation.

Each arrow represents the task allocation process of a single agent. Figure 19a depicts that every agent starts with the first action and ends with the last. Thus, all the agents perform all the actions. Figure 19b depicts that each agent performs the same actions in each cycle. Because of the different ways in which the agents can allocate the actions a task consists of, we use the concept of round to describe the specific order in which the task is performed. A round refers to the timestep in which the agent performs a specific part of the task. For instance, the order in which the group of specialists (Figure 19b) performs the task is: at round 1, agent 1 performs action a1, agent 2 performs action b1, agent 3 performs action c1. At round 2 agent 1 performs action a2, etc.

5.2.2 The multi agent system An agent is a simple model of a human being with properties that are necessary to perform tasks. The individual properties are represented as a set of skills. Each skill has two variable components: expertise and motivation, that are important components that determine group performance (Wilke and Meertens, 1994; see also Steiner, 1972). Skills are passive when they are not used and become active when they are needed for the performance of a task. In every round, each agent performs only one action. When activated, a threshold function determines whether the agents actually wants to perform a particular action. This function holds that only if both the expertise and the motivation are higher than their thresholds, the agent wants to perform the particular action. In this way every agent chooses a subset of actions he would like to perform. If the choices of all of the agents imply that there are more agents sharing the same preference as there are task-actions to perform, the agents negotiate. The negotiation process implies that the agents are trying to change the preferences of the other agents in such a way that the other agents will reach a complementary state with respect to their own (see also Zoethout, Jager, and Molleman, 2004). The influence of the agents is based on their expertise and motivation with respect to a particular skill, which implies that the agent with the highest expertise and/or motivation is more likely to get what he wants. The process ends as soon as the number of agents with a preference of a


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particular action is equal to the number of available actions. For instance, if we take a look at Figure 19b again, and we imagine that two out of three agents want to perform action a, in the first round, this will not be a problem. However, in the second round there is only one cycle of action a left, which means that they have to negotiate.

When the process of task allocation is being completed, the agents start performing the task. As a result of this, the expertise may change, i.e. the agents will increase the expertise of the skills they use and forget the skills they do not use. Furthermore, the motivation may change, i.e. the agents become bored after performing a particular action for a longer time and recover from it as soon as they stop. An important characteristic of most learning curves is that they reach a maximum asymptotically (Nembhart 2000). Therefore, we define learning by means of the relations among expertise (e) at a certain time (t), expertise in the future (t+1), the maximum expertise (emax), and a parameter (λ, [0,1]) that determines the learning speed:

maxmax

)1( eeeee t

tt−+=+ λ

(14a)

Forgetting is the inverse of learning, therefore:

µµ−

−=+

max

max)1(

)(e

eee tt

(14b)

where µ [0,1] determines the forget speed.

In real life an enormous range exists between learning and forget speed of different tasks. Motor tasks such as bicycling or swimming are, once learned, never forgotten, whereas others, such as playing chess or billiards, need to be maintained. Therefore, in the experiments, the balance between learning and forget speed is chosen on rather practical grounds instead of being based on empirical evidence. This holds that the agents are able to forget with a speed that is high enough to produce interesting dynamics, whereas a skill that has not been used for a time is not immediately forgotten.

Motivation curves can be described by applying the same characteristics: a maximum that is reached asymptotically, and recovery as the inverse of boredom. This means that formula (14b) describes the motivational decrease related to boredom and formula (14a) represents the motivational increase related to the recovery from boredom. In this case the parameters µ and ν respectively describe the recovery and the boredom speed.

The actual performance of the system is a function of expertise and motivation (Steiner, 1972; Wilke & Meertens, 1994). Both expertise and motivation are defined in terms of the time it takes to perform a task: the higher the degree of expertise or


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motivation, the sooner the task will be finished. Furthermore, we define a minimal time to complete an action, taction, which is equal to the actual time it takes to perform the action at a maximal rate of expertise and motivation. The actual performance time of a single agent, tperf., can therefore be expressed as:

∑=−+

=n

i ii

iactionperf

mm

ee

tt1

maxmax

.

)1(

_

λλ

(15)

λ represents a parameter that determines the balance between expertise and motivation. In our experiments we assumed that expertise and motivation have the same effect on the performance time. This means that in the experiments λ is set on 0.5. In the present study, the agents perform the actions simultaneously. This means that the time it takes to perform the total task, tperf., is determined by the slowest agent.

As a consequence of the expertise and motivational changes, the initial preferences of the agents are likely to change, which implies that they may wish to re-allocate their task. We call this task rotation. The way in which the agents allocate and re-allocate their task and the frequency in which the task allocation may be adjusted depends on the group the agents are a member of. Our study makes use of two kind of groups: specialists and generalists.

5.2.3 Specialisation and generalisation In both groups, the agents together have the abilities to perform the whole task. In both groups, the agents may only start with a new task when the former task has been finished. A group of specialists consists of agents that are all specialised in a particular part of the task. Although they do have the skills to perform the other actions as well, they have a clear preference to perform certain actions. Each agent has a different pattern of preferences. We could choose to let this group be a group of specialists in the strict sense, i.e. agents that specialise in only one skill. However, prior experiments have indicated that the performance would become very low because all the agents would become highly bored (Zoethout et al, 2006a). This would imply rather trivial results of our experiments. Therefore, we chose a setting in which the agents were free to self-organise task allocation whenever they want to, which opens the possibility of task rotation.

In the group of generalists, all the agents have skills with the same expertise and motivational values. Furthermore, the agents have to perform all the different actions that a task consists of instead of just one or two. This constraint implies that the group of generalists actually is not a self-organising group because they simply do not have the freedom to self-organise. However, as the results will show, the agents in the group of generalists do not have any incentive to change their allocation. Thus, although we constrained the agents to certain behaviour, they do not want it any either way.


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5.2.4 Model and hypotheses We study the expertise, the motivation and the performance of both groups in relation to the task dynamics. Figure 20 gives an overview of the model in relation to the experiments that we have conducted.

Figure 20: Model

The model is an input-process-output model. The input is a task. As we stated above, a task consists of a number of actions and a number of cycles. We studied different types of task dynamics by manipulating the number of tasks & cycles and the task variety. After the task has entered the system the process of task allocation starts. We manipulated the process of task allocation in such a way that we may speak of two groups, specialists and generalists. Both groups have different ways of allocating the task. The task allocation depends on two sets of variables, the task dynamics and the expertise and motivation of the agents. Expertise and motivation, being process variables, are mutually influenced by the process of performing the task, a process that also depends on the task allocation. The output of the system is the task that has been performed. The performance of the system, which is the dependent variable, indicates how well the group of agents has fulfilled the task.

Based on the classical principles of system theory formulated by Ashby (1956), we hypothesise a relation between task dynamics, specialisation/generalisation, and performance time as depicted in Figure 21:


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Figure 21: Overview of the hypotheses

The x-axis depicts two conditions of task dynamics, i.e. no task dynamics and high task dynamics. The y-axis depicts the performance time, i.e. the reverse of performance. Gen. and spec. respectively refer to the group of generalists and specialists. The hypotheses are depicted as roman numbers.

Hypothesis I: In a condition without task dynamics, the group of specialists will outperform the group of generalists

The rationale behind this hypothesis is based on the notion that specialisation leads to higher expertise, which implies better performance. Since the group of specialists is able to develop a certain level of task rotation, boredom will not have negative effects on performance.

Hypothesis II: In the condition of high task dynamics, the group of generalists will perform better than the group of specialists

Because the group of generalists is more flexible, they are able to adapt more quickly to task changes. As task changes occur more frequently, this flexibility will be more beneficial. Therefore:

Hypothesis III: The performance of the group of generalists will increase when task dynamics increase


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Since the group of generalists benefits from their flexibility and the group of specialists benefits from its expertise, we also state:

Hypothesis IV: The performance of the group of specialists will decrease when task dynamics increase

5.3 Experimental Design

5.3.1 Variables and design The experimental design is aimed at identifying the performance of groups of specialists versus generalists in varying conditions of task dynamics. We used 2 independent variables. The first independent variable is called task dynamics. This construct is split up into two components. The first component is called number of tasks and cycles. This component consists of 4 conditions in which the agents have to perform 200 cycles: in the first condition the agents have to perform 1 task of 200 cycles, in the second they have to perform 2 tasks of 100 cycles, in the third 4 tasks of 50 cycles, and in the fourth 8 tasks of 25 cycles. The second component is task variety, in which we used 4 conditions: no variety, low variety, which indicates a change of 1 action from one task to another. Moderate variety refers to a condition in which a new task requires 3 new skills, and high variety if a new tasks demands 5 new skills. Since all the tasks consist of 5 actions, high variety implies that every new task differs completely from the former one. Of course, these conditions, are not applicable to the condition in which the agents must only perform 1 task, because task variety is defined as a difference between multiple tasks.

The second independent variable concerns the group of agents. We used two kinds of groups, a group of specialists and a group of generalists. We measured two process variables, i.e. expertise and motivation and one dependent variables, i.e. performance time. Performance time refers to the time it takes to complete a task (see also Formula 15). We used the performance time of the slowest agent to indicate the performance time of the group. Since the agents perform together, the slowest agents indicates when the task is finished.

Table 6 summarises the independent variables into a research design:


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Table 6: Research design for the group of specialists and the group of generalists

Variety

Tasks - Cycles 0 (no) 1 (low) 3 (moderate) 5 (high)

1 - 200 Condition 1 - - -

2 - 100 - C2 C3 C4

4 - 50 - C5 C6 C7

8 - 25 - C8 C9 C10

The table shows all 10 conditions for both groups which means that there are 10 x 2 = 20 conditions. C2, C3, etc. refer to condition 2, condition 3, etc. By definition, the condition of 1 task of 200 cycle has no variety because variety is defined as a property of multiple tasks.

5.3.2 parameter values and initial settings of the agents In the experiments we used the following parameter values:

The system consists of 5 agents

A task consists of 5 actions

All of the tasks together take 200 cycles

The initial values of expertise and motivation are equal

The maxima of both motivation and expertise are set on 25

The motivation – and expertise thresholds are set on 10

The learning speed is 100

The forget speed is 3

The boredom rate is 100, the recovery rate is 100

After conducting numerous trials, we found out that these values mark the parameter space in which the processes occurred that we want to study (see also Zoethout et al., 2006a).

In the condition of generalists, all the skills of one single agent have the same initial value, but as Table 7a shows, the agents have different skill values:


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Table 7a: Initial values of the generalists

Skill Agent 1 Agent 2 Agent 3 Agent 4 Agent 5

1 14 15 16 17 18

2 14 15 16 17 18

3 14 15 16 17 18

4 14 15 16 17 18

5 14 15 16 17 18

Since the initial values of expertise and motivation are equal, the values in Table 7a represent both. In the condition of specialists, the values of the skills of the agents are all different whereas each agent has another best skill:

Table 7b: Initial values of the specialists


1 14 15 16 17 18

2 15 16 17 18 14

3 16 17 18 14 15

4 17 18 14 15 16

5 18 14 15 16 17

After the agents start working, the values presented in Table 7a and 7b change due to learning and boredom and, therefore, these values only apply to the first task. New skills, i.e. skill 6, 7, etc., that are required to perform next tasks, all start with the value of 14: this value offers the agents enough expertise to perform the task, but it is nonetheless relatively low because the agents just start to use it.

5.4 Results For every condition we analysed the performance time of both groups as well as the process variables expertise and motivation. But first we will discuss how the different conditions are related to the total performance time after the task. In this way we hope to find an answer to the question, what group performs the best under what conditions.

5.4.1 Total performance time Figure 22a and 22b depict the total performance time of both groups in all conditions:


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Figure 22a (left) and 22b (right): Total performance time of specialists and generalists in all conditions

1 T. 200 c. means 1 task of 200 cycles, etc. The performance time in the figures is the sum of the performance time of every cycle. We see that the performance time after performing 1 task of 200 cycles (bottom left line) is the same as the performance time in the condition of no task variety (bottom right line) for reasons we stated in section 5.3.1.

By looking at the condition of no variety (bottom lines), i.e. C1, we observe that the performance time of the specialists is much lower than the performance time of the generalists.

The reason for this comports with our intuition and common sense and is explained more elaborately in the next section about the underlying processes: When there is no task variety, driven by boredom, each specialist will alternately use his best two skills. In this condition, specialists will attain high levels of expertise for both these skills and, therefore, performance will be highest (i.e., performance time lowest). Generalists on the other hand will use all skills and reach a lower level of expertise, and, therefore, performance will be substantially lower (i.e. a higher performance time).

In the other conditions, the following holds for generalists and specialists: The higher the level of task dynamics, the more new skills are needed to complete new tasks that enter the system. When new tasks enter the system, generalists will start using all new skills that are needed for task completion. This will lower their average expertise and, therefore, their performance. The more new skill are needed to complete new tasks, the lower the average expertise level will become and, therefore, the lower the performance. Figure 22b shows that the relationship between variety and performance is more or less linear for generalists (see also Figure 22c). When a new task that requires novel skills enters the system, specialists prefer to continue using the two skills they already used. If one of these skills is not required anymore, they prefer to start using the skill for which they have the highest expertise. For none of the agents this will be the new skill. Therefore, they will postpone the use of the new skill until all


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the other actions are completed. At that moment all the agents start using the new skill. Their expertise is low and there are no opportunities for rotation anymore, which causes boredom to become high. As a result performance time increases. This increase in performance time is largest when we move from the condition without variety to a condition with low variety (see also Figure 22c).

Figure 22c: Performance time differences of both groups

Figure 22c compares the specialists and the generalists at the condition of 2 tasks of 100 cycles. As we already stated, the relationship between task variety and performance time is more or less linear for the generalists. The specialists however, show a maximum at moderate variety: as task variety increases, new tasks that require more novel skills enter the system more often and more old skills are not needed anymore. This has a negative effect on both the specialists and the generalists. However, this gives the specialists less leeway to postpone the use of new skills, and, moreover, when more new skills come in, more opportunities to rotate will remain. This has a positive effect on the motivation. Hence, for both groups, expertise decreases when task dynamics increase. For the group of specialists, motivation increases as task dynamics increase. This implies that no task dynamics cause the highest expertise and high task dynamics cause the highest motivation. Therefore, somewhere between both conditions, i.e. moderate task variety, the agents profit the least from both benefits, which explains the curvilinear relationship task variety and performance time of the specialists.

5.4.2 Acceptance of the hypotheses On the basis of these results, we will now accept or reject the hypotheses as formulated in section 5.2.4


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Hypothesis 1: In the condition of no task dynamics, the group of specialists will perform better than the group of generalists

According to the Figures 22 a and 22b, in the condition with no task dynamics the group of specialists clearly performs better than the group of generalists. Therefore, hypothesis I is supported.

Hypothesis II: In the condition of high task dynamics, the group of generalists will perform better than the group of specialists

Although the dynamics of the group of specialists is different from the group of specialists, we may conclude that the performance of specialists in case of variety is still somewhat better than that of the generalists. Besides, we noticed that specialists are more vulnerable to task variety, especially if we move from no to a low level of variety. These findings do not support hypothesis II.

Hypothesis III: The performance of the group of generalists will increase when task dynamics increase

and

Hypothesis IV: The performance of the group of specialists will decrease when task dynamics increase

In both groups the increase of task dynamics led to a worse performance. This supports hypothesis IV but not hypothesis III.

5.4.3 Underlying processes We already mentioned the differences in performance time of the specialists and generalists. To comprehend these differences in more detail, we now focus on the processes of task allocation in relation to performance time, expertise and motivation. We describe three conditions in detail that are typical for the description in the former section, i.e. condition 1, 3 and 10 (Table 6).

5.4.3.1 Condition 1: 1 task of 200 cycles, no variety With regards to the group of specialists, in all conditions the expertise development can be characterised by the following steps. First the agent starts with its best skill, whereas the expertise of the other skills decreases. Second, because boredom increases, the agents start rotating between their best – and second best skill. Both skills more or less


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reach their maximum with respect to expertise. In the condition of no task variety, these two steps describe the whole process.

The group of generalists develop all skills evenly. Because the agents develop more skills at the same time, i.e. 5 instead of 2, their expertise develops slower, which cause a lower final expertise value (and, therefore, a lower performance).

In the group of specialists, according to the boredom function, skills that are actually used lead to a motivational decrease. When the agent stops using a particular skill, according to the recovery function, motivation increases again. But although the motivation stabilises, in the beginning the motivation is higher (17 and 18) than at the end of the task (round 15).

In all conditions, the motivation of the group of generalists remains the same. Since they use all their skills instead of just one they do not develop any boredom. Therefore, they do not have any incentive to rotate actions.

The performance time of the group of specialists during the process of task allocation and performance starts with an increase caused by the motivational decrease. Second, a slight decrease occurs, that is caused by task rotation, and increase of expertise: Task rotation causes the motivation not to decrease further, but to stabilise instead, whereas the increase of expertise causes the performance time to finally reach a minimum of about 12.5 (see Figure 23a):

Figure 23a: Performance time of all agents in the group of specialists in condition 1

As a result of their initial values, the performance time of all agents is identical. Therefore, the Figure only depicts one curve. The maximum at the 16th round represents the point from which the agents start rotating the task.

Since the group of generalists does not develop boredom, their performance time only decreases from the start as a result of the increase of expertise(see Figure 23b):


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Figure 23b: Performance time of all agents in the group of generalists in condition 1

However, the performance time of the generalists decreases slower than the performance time of the specialists. This is the most important reason why the lowest value of the performance time of the generalists is higher than that of the specialists. For the sake of completeness, we mention one other reason: The performance time of both groups is determined by the worst agent. In the group of specialists, all agents perform equally whereas all agents only use their best two skills. In the group of generalists however, as Figure 23b depicts, all agents perform differently whereas all agents use all their skills. This implies that the performance of the specialists is determined by their best skills, whereas the performance of the generalists is determined by their worst skills. Thus, although Figure 23b may suggest that performance time may decrease further, it will never be lower than the performance time of the group of specialists.

Therefore, in this condition, the combination of expertise increase and motivational stability causes the group of specialists to be the best performing group. This clearly supports hypothesis I that states that in a condition without task dynamics, specialists perform better than generalists.

5.4.3.2 Condition 3: moderate variety, 2 tasks of 100 cycles In the group of specialists, during the first task, i.e. the first 100 rounds, the process of expertise development is identical to condition 1: First the agent starts with its best skill, whereas the expertise of the other skills decreases. Second, because boredom increases, the agent starts rotating between its best – and its second best skill. Third, the second task starts, that requires 3 new skills. Depending on the specialisation of the agent, this may lead to three different situations: First, when the new task does not forces the agent to use any new skills, he simply proceeds rotating between the same ‘old’ skills. Second, when the new task forces the agent only to use new skills, he starts using them in a way similar to the first task: first he uses his best skill and when boredom reaches a certain level, he rotates between his best and second best skill. Third, when the new task permits the agents to use only one of his ‘old’ skills, the agent proceeds in using only this skill until boredom forces him to rotate to his second best skill. Figure 24a depicts the expertise development of agent 5 that resembles the third situation:


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Figure 24a: Expertise of agent 5 of the group of specialists in condition 3

The x-axis shows the number of rounds. The y-axis shows the expertise values. When the second task enters the system at the 101st round, agent 5 does not use skill 1 anymore, because the part of the task that requires this skill is completed. Until the 116th round, he only uses skill 5 (originally his second best skill). Then he starts with his skill that is second best at that time. The fourth and last phase starts when either one of the actions the agent is working on has been completed. In this phase each agent consecutively picks up the remaining actions that correspond to their next best skills and finally they finish with their worst skill.

The expertise development of the group of generalists is much simpler (see Figure 24b): the first task shows an identical process as in the former condition. When the second task enters the system the ‘old’ skills of each agent develop further, identical to condition 1. The three ‘new’ skills (6,7, and 8) start at a lower value but then develop in the same way as the old skills do (see Figure 24b):

Figure 24b: Expertise of agent 5 in the group of generalists in condition 3

During the first task, the way in which the motivation of the group of specialists develops, is the same as in the former condition (condition 1). From the start of the second task, motivation decreases when agents only use one skill for a certain period (see Figure 24c):


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Figure 24c: Motivation of agent 5 in the group of specialists in condition 3

Figure 24c depicts the motivational development of agent 5. Skills that are not used are represented as a flat line because the motivation of these skills are not influenced. The first motivational decrease occurs right after the second task enters the system when the agent uses only one ‘old’ skill. This decrease continuous until the 116th round. From that point on , task rotation stabilises the motivation. From the 180th round, the agents work on their last action and do not have any possibilities left to rotate, which results in a dramatic motivational decrease of all agents.

This just mentioned motivational decrease has a strong effect on the performance time of the specialists resulting in an increase from the 180th round (see Figure 24d):

Figure 24d: Performance time of all agents in the group of specialists in condition 3

From the 101st round, performance time increases because some agents start using new skills, for which they have a lower expertise. These new skills cause the same performance time development as in the first task: at the beginning, boredom causes the agents to perform worse, until they start rotating their actions. This effect is repeated at the 140th round, when the agents start with a new action. From the 180th round, the agents only work on one action, with no opportunities for task rotation. This causes boredom and related to this, an increase of performance time.

In the group of generalists, the ‘new’ skills, that are related to the actions of the second task, cause local maxima for every 5 rounds in which the agents perform one cycle of


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the task: every agent uses 2 ‘old’ skills that cause low performance time, and 3 ‘new’ skills that cause high performance time (see Figure 24e):

Figure 24e: Performance time of all agents in the group of generalists in condition 3

In Figure 24e we see that the expertise of the ‘new’ skills increases in the same way as the expertise of the ‘old’ skills.

Therefore, although the expertise of the specialists reaches a high level at an earlier stage than the expertise of the generalists, the motivational decrease of the specialists compensates for this. As a result, in these conditions the performance of both groups is about the same (see also Figure 22c). For the specialists, higher levels of task dynamics result in a lower motivational decrease, whereas lover levels of task dynamics result in a higher expertise development.

5.4.3.3 Condition 10 high variety, 8 tasks of 25 cycles This condition represents the highest level of task dynamics in which the agents perform tasks that are all different. During the first task the agents demonstrate the same behaviour as in the other conditions. From the second task on however, all skills are new. Since we defined new skills as skills with low expertise and motivation, this results in groups of agents, both specialists and generalists, with identical skills. This implies that the specialists are not really specialists anymore. Nevertheless, since the specialists are free to allocate the task whereas the generalists are forced to use all their skills consecutively, both groups behave differently.

From the second task on the expertise development of the group of specialists during the execution of one task can be described in three phases: First, all agents have identical motivation and expertise for all their skills and, therefore, simply start with their first skill. At that moment the increase of expertise is just a bit smaller than the decrease in motivation, and, consequently, they immediately start task rotation after action 1. Second, as soon as action 1 and 2 have been finished, the agents start performing action 3 and 4 in the same way. Third, the agents perform action 5. This process is repeated for every task. Because the expertise of the skills decreases when the time in which the agents used them increases, every next task starts with lower expertise.


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As regards the group of generalists, every task shows an increase of expertise, whereas every next task start somewhat lower than the former. Although this also holds for the specialists, the generalists perform all actions consecutively.

From the second task on the motivation of the group of specialists is stable, which is caused by task rotation. It ends in a decrease because during the performance of the last action there is no possibility to rotate anymore. Every next task develops in the same way. This process is comparable to the motivational process of condition 3 that also alternates motivational stability and decrease. The most important difference is that a task of 25 cycles does not offer that much time for boredom, which limits the motivational decrease. Therefore, the performance time of the specialists is mainly determined by the slow decrease of expertise (see Figure 25a):

Figure 25a: Performance time of all agents in the group of specialists in condition 10

As a result of their initial values, the performance time of all agents is identical. Therefore, the Figure only depicts one curve. We see that in the beginning the performance curve clearly depicts the starting points of every new task. From the 100th round however, this diminishes. This is caused by a slight change of task allocation: because of the learning function (see Formulas 14a and 14b), agents with identical expertise values allocate their tasks differently when their expertise and motivation changes, because the change of expertise and motivation is a function of the ‘old’ expertise and motivation. For instance, when a skill with a value of 15 is used, it changes in a different way then a skill with a value of 20, which may lead to a different task allocation.

The performance time of the group of generalists follows the expertise development: every task shows a slight decrease, whereas every next task starts with a performance time that is a bit higher. This is caused by the decrease of expertise during the time in which the agents did not use the skills related to the new actions (see Figure 25b):


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Figure 25b: Performance time of all agents in the group of generalists in condition 10

Although the process of task allocation is different, the performance of both groups is about the same. In both groups, the high level of task dynamics limits the possibility of boredom, but decreases the development of expertise dramatically. Therefore, these conditions cause the worst performance for both groups. This conclusion supports hypothesis IV that states that the performance of the specialists decreases when task dynamics increase, but it rejects hypothesis III that states the opposite for the generalists. In sum, in case of extremely high levels of task variety specialists have no time specialise and generalists have no time to become generalists, and, therefore, their processes and performance become quite similar.

5.5 Conclusion and Discussion Although the total performance time, as depicted in Figures 22a and 22b, clearly indicates the differences between both groups, the underlying processes can explain how these results relate to the hypotheses. In general we found two opposite effects: The first effect concerns the expertise development that decreases in both groups when task dynamics increase. This effect is the main cause of the mountain-like shape of Figures 22a and 22b, with the highest task dynamics being on top. The second effect concerns the increase of motivation when task dynamics increase. This effect only holds for the group of specialists because the motivation of the generalists remains unaffected. This effect does not apply to the condition of no task dynamics.

As our description of condition 3 states, a combination of both effects leads to the curvilinear relationship between both groups as described in Figure 22c.

These results only support our hypotheses concerning the performance of the specialists: According to our study, in a condition with no task variety specialists perform better than generalists. Further, the performance of specialists decreases when task dynamics increase. As we stated, the main reason behind this is the decrease of expertise development that does not allow the specialists to maximise their performance. This reason comports with the rationale behind the hypotheses, which is based on the principles as formulated by Ashby (1956). This principle implies that specialists will benefit from their high expertise in situations with no task dynamics.


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Generalists on the other hand should outperform specialists in conditions with higher task dynamics because they are more flexible than specialists and, therefore are better able to adapt to changing situations. In a way the flexibility of generalists compensates for the profit of high expertise that they lack in conditions with low task dynamics. Hence both specialists and generalists have their own specific benefits. Thus, we hypothesised that specialists should be better with no variety and generalists with high variety.

But why do our results not comport with the second half of this principle? Why does the performance of the generalists differ from what we hypothesised? The results show that with high task dynamics the generalists are as much the victim of the decrease of expertise development as the specialists. But the generalists do not compensate this decrease with their benefit, their flexibility, at all. On the contrary, their flexibility it is more or less shared by the specialists: in conditions of higher task dynamics, the specialists appear to behave more like generalists! This is partly caused by our assumption that new skills start with low expertise. During the first stage of our experiments the generalists and the specialists differ in two ways. The way expertise and motivation is distributed among the agents differs (see Table 7a and 7b) and the way they allocate tasks differs. The more new tasks differ from previous ones, the more the starting situation for both groups in terms of expertise and motivation become similar, due to our assumption of low expertise for new skills for both groups. Besides, a higher level of task dynamics implies the need for more new skills. Therefore task dynamics decrease opportunities to specialise, and, therefore, the performance of specialists become more or less similar to the performance of generalist in case of very high levels of task variety. But another cause for the decrease of specialisation can be found in the effect, that agents in the specialist group tend to start with their best skill, then their second best, etc. and finish with their worst skill. This effect shows up in all conditions with task dynamics. This implies that the specialists do not restrict themselves to their own speciality, but finally help each other to finish the team task. Actually, in our experiments the specialists were not true specialists because they were able to use all the skills, although their expertise was higher for some than for others. Moreover, due to boredom, they tend to specialise in two skills, and, therefore, probably can be better typified as ‘minimal generalists’ than true specialists. Previous studies have shown that a low level of multifunctionality mostly outperforms a high level of multifunctionality as well as a situation with no multifunctionality at all (i.e., when there are only ‘true specialists’; Molleman & Slomp, 1999; Van den Beukel, 2003). Both reasons indicate that high task dynamics cause a group of specialists to self-organise into a group of generalists. Hence, this study does not confirm a classic relationship between performance and task dynamics with respect to generalisation and specialisation. Nevertheless, the results support the underlying proposition that a situation with high task dynamics asks for generalists and a situation with low and no task dynamics needs specialists.

An important difference between the specialists and the generalists in this study is the freedom to self-organise. The specialists are free to re-allocate the task whenever they feel the need to do so, which may result in a shift for specialisation to generalisation. The generalists on the other hand, do not have any freedom to self-organise, since they


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must simply perform all actions consecutively. Although this implies that the specialists are able to stabilise their motivation by task rotation, the generalists do not have to stabilise anything because they are already satisfied with their situation. This brings up one of the fundamental question of management science: should an organisation or team be forced to fit into a design or should we give it enough freedom to self-organise? Of course we cannot give a definite answer to this. Given the freedom to self-organise, no matter what the original team structure is, the team will manage to reshape itself according to the demands of its environment. But then again, as the group of generalists demonstrated, sometimes the absence of freedom leads to a well-ordered structure in which motivated workers perform quite well. In fact, our study indicates that the difference between design and self-organisation does not lead to spectacular performance differences, except for the condition of no variety. This suggests that we might put the importance of team design into perspective. All in all, we may conclude that it is difficult to catch group dynamical processes in a simple system theoretical description. However, the use of multi-agent simulation based on psychological theory may certainly help to understand how basic individual characteristics are related to complex group dynamics.

Further, we may ask ourselves whether or not our conclusions have real empirical value? First of all, we did not limit our experiments by using agents with cognitive properties only, but used a model in which we combined a simplified cognitive architecture with variable motivational states. Because of this, the specialists behaved differently from more traditional agent models: The agents developed task rotation and tasks that were highly repetitive cause a larger motivational decrease than tasks that were less repetitive. This effect appears in real life as well. The specialists were able to reduce their motivation loss by performing two actions instead of one and the generalists showed no motivation loss at all. In a way, this comports with the findings that workers performing a task as a whole feel more motivated (e.g. Hackman & Oldham, 1980).

The empirical value of the parameter values, i.e. learn, forget, boredom, and recovery speed, as well as the relation between motivation and expertise, we have used, can be questioned. We simply selected a parameter space that produced behaviour that we could study: For instance, a higher forget speed would result in a group of agents that is not able to perform anymore. In future research we could vary the boredom and recovery rate. But empirical studies that indicate such parameter values are yet to be done. This study may serve as a start to formalise group dynamical processes concerning expertise, motivational and performance development and relate its parameter values to specific types of tasks.

But the strongest contribution of our research concerns the question it evokes regarding group dynamical processes in work teams: how can differences between specialists and generalists be explained in terms of processes of task allocation? What processes should be altered to increase their performance? How is the motivation of workers related to traditional approaches concerning specialisation and generalisation? Although this study does not answer all these questions fully, it may elucidate our view and changes our perspective on traditional problems.

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Chapter 6 Newcomers in Self-Organising Task Groups10 Abstract This chapter describes the consequences of turnover, especially how a work group and a newcomer mutually adapt. We studied two types of groups that need an extra worker, either because of its workload, or because a former employee had left the group. For both groups, we tested conditions with newcomers being specialists, newcomers being generalists, and a control condition with no newcomer. We hypothesised that the group that needed an extra worker because of its workload would perform the best with a newcomer being a generalist. The group that needed an extra worker because a former employee had left the group, would perform better with a specialist newcomer. We studied the development of task allocation and performance, with expertise and motivation as process variables. The results only partly supported our hypotheses since both the specialists and the generalists only contributed to a better performance in the group that was left by the former employee.

6.1 Introduction Suppose you are an employee working in a project team. Everybody is busy writing texts, printing, copying, putting covers on large piles of paper, and sell this to customers. Everyone knows what to do and everything works out fine like a well oiled machine, but an increasing workload causes everybody to work overtime in order to meet the deadline. Therefore, your team decides that you need an extra employee. And so happens. The new colleague is nice, works hard and tries to help wherever he or she can. But after a while it seems that you have made a mistake. Although the newcomer helps you fixing the team tasks, sometimes team members now have to do tasks they do not like or are less qualified for. In fact, since the entry of the newcomer the whole team seems to be imbalanced and performs worse.

This is an example of a newcomer influencing team performance negatively. The impact of a newcomer may partly be dependent on the type of the team task. Sometimes team performance is primarily determined by the best worker, such as in the case of specific mental tasks, or the worst worker, such as in an assembly line (e.g.

10 Submitted to Computational and Mathematical Organization Theory as Zoethout, K., Jager., W, & Molleman, E., Newcomers in Self-Organising Task Groups: When Does a Newcomer Really Contributes To a Better Performance?


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Steiner 1972). But even when the interdependence among team members is rather low and workers perform an additive task (the subtasks are independent), where all team members contribute to the total, group performance may decrease when a newcomer joins the group. He may disturb the task allocation structure which may result in a situation that the old team members have to perform tasks they like and/or master less. Furthermore, when a newcomer is less experienced, he might perform tasks that some other team members could perform much better. Moreover, if more workers perform the same task this implies that there will be less chance for those workers to improve their skills concerning this task.

When does a newcomer in a workgroup contribute to a better performance? How is group performance related to the process of task allocation when a newcomer enters the group? Such questions pertain to the impact of turnover. Turnover refers to team members entering or leaving a workgroup or organisation, which often is associated with changes of performance and expertise (e.g.Levine, Moreland, Argote, & Carley 2005). These changes may have positive effects on performance, for instance when newcomers are highly skilled but also may be negative, if it disturbs a team’s steady state (Levine et al. 2005). Moreover, the recruitment, selection, training and socialisation in general of newcomers may be costly to firms (Glebbeek & Bax 2004). On the other hand, prevention of turnover may also be expensive (Glebbeek & Bax 2004).

Literature mostly focuses on turnover being a dependent variable, whereas studies about the effects of turnover have been less emphasised (Glebbeek & Bax, 2004; Dineen & Noe 2003). Further, most of these studies only looked at outcome variables such as performance or transactive memory system (e.g.Levine et al. 2005), while neglecting the effects on group dynamical processes (Dineen & Noe, 2003). Others have studied process variables with membership change being an independent variable, but these studies either focus on conflict (O’Connor, Gruenfeld & McGrath 1993) or learning (Carley 1992), but do not involve task allocation processes (e.g. Marks, Mathieu, and Zaccaro 2001). Studies that have included team processes as an outcome of turnover mostly focus on general mechanisms regarding membership change (Dineen & Noe, 2003; Marks et al. 2001) or team processes in general (Arrow & McGrath, 1995) but focus less on the underlying processes such as social interactions. Moreover, although literature about person-job fit focuses on individual and organisational characteristics (e.g. Edwards 1991; Kristof 1996), it does not concern task allocation processes related to the mutual adaptation of newcomers and teams.

Thus, whereas the effects of separate variables – or limited combinations - have been empirically investigated, it is difficult to derive empirically based conclusions on how the combination of these variables affects the performance and its underlying processes of task allocation when a newcomer enters the team. Social simulation offers a methodology to systematically explore a large number of conditions, and thus may contribute to deriving such conclusions (e.g. Gilbert and Troitzsch 1999). In this chapter, by conducting experiments in which we vary characteristics of newcomers and tasks, we explore how newcomers affect the performance of a team and how a team and a newcomer mutually adapt. We study the effects of two types of newcomers, generalists and specialists, on two types of self-organising task groups. The first task

Chapter 6: Newcomers in Self-Organising Task Groups

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group represents a project team in which the whole project was allocated to all members. This team needs an extra member because of its high workload. We hypothesise that this group will perform better with a generalist newcomer. The second task group represents a project team that recently lost one of its members. This team needs an extra member to fill in the gap that was created by the loss of his predecessor. We hypothesise that this group will perform better with a specialist newcomer.

In the first section of the chapter we focus on the theories and models we use and their formalisation, which form the basis of WORKMATE, the simulation program that we developed to study self-organising processes of task allocation (Zoethout, Jager, and Molleman 2006a; 2006b). WORKMATE is used to test hypotheses concerning the relation between different types of newcomers, task allocation processes, and performance. The second section describes the experimental design and the parameter settings. Next we will describe the results and we end up with conclusions and a discussion.

6.2 The Model WORKMATE III is a deterministic discrete event based simulation program developed in DELPHI6 for simulating self-organising processes of task allocation. It is an elaborated version of the simulation program that we used for experiments on the emergence of job rotation (Zoethout et al. 2006a), and the relation between task variety and coordination time (Zoethout et al. 2006b). In this section we shortly describe the theoretical framework WORKMATE III is based on.

6.2.1 The multi agent system An agent is a simple model of a human being with properties that are necessary to perform tasks. A task is considered as a set of actions in such a way that each action is related to a single skill (Hunt 1976; Weick 1979; Tschan & von Cranach 1996). During every timestep, i.e. round, each agent performs one action. The individual properties of the agents are represented as a set of skills. Each skill has two variable components: expertise and motivation, that are important components determining group performance (Wilke & Meertens 1994; see also Steiner, 1972). Skills are passive when they are not used and become active when they are needed for the performance of a task. When activated, a threshold function determines whether the agent actually wants to perform a particular action. This function implies that only if both expertise and motivation are higher than their thresholds, the agent wants to perform the particular action. In this way every agent chooses a subset of actions he would like to perform. If the choices of all agents imply that there are more agents sharing the same preference than there are actions to perform, the agents start negotiating. The negotiation process implies that the agents are trying to change the preferences of the other agents in such a way that the other agents will reach a complementary state with respect to their own (see also Zoethout et al. 2006b). The influence of the agents is based on their expertise and motivation of the particular skill, which implies that the agent with the highest expertise and/or motivation is more likely to get what he wants. The process ends as


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soon as the number of agents with a preference for a particular action is equal to the number of available actions. For instance, if we take a look at Figure 26, and we imagine that two out of three agents want to perform action a, in the first round, this will not be a problem. However, in the second round there is only one cycle of action a left, which means that they have to negotiate.

Figure 26: Actions and cycles

6.2.2 Task and task performance Each action has to be performed a number of times, i.e. cycles, before it is finished. In this way, a task can be represented as a matrix of actions (what) and cycles (how often). In Figure 26 we see a task consisting of 3 actions, a, b, c and 3 cycles, i.e., 1, 2 and 3. Thus, the 3 actions need to be performed 3 times before the task is finished. The agents may perform the task in a number of ways, for instance cycle by cycle, action by action, or something in between. Two general allocation types, generalisation and specialisation bound the possible ways a task can be allocated. We use the concept of round to describe the specific order in which a task is performed. For instance, a group of specialists performs the task as depicted in Figure 26 in the following order; round 1: agent 1 performs action a1, agent 2 performs action b1, agent 3 performs action c1. At round 2, agent 1 performs action a2, etc. The number of agents that a group consists of determines the number of rounds it takes to finish the task. For instance, to finish the task as depicted in Figure 26, it takes 3 rounds for 3 agents, 5 rounds for 2 agents, and 9 rounds for 1 agent. Hence, it takes fewer rounds to perform a task when more agents are involved. This means that the concept of rounds indicates performance differences regarding experiments with groups with a variable number of agents. However, results that are based on this notion will be quite trivial. Instead we use a performance indicator that is corrected for the fact that more agents working on the same task imply fewer rounds to finish it. This performance indicator is based on a function of expertise and motivation being important components that determine group performance (see also Steiner 1972; Wilke & Meertens, 1994). Expertise and motivation may change as a result of task allocation and task performance. This implies that agents will increase the expertise of the skills they use and forget the skills they do not use. Furthermore, the motivation may change, i.e. the agents become bored after performing a particular action for a longer time and recover from it as soon as they stop (see also Zoethout et al, 2006a; 2006b).

Both expertise and motivation are defined in terms of the time it takes to perform a task: the higher the expertise or motivation, the sooner the task will be finished.


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Furthermore, we define a minimal time to complete an action, taction, which is equal to the actual time it takes to perform the action at a maximal rate of expertise and motivation. The actual performance time of a single agent, tper_agent can therefore be expressed as:

∑=−+

=n

i ii

iactionperf

mm

ee

tt1

maxmax

.

)1(

_

λλ

(16a)

λ represents a parameter that determines the balance between expertise and motivation. n represents the number of actions that a task consists of. In our experiments we assume that expertise and motivation have the same effect on the performance time. This means that in the experiments λ is set on 0.5.

Since the actions of a task consists of multiple cycles, the total contribution of a single agent to the whole task can be expressed as:

∑ ∑= =−+

=k

j

n

i ijij

ijcellagenttotperf

mm

ee

tt1 1

maxmax

___

)1( λλ

(16b)

k represents the number of cycles that a task consists of. tcell_ij represents the specific cell of the task matrix as represented in Figure 26. eij and mij represent the expertise and motivation at the moment the action of a particular cell is being performed.

In the present study, the agents perform the actions simultaneously. The task is being finished when all cycles of all actions have been completed. This means that the performance time of the group can be measured by taking the sum of the performance time of the individual agents:

∑ ==

s

iiagenttotperfperf tT

1___.

(16c)

s represents the number of agents that work on the particular task. Note that Tperf. only indicates the total performance time based on the performance time of every agent per single cell, the number of cycles, and the number of actions. It does not concern the number of rounds that it takes to finish a task.


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Thus, we propose a performance indicator that is corrected for the obvious benefit that more workers need fewer rounds to complete the task. Because of this, we are able to indicate the relative contribution of a newcomer. For instance, 2 groups of agents must perform the task as described in Figure 26. The first group consists of 3 agents, each having a total performance time of 100. This results in a group performance time of 300, whereas it takes 3 rounds to finish the task. The second group consists of 9 agents, each having a performance time of 40. This results in a group performance time of 360, whereas it takes only 1 round to finish the task. This implies that although it takes fewer rounds for the second group to finish the task, their performance is still worse because the first group performs its rounds a lot quicker than the second.

6.2.3 Model and hypotheses We study performance and task allocation in relation to the task and the newcomer. Figure 27 gives an overview of the model in relation to the experiments that we conduct:

Figure 27: The model

The model can be described as a classic IPO (input-process-output) model as well as an IMOI (Input-Mediator-Output-Input) model (Ilgen, Hollenbeck, Johnson, and Jundt


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2005). Being an IPO model, the Input is a task, consisting of a number of actions and a number of cycles. The Process is the combined process of task allocation, performing, and the changes in expertise and motivation of the agents within the system. The Output is the task that has been completed with a certain performance, which is the dependent variable. As an IMOI model, the Input is the task. Then, the task allocation (M) takes place on the basis of the expertise and motivation of the individual agents. Task allocation therefore depends on three sets of variables, the values of the task (number of actions and number of cycles), the values of the newcomer (expertise and motivation, specialist or generalist) and the values of the agents (expertise and motivation). On the basis of that, the agents start performing (O), which affects their expertise and motivation (I), etc. However, in our opinion, the discussion between IPO and IMOI is just a matter of choosing the system boundaries.

We studied two groups of 5 agents, a group performing a task consisting of 5 actions and a group performing a task consisting of 6 actions. The first group represents the project team that needs an extra co-worker because of its workload. 5 agents that perform a task of 5 actions will result in a symmetric task allocation in which the whole task is allocated evenly to all agents. The second group represents a project team that needs extra help because one of its members left the team. 5 agents performing a task of 6 actions will result in a asymmetric task allocation, with a ‘gap’ in which an additional worker may fit. We studied the effects of two types of newcomers, generalists and specialists. On the basis of these manipulations, we formulated the following hypotheses:

Hypothesis I: In a project team that needs an extra worker because of its workload, group performance will improve more when the newcomer is a generalist than if he is a specialist.

The rationale behind this hypothesis is based on the notion that a generalist is better able to perform all different ‘loose ends’ that the workers leave when they reach the end of the task. A specialist would only contribute when the group needs some specific skills. Therefore:

Hypothesis II: In a project team that needs an extra worker because one of its members left the team, group performance will improve more when the newcomer is a specialist on the part that the former member left than if he is a generalist.


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6.3 Experimental Design

6.3.1 Variables and design The experiment simulates a group of 5 agents who are all specialised in a particular part of the task. Although they do have the skills to perform the other actions as well, they have a clear preference to perform certain actions. Each agent has a different pattern of preferences. All agents are free to self-organise the task allocation whenever they want to, which opens the possibility of task rotation. Task rotation refers to the change of the preferences of the agents as a consequence of their expertise and motivational changes, which implies that they may wish to re-allocate their task.

We studied two groups, a group performing a task of 5 actions and 200 cycles and a group performing a task of 6 actions and 200 cycles. In the first group the agents easily develop a symmetric rotation mechanism. This mechanism holds that each agent rotates between his best and his second best skill. For instance, agent 1 rotates between action 5 and 4, agent 2 between 4 and 3, etc. With this rotation mechanism, it is hard for new members to easily fit in the existing task allocation process. Therefore, we labelled this condition as no fit. In the second group, because of the extra action, the agents allocate the task in an asymmetric way. Every agent still rotates between his best and his second best skill, but now 5 agents must allocate 6 actions, which leaves some kind of ‘gap’. This gap is likely to facilitate the adaptation of a new member. Therefore, this condition is labelled as fit.

Then the newcomer comes in. In both groups the newcomer starts at the 101st round. This offers the group enough time to have set the rotation mechanism and specialise further, i.e. to set a steady state that resembles a group of workers existing for a longer period of time.

We tested five conditions: Two conditions in which the newcomer is a specialist, with either low or high expertise and motivation, two conditions in which the newcomer is a generalist, with either low or high expertise and motivation, and one control condition with no newcomer at all. A specialist is defined as an agent with skills having all different values, which results in a preference for the best skills. A generalist is defined as an agent with all skills having the same value for motivation and expertise, whereas the agent must use them consecutively. Table 8 summarises the research design:


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Table 8: Design

Newcomer\Task 5 actions (no fit) 6 actions (fit)

specialist low C1 C2

specialist high C3 C4

generalist low C5 C6

generalist high C7 C8

no newcomer C9 C10

C1,…C10 refer to condition 1, …condition 10, also in the rest of the text. We choose two conditions for both the specialist and the generalist because these may indicate a range in which a newcomer actually leads to a better performance. We study the effects of these conditions on task allocation being a process variable, and performance being a dependent variable.

6.3.2 Agent values and parameter settings The following parameter settings are equal for all experiments:

The system consists of 5 agents in the control condition + 1 newcomer in the other conditions

In the no fit condition, a task consists of 5 actions

In the fit condition, a task consists of 6 actions

The task consists of 200 cycles

The initial values of expertise and motivation are equal

The maxima of both motivation and expertise are set on 25

The motivation – and expertise thresholds are set on 9

The learning speed is 100

the forget speed is 3

The boredom rate is 100, the recovery rate is 100

The parameter values are not chosen on the basis of empirical criteria, since empirical studies that indicate such parameter values are yet to be done. Instead, we simply selected a parameter space that produced behaviour that we are interested in.

The newcomer comes in after 100 rounds. In the condition of no fit, the initial values of the agents are chosen as follows (see Table 9a):


100

Table 9a: First condition: 1 task of 5 actions (no fit)


1 18 14 15 16 17

2 14 15 16 17 18

3 15 16 17 18 14

4 16 17 18 14 15

5 17 18 14 15 16

The values (expertise and motivation) of the agents are symmetric. This implies that the performance of every agent will be about the same, whereas the agents are being specialised in different skills. Since the number of agents matches the number of actions the task consists of, they are more likely to develop a stable rotation mechanism. The initial values of the newcomers are chosen as follows: (see Table 9b):

Table 9b: Values of the newcomers in the first condition

Skill Agent 6 (spec. low.) Agent 6 ( spec. high) Agent 6 (gen. low.) Agent 6 (gen. high)

1 14 18 16 20

2 15 19 16 20

3 16 20 16 20

4 17 21 16 20

5 18 22 16 20

Spec. low refers to the new agent being a specialist with low values, spec. high refers to the new agent being a specialist with high values, gen. low refers to the new agent being a generalist with low values, gen. high refers to the new agent being a generalist with high values. The specialist newcomer with low values has the same initial values as agent 2. All skill values of the generalist newcomer are the same.

The values of the agents in the condition of fit are described in Table 9c:


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Table 9c: Second condition: 1 task of 6 actions (fit)


1 18.5 13.5 14.5 15.5 16.5

2 13.5 14.5 15.5 16.5 17.5

3 14.5 15.5 16.5 17.5 18.5

4 15.5 16.5 17.5 18.5 13.5

5 16.5 17.5 18.5 13.5 14.5

6 17.5 18.5 13.5 14.5 15.5

Comparing the tables 2a and 2c, we see that the initial values of the agents in the second condition differ from the first condition. The highest value of the second condition is 18.5 instead of 18 in the first condition. This is related to the number of actions the task consists of. Because of this, the values of the newcomers also differ (see Table 9d):

Table 9d: Values of the newcomers in the second condition

Skill Agent 6 (spec. low.) Agent 6 ( spec. high) Agent 6 (gen. low.) Agent 6 (gen. high)

1 17.5 21.5 16 20

2 18.5 22.5 16 20

3 13.5 17.5 16 20

4 14.5 18.5 16 20

5 15.5 19.5 16 20

6 16.5 20.5 16 20

In both the no fit and the fit condition, the mean of the expertise and motivation of the agents in the group is 16. The mean of the newcomer with low values is 16. The newcomer with high values has a mean of 20.

6.4 Results For every condition we analysed the performance time as well as the task allocation process of both groups. But first we will discuss how the different conditions are related to the total performance time after the task has been finished. In this way we hope to find an answer to the question, which group performs the best under which condition.


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6.4.1 Total performance time In the no fit condition, without a newcomer it took 200 rounds to complete the task. With a newcomer entering the group, at the 101st cycle, in all four conditions, it only took 184 rounds, i.e. 100 rounds without the newcomer and 84 rounds (which is about 5/6 * 100) with the newcomer. In the fit condition, without a newcomer it took 240 rounds to complete the task (which is 6/5 * 200). With a newcomer entering at the 101st cycle, in all four conditions, it only took 217 rounds, i.e. 100 rounds without the newcomer and 117 rounds (which is about 5/6 * 140) with the newcomer. Obviously, with a newcomer it takes fewer rounds to finish a task and it takes more rounds to perform the task of 6 actions in the fit condition, than the task of 5 actions in the no fit condition.

The total performance time for all conditions is depicted in Figure 28a and 28b.

Figure 28a (left) and 28b (right): Total performance time of the groups in all conditions with specialists and generalists as newcomers

Low refers to a newcomer with low expertise and motivation and high refers to a newcomer with high expertise and motivation. The performance time in the figures is the sum of the performance time of all agents of all cycles, as indicated by formula (1c). In order to compare the data of the no fit (5 actions) and the fit condition (6 actions), we multiplied the total performance time of the fit condition with 5/6.

By comparing both figures, we observe four distinct effects. First, the performance time with no newcomer is better (i.e., lower) in the no fit condition (13055) than in the fit condition (13458,3). Second, in the no fit condition, all newcomers, both specialists and generalists, contribute negatively to the total performance time. Even a highly skilled newcomer only gets in the way, since the performance time without him is lower. In the fit condition on the other hand, all newcomers contribute positively to the total performance time. Third, the performance time of the group with the generalist newcomer is the best in the no fit condition. The group with the specialist newcomer performs the best in the fit condition. However, these differences are rather small. Fourth, and rather obviously, irrespective of being a specialist or a generalist, a newcomer with high expertise and motivation outperforms a newcomer with low


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expertise and motivation. Moreover, these effects are the same for both the no fit condition and the fit condition.

To better understand these findings, we must take a closer look at the underlying processes. In the next section we will therefore discuss some conditions in more detail, by giving an elaborate description of the development of the task allocation process and the performance time.

6.4.2 Underlying processes In case there is no newcomer, the task allocation process in the no fit condition (C9) is quite simple: First, the agents start with their best skills. Then boredom forces them to rotate between their best and their second best skills until the task is finished. In the fit condition, the agents start in the same way. Based on the values in Table 9c. agent 1 performs action 1 and 6, agent 2 performs 6 and 5, agent 3 performs 5 and 4, agent 4 performs 4 and 3, and agent 5 performs 3 and 2. This implies that each action is performed by 2 agents, except for action 1 and action 2 that are only performed by 1 agent. These actions are performed after the agents have completed their best and second best action. Since the agents are less skilled in performing the remaining actions, performance time increases. Thus, the performance time with no newcomer is lower in the no fit condition than in the fit condition.

In the other conditions in which a newcomer enters the system after 100 rounds, the task allocation process can be described by using 3 phases. In the first phase, the agents start specialising a particular action until boredom forces them to rotate. In fact, this phase describes what happens with a group with no newcomer. In the second phase the newcomer comes in and starts performing. This implies that not all actions are finished at the same time. Phase 3 starts as soon as at least one action has been completely finished and the task must be re-allocated. After re-allocating the task, the agents proceed until another action has been finished, etc. In this serial way the agents continue until all actions have been completed.

In the last phase, there is a significant difference between the no fit condition and the fit condition that holds for all condition with a newcomer. In the no fit condition, the newcomer starts with his best two skills (or with his first two when he is a generalist) more or less in the same way as the other agents. Because the actions that the newcomer performs are also performed by some other agents as well (see Table 9a and 9b) these actions are finished first. From that point on, the newcomer switches to other actions to help the rest of the group. In the fit condition, the newcomer starts with his best two skills (or with his first two when he is a generalist). These skills correspond to the actions that were only performed by one agent instead of two. Being a newcomer, he starts later than the other agents. Therefore, his actions are finished later than the actions of the other agents. From that point on, the other agents have to switch to these actions to help the newcomer.

This means that in the no fit condition, in the third phase, the agents have to re-allocate a lot more than in the fit condition. This causes the main difference in performance time of both conditions. Although the ‘peaks’ in the third phase, representing the worst


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agent, are about the same in both conditions, we see a clear difference between the no fit and the fit condition during the third phase (see Figures 29a and 29b).

Figure 29a: Performance development in condition C3: no fit, high specialist

Figure 29a depicts the performance time (y-axis) at every round (x-axis), for all agents. During the first phase, all agents have the same performance time, which results in a single graph. From the 100th round, the newcomer enters the group, who initially performs better than the rest of the group. However, from the third phase (160th round), it turns out that the newcomer only appears to be in the way. His help during the second phase causes the other agents to shift to actions with low expertise and motivation. Further, the task allocation process is disturbed, which hinders the process of task rotation, which leads to further performance loss. This results in high peaks that are caused by agents working on actions they are least skilled for and by motivational decrease. Since the no fit condition with no newcomer shows no peaks at all, the group performs worse with a newcomer than without.

Figure 29b shows the performance development in the fit condition. Again the newcomer starts with a better performance than the rest of the group. From the start of the third phase (200th round), the performance peaks are about as high as in the former condition. However, because the agents do not switch that often, Figure 29b shows a graphic that is not as erratic as Figure 29a.

Figure 29b Performance development in condition C4: fit, high specialist

Thus, as regard the second finding, in the no fit condition, without a newcomer the task is performed quite well, with a nicely balanced task allocation process. When a


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newcomer enters the group, at first it looks that he is positively contributing. However, during the last phase, when everybody needs to help to finish the ‘loose ends’, it turns out that the newcomer is only in the way. Therefore, the no fit condition is better of without a newcomer. In the fit condition, when the newcomer enters, the specific task requires much more actions before it is completed than the other task. During the last phase all agents contribute evenly to this part. Because these agents are not highly skilled to do so, performance goes down. A newcomer, who is especially skilled in performing this specific part, contributes relatively more to team performance. Although at the end the ‘loose ends’ still cause high performance time peaks, performance with a newcomer is a lot better than without.

In the no fit condition, the contribution of a newcomer is dual. First, when he enters the group, his expertise and motivation lead to a better performance when his performance time is lower than the average group performance (i.e., he has high expertise and motivation). Second, during the last phase of task performance, he contributes to the ‘loose ends’ of the task. In the fit condition, during the last phase the newcomer simply continues with what he was doing (see also Figure 29b). Therefore, he does not contribute to the loose ends by re-allocating his actions.

Figure 29a depicts that in the no fit condition, the contribution to the newcomer to the last phase of the task is rather poor. In fact, because of this, the total performance time is lower than without a newcomer. Figure 29c depicts the performance time in the no fit condition when the newcomer is a generalist:

Figure 29c: Performance development in condition C7: no fit, high generalist

Instead of the initial increase, the performance time of the generalist newcomer immediately decreases: Because all his skills are identical he immediately starts rotating between two actions instead of building up boredom during the first 15 rounds. Because of this, his performance time in the second phase (100th -167th round), i.e. after he has entered the group, is somewhat higher than of the specialist in the no fit condition (see Figure 29a). However, the generalist newcomer is able to compensate for this by working on the different loose ends a lot better than the specialist newcomer. As regard the third finding, this explains why in the no fit condition, a group with a generalist newcomer performs better than a group with a specialist newcomer.


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The benefit of the generalists in the last phase does not apply to the fit condition because the newcomer simply proceeds in what he is doing. Instead, the influence of the newcomer is only determined by his expertise and motivation in the second phase. Therefore, in the fit condition, a specialist newcomer performs better than a generalist newcomer. However, this benefit is quite small. The most important components that influence group performance time are the expertise and motivation of the newcomer. This explains the small differences in both conditions between the group with a specialist and the group with a generalist. Since expertise and motivation of the newcomer have a linear effect on group performance time, the slopes of the group with a specialist newcomer and the group with a generalist newcomer are the same. Further, the slopes of the groups in both the no fit condition and the fit condition are the same, which explains the fourth finding.

6.4.3 Acceptance of the hypotheses Our hypotheses as formulated in 2.3 are based on the general idea that generalists may adapt more easily to a no fit condition because this demands a worker being able to work on multiple actions. A specialist on the other hand would be better able to fill the ‘gap’ in the fit condition. However, the results indicate that it does not matter that much whether the newcomer is a specialist or a generalist. Much more important is the possibility to fit in the group: In the no fit condition, none of the newcomers contributes positively to group performance, although the generalists contributed somewhat more than the specialists. On the other hand, in the fit condition, all newcomers improved group performance, whereas the specialists offered the best contribution.

On the basis of the results, the hypotheses are only partly supported. Hypothesis I, that stated that in the no fit condition group performance will improve more when the newcomer is a generalist than if he is a specialist, is not supported. Although group performance is better with a generalist than with a specialist, none of the newcomers actually improved group performance. Hypothesis II stated that in the fit condition group performance would improve more when the newcomer is a specialist than if he is generalist. Although the performance differences were small, this hypothesis is supported.

6.5 Conclusion and Discussion We simulated the task allocation processes of two artificial work groups that both required an extra worker. The group in the no fit condition represented a project team in which the whole project was allocated to all members, whereas each member contributed evenly to the whole task. Because of the workload of the team it was decided, that an extra member would facilitate the work. We expected that the team would especially benefit from an extra worker when he was a generalist. However, the results showed that despite of the obvious benefit of more hands imply less work, the team did not benefit from a newcomer at all. This yielded for both specialists, and generalists, no matter how high their expertise and motivation were. The group in the


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fit condition represented a project team that recently lost one of its members. Although the remaining workers were able to finish the task, it was decided that the team was better of with an extra employee to fulfil the task. We expected that only a specialist would positively contribute to the team. However, it turned out, that any newcomer would come in handy, not only highly skilled specialists, but lowly skilled generalists as well.

On the basis of the results we may draw two conclusions. First, the general idea behind our hypotheses, that specialists will match the best with groups that have ‘gaps’ to be filled and generalists will contribute the best in groups without gaps, is only party supported. Although specialists actually fit in groups with gaps, generalists do not contribute in groups without gaps, since the benefit of more hands does not balance out the performance loss and costs related to hiring extra personnel. Therefore, we must conclude that only in groups with the possibility for a newcomer to fit in, a newcomer will contribute to a better performance. This implies that for a project team with a high workload and close to a deadline it only may seem a good solution to hire an extra worker. In practice, that worker may only hinder, decreasing group performance instead of contributing positively to the team.

Second, the results indicate that even in case of additive tasks the principle ‘the more workers, the better’ does not always apply. By using a performance indicator that has been corrected for the obvious benefit that more hands imply less work, we found that a newcomer only contributed to a better performance when a combination of the group and task structure offers a possibility to fit in. This not only yields for specialists but for generalists as well. When this possibility does not exist, disturbance in the allocation process will cause a decrease of performance caused by motivational decrease and ineffective use of capacities.

On the basis of this we may conclude that the combination of work group properties and task structure, as well as the task allocation process, are components that are more important than characteristics of newcomers. In general, the insights of our study may contribute to the existing literature of turnover, especially the studies that focus on team processes regarding newcomers (Dineen & Noe, 2003; see also Marks et al. 2001; Arrow & McGrath, 1995). In general, computer simulation is a useful method to understand group dynamical processes regarding newcomers. This yields not only for learning (e.g. Carley 1992), processes regarding the transactive memory system (Levine et al. 2005), or outcome variables such as performance (Levine et al. 2005), but for task allocation processes as well. Thus, to comprehend the mutual adaptation process of teams and newcomers, both computer simulation studies and the study of self-organising processes of task allocation may offer promising insights.

But to what extent is our study in fact useful? What do simulation results based on a simple model of a workgroup say about real life processes? First of all, we did not limit our experiments by using agents with cognitive properties only, but used a model in which we combined a simplified cognitive architecture with variable motivational states. Although this does not necessarily imply that the results of this study can easily be related to real life events, the combination of cognitive and motivational properties


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may result in more realistic dynamics than a model that only focuses on cognitive properties.

We used a performance indicator that we corrected for the benefit of more hands imply less work by constructing two ways of measuring the time that is necessary to finish a task. Both ways concerns the number of rounds, i.e. time steps, that workers need to finish a task: the first way is a function of task size and number of workers and the second way is based on the expertise and motivation of the workers. On the basis of this, we concluded that in some cases an extra worker did not benefit at all. However, we can imagine situations in which this conclusion does not hold. For instance, when a task can be split up in easy operational activities such as copying or printing, and complex activities such as writing text, a group would be able to finish a task a lot quicker with the help of some temporary workers, doing the easy work, while leaving the complex work to the rest of the staff. Moreover, the extra costs of recruiting and hiring extra personnel which lead to a less efficient way of task allocation are sometimes necessary, especially when the team has to meet a deadline. To enhance the realism of simulation studies about newcomers, these components may be studied in future research.

Future research may also involve task interdependencies and the motivation of the agents being dependent of the task, because one might state that every task contains elements that everyone likes or dislikes. We did not include this into this study because the then, the results were probably too complex to analyse. Only now that we comprehend the processes in a simpler way, we are able to add these components to study more realistic scenarios.

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Chapter 7 Conclusion In this section I will relate the conclusions of the experiments in the different chapters, to the conditions of self-organisation that Morgan (1986) has described. The conclusions of chapter two focus on the paradox that a model can be both simple and integrative. The conclusions of chapter three involve the verification of the model and the program. The conclusions of chapter four are related to the condition of ‘minimal critical specification’. Chapter five and six focussed on the variety of demand (five) and supply (six) in relation to the behaviour of specialists and generalists. Their conclusions are related to the conditions of ‘requisite variety’ and ‘redundancy of functions’. The condition of ‘requisite variety’ is somewhat interwoven with the other conditions, for instance because less redundancy and less critical specifications implies less variety (see also Molleman, 1996). In all experiments, expertise and motivation are process variables. They are related to the general concept of learning. I end with a final conclusion concerning this thesis.

7.1 Modelling Self-Organising Processes of Task Allocation A multi-agent model that describes self-organising processes of task allocation in a comprehensive way should preferably encompass different psychological theories and models at both the individual and the group level and should also interrelate these levels. This, however, may also easily lead to complications. The first complication is related to the multi-disciplinary nature of such multi-level research. A combination of different models at different aggregation levels may result in misunderstanding between the different disciplines these models come from (see also Klein & Kozlowski, 2000). As a result of this, we may end up with an unclear model that does not contribute to scientific progress in the respective disciplines. For instance, for a sociologist the term structural learning refers to changes of the structure of the social network. However, for a cognitive psychologist, since learning can be described by means of change of neural connections, the term may as well refer to changes of the structure of the neural network. The second complication is related to ‘Bonini’s paradox’: ‘the more realistic and detailed one’s model, the more the model resembles the modelled organisation, including resemblance in the directions of incomprehensibility and indescribability’ (Starbuck, 1976, p 1101, cited in Weick, 1979). This paradox yields for simulation models in general (Weick, 1979), but certainly applies to multi-disciplinary models.

This implies that my model needed to be both integrative and simple. This evokes two questions. First, have I been able to build a model that was multi-disciplinary and yet


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easy to comprehend? Second, if yes, how did I manage to do so? To answer these questions, I am going to explicate how I built the model. First of all, all kinds of approaches, disciplines and views that are related to a certain phenomenon have one thing in common: the phenomenon itself. Therefore, when I build the model I tried not to focus on the theories and models underlying it itself, but considered them only as a vehicle that could lead me to the collection of phenomena that they describe. The next step was to describe this collection of phenomena in simple terms. In my case, this implied the use of some neural network concepts such as activation, excitation, inhibition, threshold, and connection. The result of this model-building-strategy was a model that was funded on empirically based theory with an important benefit: the model was based on a collection of underlying phenomena and was not restricted to a specific research area or discipline. Therefore, it was not only capable of integrating the phenomena that the underlying theories described, but it turned out that it could describe other relevant phenomena as well.

To explain all this I will give three examples. The first example considers the integration of multiple theories into a simple description: Both the similarity/attraction effect (Newcomb, 1960), the proximity/attraction effect (Festinger, Schachter & Back, 1950), and the effect of mere exposure (Zajonc, 1968) describe the general principle that is also formulated as Hebb’s learning rule (Hebb, 1949). This rule describes that the simultaneous activation of two neurons increases the change for a connection to grow between them. If we would replace the term ‘neurons’ with ‘elements’ we could use Hebb’s learning rule as a general principle that describes the phenomenon of connection changes at both the neural and the social aggregation level (Zoethout, 1994). Besides, it is much easier to model this general principle than to incorporate different social psychological effects into a model.

The second example illustrates how my model not only describes phenomena related to the underlying theory, but proposes a description of another relevant phenomenon as well. My model describes the influence of motivation on performance, by considering motivation as a skill component. In this way the motivation of an agent is a function of the motivation of his active skills. During the allocation process the agents start with what is called an ‘initial choice’ This resembles the part of the task that they individually want to perform, based on their expertise and motivation. As a result of this ‘initial choice’ the agent start to negotiate which leads to, what is called the ‘final allocation’. According to the model, a discrepancy between ‘initial choice’ (what they want) and ‘final allocation’ (what they get) may result in motivation loss because then the agents are forced to use skills for which their motivation is lower. This phenomenon is described in theories on extrinsic an intrinsic motivation because studies indicate that in general, intrinsic motivation leads to higher performance than extrinsic motivation (e.g. Hirst, 1988). Although I did not model nor study the differences between extrinsic and intrinsic motivation, the phenomenon itself is relevant for describing the relation between motivation and performance. Moreover, my model describes this phenomenon although it was not based on it in the first place.

The last example shows how a complex property can be modelled in a simple way. This concerns the negotiation process between the agents itself. Both the individual decisions and the negotiation process describe whether or not particular skills should be

Chapter 7: Conclusion

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used. In the model the mutual influence of agents is described as mutual influence of skills (see Figure 4b in chapter two). At the skill level, influence is based on expertise, motivation, thresholds, and a set of inhibitory and excitatory connections. This influence results in a state in which a skill is used or not. An agent is being defined by means of a set of skills. At the agent level, it seems that each agent has a specific preference, makes an individual choice on the basis of that, influences the other agents to let him proceed in what he wants, and may become de-motivated when he cannot get what he wants. However, a negotiation process concerning all these elements is only possible for a being with cognitive and social abilities that enable him to choose for himself and oppose others that interfere with this choice. Furthermore, he would need an internal representation of his co-workers and the task. And yet, with a model as simple as mine, without all these properties, it is possible to describe these complicated processes.

These examples illustrate that my model is both simple and integrative. The design of a simple model forced me to describe the common phenomena as studied within the different disciplines. Therefore it does not create confusion of tongues but offers a platform for integration instead. Further, a focus on simplicity protects us against the disadvantages of Bonini’s paradox. Finally, the model satisfies two benefits of simulation models in general as mentioned in the introduction of this thesis (see also Arrow et al. 2000): first, it does not tolerate vague ambiguous theories because it forced me to explicitly formalise theory into computational algorithms. Second, it offers a possibility to integrate all kinds of theories and models related to the same phenomenon.

7.2 Verification of the Model and the Program After formalising the model into the simulation program called WORKMATE, I conducted three experiments to verify the model and the program (Chapter 3). The first experiment in which I studied the relationship between specialisation and coordination time showed that WORKMATE generated dynamics in accordance with the expectations as derived from the model. The data indicated that in a stable condition without boredom, the system would always end up in a stable state. This state was reached according to the principle that the best becomes better and the worst becomes worse. This principle holds that the use of a particular skill leads to the improvement of that skill. This increases the chance that this skill will be chosen again in the future, which leads to further specialisation in that skill, while the other skills are forgotten, etc.

The second experiment that concerned the relationship between task variety and coordination time again showed that WORKMATE worked according to my model. The results indicated a similar specialisation effect as described in the first experiment within one task. From one task to another the coordination time increased, which indicated that it took more time to allocate the new parts.

The third experiment that dealt with the consequences of boredom effects indicated that WORKMATE was able to generate emergent phenomena. Skill use implied that agents


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learned and enhanced their expertise, while at the same time got bored and less motivated to do that task. Not using a skill implied that the agents lost expertise, but also recovered from boredom for this task. This causes task rotation to occur, which showed that the model was able to produce self-organising processes that lead to new properties at the group level.

7.3 Task Rotation and Minimal Critical Specification In chapter four I varied different types of self-organisation: self-organisation (purely bottom up processes), semi-self organisation (bottom up processes with little top down restrictions), and no self-organisation (only top down restrictions). These experiments are related to the condition of minimal critical specification that states that only critical issues should be fixed (Herbst, 1974). The results showed that in situations where task rotation could emerge because of self-organisation, the system performed better than in case of no self-organisation. These results are in accordance with the condition of minimal critical specification. .

Further, I varied different levels of boredom and introduced the independent variable of task rotation frequency, which, of course, did not apply to a condition in which the agents were free to self-organise, where task rotation was more an outcome or process variable. As regards boredom and recovery, I found that a decrease in the boredom and recovery rate resulted in agents delaying their start of task rotation. As soon as the boredom/recovery rate dropped beneath a certain point, for two reasons the agents did not rotate anymore. First, at the time the agents got bored enough to rotate, their expertise level had become lower than the threshold, which made rotation impossible. Second, the long period before the first rotation caused the agents to specialise in a single skill, which weighted stronger than the motivation loss. This implies that a task that leads to high levels of boredom will be performed better than a task causing a low level of boredom, because in case of highly boring tasks rotation will emerge and in case boredom comes slowly task rotation will not come. As regards to the task rotation frequency, I conclude that with respect to expertise, the decrease in the rotation frequency has the same effect as the decrease in boredom/recovery: as I stated, a decrease of boredom/recovery delayed the start of task rotation. By definition, a decrease in rotation frequency leads to the same.

7.4 Task Dynamics and Requisite Variety In chapter five I tested hypotheses that were based on the condition of requisite variety. This condition implies that a stable environment matches the best with a mechanistic centralised organisation, a turbulent environment demands an organic organisation with high individual autonomy, and somewhere in between, autonomous teams would match the demands of the environment the best (Burns & Stalker, 1961; Molleman, 1998). To test this condition I used a design with groups of specialists and generalists under different conditions of task variety. But although it turned out that in stable situations the specialists performed better, the generalists did not outperform the specialists in


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turbulent situations. Instead, since there is hardly any space for learning in turbulent situations, the behaviour of specialists and generalists becomes more similar and, consequently also their performance. Although these conclusions more or less comport with existing research, the experiments did not clearly indicate the relation between organisations and environment that can be expected on the basis of the condition of requisite variety.

An explanation for this can be found in the way in which we defined specialists and generalists. Specialists are being defined as minimal generalists, with the capacity to perform all parts of the task but with a specific preference for a small portion. Generalists are being defined as agents with no preference for a specific part of the task. New tasks however imply the use of new skills. Neither the specialists, nor the generalists were equipped with high expertise regarding these skills. With regards to the specialists, this is a logical consequence of being a specialist. But the benefit of generalists of being able to use all kinds of different skills does not apply here. Moreover, empirical studies indicate that ‘minimal generalisation’ is sufficient to deal with variety (Van den Beukel, 2003). Thus, in my research the definition of generalists does not hold because they lack the ability to deal with new tasks and the definition of specialists does not hold because they are defined as minimal generalists, being able to deal with variety. Therefore, although the study revealed some principles related to Ashby’s law, this condition still needs more research.

7.5 Task Rotation, Flexibility and Redundancy of Functions In chapter four I introduced the concept of task rotation based on the notion that agents start to re-allocate tasks when their motivation to proceed with the same action was too low. Of course the process of task rotation only occurs if the team members share some skills. This refers to the condition of redundancy of functions, which constitutes a prerequisite for task rotation to emerge. Task rotation is the most important self-organising principle in the studies I described in this thesis, not only because it enables a group to cope with boredom, but it offers a way to flexibly adapt to new situations as well.

The chapters five and six describe experiments about the flexibility of self-organising task groups. Chapter five describes how a task group reacts upon external changes such as task dynamics. Even the least flexible group that I tested, the specialists, still consists of minimal generalists, because a group with real specialists, i.e. without any redundancy of functions, would not be able to cope with any changes at all, which would only lead to trivial results.

Chapter six describes processes related to internal changes such as turnover. I simulated the task allocation processes of two artificial work groups that both required an extra worker. The group in the no fit condition represented a project team in which the whole project was assigned to the complete group, whereas each member contributed evenly to the whole task. The group in the fit condition represented a project team that recently lost one of its members. To both groups, one newcomer was added. This could be a specialist or a generalist. The results showed that the generalists


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performed better than the specialists in the no fit condition and the specialists performed better than the generalists in the fit condition. However, an effect that was much stronger indicated that the characteristics of the newcomer did not matter that much: In the fit condition every newcomer improved the group performance, whereas none of the newcomers contributed positively to the group performance in the no fit condition. In groups without the possibility for the newcomer to fit in, the newcomer was just in the way, which led to performance loss. Since in all conditions the adaptation processes are processes of task re-allocation, these processes could only occur because of redundancy.

Further, without redundancy, the group in the fit condition would not have been able to perform its task anymore until the newcomer arrived because none of the workers would have the skills to take care of the work of their former co-worker. The group in the no fit condition and the newcomer would not have been able to mutually adapt at all, because in this group adaptation automatically implies re-allocation, and re-allocation is impossible without redundancy.

Therefore, I conclude that none of the experiments on self-organising processes of task allocation as described in the chapters four, five and six, could have been conducted without a certain minimal level of redundancy of functions. It is conditional for task rotation and for self-organisation.

7.6 Expertise and Motivation Processes and Learning As I stated in the introduction, the condition of double loop learning, i.e. monitoring the tasks (including its goal) itself and constantly looking for better alternatives, did not apply to the experiments in this thesis. Instead, the agents had to perform a rather abstract task that was designed by me. This implies that although I studied processes of self-organisation, I explicitly formulated the context under which this took place. As the condition indicates, in real life a self-organising system defines its own context (Varela, 1984). This touches the fact that the question whether a system is self-organising or not, is defined by the boundaries the researcher defines. This leads to discussions and reflections I choose not to address in this thesis. Instead I focused on the internal learning principles and mechanisms in relation to Krippendorf’s (1986) definition of learning that I described in the second chapter of this thesis. This definition states that learning can be considered as a process of increasing success in a fixed environment (Krippendorf, 1986). This definition not only applies to increase in expertise, but also refers to the increase in motivation, since motivation and performance are positively correlated (Hackman and Oldham, 1980). Furthermore, it refers both to individual and to structural learning. But, as I stated in the introduction, the notion of structural learning is only used in the general model that I described in chapter two, but has not been part of the experiments I conducted. Therefore, I only now describe principles related to individual learning. Four principles are considered as the most important with respect to the description of the processes that I studied.

The first principle involves the specialisation of the agents. According to the model, the results of the experiments in chapter three demonstrate that without the influence of


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boredom, agents simply specialise in the skill they use when they start performing a task. I called this principle: ‘the best become better and the worst become worse’. Evidently this results in an increase of performance. The second principle involves the boredom of the agents. According to both the model and the results of the experiments in chapter three, four, and five, the boredom concerning the skills that the agents use for a longer period of time increases. Evidently this results in a decrease of performance. Experiments showed that both principles together lead to a performance decrease. This shows that boredom had more effect than specialisation, which can be explained with the parameter settings of boredom and learning and the consequences of the boredom and learning functions that the formulas describe. But the combination of both principles had another effect: under the circumstances as mentioned in the description of the experiments, the agents started to re-allocate their task. This third principle is called ‘task rotation’. These three principles form the basis of the complex mutual interaction between expertise and motivation, task performance, and task allocation, that the model describes. The last principle is a consequence of the external and internal dynamics I described in the chapters five and six. It holds that the agents start using their best skills, then their second best skill, and finally finish using their worst skills. For two reasons, this principle causes performance loss when a task is nearly finished. First of all, by definition the worst skill itself indicates the lowest performance. Second, keeping one single skill to the end unused, results in the absence of possibilities for task rotation as a way to cope with boredom. This results in high motivation loss and as a consequence to this, low performance.

Although these principles are logical consequences of the model, the complex mutual interaction between the variables does not result in trivial results. Instead, as the principles showed, the model offered a way of systematically describing the individual learning processes and the relationship of their underlying mutual relationships.

7.7 Final Conclusion In my experiments I related three conditions of Morgan’s ‘principles of holographic design’ to self-organising processes on the basis of behavioural theory. In relation to these experiments, the conditions of minimum critical specification and redundancy of functions appeared to be more or less evident: more specifications imply less individual freedom, because behaviour is forced upon the workers, which implies less possibilities to self-organise. Without redundancy of functions, workers are not able to choose what to do, not because they are not allowed to do so, but because they simply do not have the potential to choose another task.

It is less evidently to relate the condition of requisite variety to self-organising processes. According to this condition, a task with little or no variety matched the best with a group with more specifications and less redundancy, i.e. low variety (Burns & Stalker, 1961; see also Molleman, 1996; 1998). However, the only relation with self-organisation I would be able to give is that a group with specialists, representing a group with low variety, shows the best performance concerning a task with low variety. Furthermore, high task variety results in a slight tendency towards generalisation, i.e.


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high redundancy of the workers. However, although the law of requisite variety indicates that in the latter condition, generalists would outperform specialists, this did not happen. Moreover, the tendency of the group of specialist to behave like generalists is the result of the inability to specialise because of the high task variety, which is more or less trivial. Finally, high task variety would not only imply high generalisation concerning the original task to perform, but would also indicate expertise concerning the new tasks to come. Therefore, on the basis of the results of the experiments I must conclude that the process of generalisation and specialisation within a group, caused by different levels of task variety, is not fully understood and needs further research. Nevertheless, I will conclude this chapter by stating that although this thesis only partly succeeded in relating self-organising processes to the conditions that Morgan has stated, it was successful in relating self-organising processes to behavioural theory

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Chapter 8 Discussion The papers that are part of this thesis describe simulation studies of self-organising processes of task allocation. I described the model, its formalisation, and some pilot experiments to verify the model and WORKMATE, the program. On the basis of this I conducted experiments about the emergence of task rotation under diverse conditions. These experiments have brought us further insight in the processes within self-organising systems, which led to two more advanced experiments in which I tested the flexibility of the system by manipulating external and internal variables. The external variables concerned the influence of task variety on the performance of specialists and generalists. The internal variables dealt with the influence of two types of newcomers entering two kinds of task groups. In each chapter I ended with a discussion part that reflected on the particular study. In this final chapter I will discuss the most important subjects of the preceding chapters in a more comprehensive way. I will discuss four topics, the scientific contribution of this thesis, its contribution to practice, the validation of the studies that I have conducted, and suggestions for further research.

8.1 Scientific Contribution In this section I propose five ways in which my research contributes to science. First, my approach can be used as a platform to integrate various psychological theories and models. My research focuses on two different aggregation levels, involves principles and theories from different fields and is therefore multi-disciplinary by nature. In this sense, my model is an example of an integrative approach that may contribute to social and organisational psychology.

Second, the model I used indicates a psychologically more realistic description than most existing multi-agents models. As I stated in the introduction, within the area of social simulations two approaches may be distinguished, the social approach and the cognitive approach, whereas both approaches lack the benefit of the other. My research tries to encompass both by combining a cognitive architecture with social realism. Although some scholars from both disciplines could claim that I emphasise their part to little, I would argue that this criticism may yield for multi-disciplinary research in general. Further, my model is not based on cognitive properties only but uses variable motivational states as well. Although this does not necessarily mean that the results of this study can easily be related to real life events, the components that the model incorporates are relevant in relation to the outcome variables of the experiments.

Because I used a formalised description of psychological theories, my model can relatively easy be related to other formalised disciplines within management science


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such as Operations Management. Since these disciplines in general lack the attendance of psychological plausible models but yet pose propositions related to human behaviour, a formalised description such as my model may contribute to this field.

Third, my studies offer a systematic description of underlying processes. One of the advantages of multi-agent simulation is the systematic description of processes leading to a certain result. In daily life these processes are difficult to study for reasons I mentioned in the introduction. My research has not only highlighted the outcomes of experiments, but has especially focused on the importance of the processes leading to those outcomes. In this way my research not only shows what happens, but systematically describes how this happens as well.

Fourth, the results indicate that self-organising processes of task allocation are highly relevant processes to study. In chapter five I stated that self-organising processes of task allocation may explain how differences between groups of specialists and generalists lead to performance differences. In chapter six I indicated how these processes describe the mutual adaptation of newcomers and work teams. In general, the concept of self-organising processes of task allocation describes how people organise without an external instance dictating order. Therefore, the study of this concept elucidates some fundamental organising principles. As I stated in the introduction, we can only indicate the benefit of organisations if we know what our behaviour would be without them.

Fifth, I not only studied some relevant aspects of group processes, but developed a new research instrument as well. WORKMATE is able to describe processes of task allocation on the basis of task and team characteristics. It was used for the simulation of various experimental designs, it was able to generate emergent behaviour such as task rotation, and it generated process descriptions of expertise, motivation, performance, and task allocation, at the agent level as well as at the group level. With some adaptations it can be used for simulation experiments concerning group dynamics in general. In the section about future research I will elaborate on this.

8.2 Managerial Contribution To phrase Kurt Lewin that there is nothing so practical as a good theory, the most important managerial contribution my research has to offer refers to one of the benefits of computer simulation that I stated in the introduction, i.e. the possibility to build theories. Regarding my thesis, these theories describe processes in organisations in a way that contributes to improving practical management issues in daily life. In this section I will elaborate on this. Furthermore, the method of computer simulation that I used, has been a part of a much broader development concerning the use of complexity theory and advanced information systems. Nowadays, this development has lead to a growing need for computer simulation instruments, for instance within the area of business consultancy. Therefore, the second contribution to practice of my research will be related to the connection to this area.

Chapter 8: Discussion

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With regards to the contribution to theory building, as I have stated in the former section, my research offered a description how processes take place instead of just describing what their result are. Further, I indicated that the concept of self-organising processes of task allocation elucidates some fundamental organising principles. Although at this stage the descriptions of these processes are rather abstract and far away from real life events, they may give rise to new perspectives on team issues. I will elaborate on this by means of the conditions for self-organisation that Morgan has described.

The condition of requisite variety focuses on the relation between organisation and environment. This condition can be used to indicate the benefit of teams in organisations under certain environmental circumstances (e.g. Molleman, 1998). As chapter five indicates, the condition can also be used to describe the relation between a team and its environment, i.e. the task. Although the results of the experiments do not indicate a clear relation between the condition and its related processes, it shows the relative importance of team design. In general, in the introductory chapter I questioned the use of organisational design because if bees and ants do not need such, why do we? Of course, the discussion about design and development involves a lot more issues than dealt with in the present study. However, as chapter five states, my study indicates that the difference between design and self-organisation does not lead to spectacular performance differences. On the basis of that I may conclude that in some cases self-organising processes may replace top-down management. Furthermore, the study offers a systematic description that not only concerns traditional variables such as performance and expertise, but involves motivational processes as well. The condition of minimal critical specification indicates the space that is needed for self-organising processes. The experiments -especially in chapter four- not only confirm the importance of this condition, i.e. the proper balance between structure and freedom related to group performance, they also clearly show the underlying self-organising processes related to this. The condition of redundancy of functions is related to the flexibility of the workers. Limited flexibility may lead to performance loss, especially in turbulent environments or in the case of turnover. In my experiments, this condition is not only related to expertise but also to motivation. The motivational effects concerning (the lack of) redundancy that my research shows, offers insight in real life processes, for instance because it shows a balance between the benefit of specialisation, i.e. high expertise, and the disadvantage of it, i.e. boredom.

Thus, my studies describe a first outline for the balance between team and task, the balance between organisational constraints and self-organising processes, and a balance between expertise and motivation. This outline can be considered as a the beginning of a theory about the balance of self-organising processes within teams with respect to their performance.

Whereas the systematic description concerns the theory building part of my research, another contribution of this thesis may be the applicability of the model itself. As I stated, my research can be seen as a part of a larger development towards the use of computational models for business purposes. My model may serve two kinds of applications. First, it may serve as a tool to train and assess managers. I used WORKMATE to study team processes by manipulating different psychologically relevant variables and parameters. The underlying model may serve as a platform for


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gaming purposes. For instance it can be used by managers as a simulated team to practice their skills, for instance regarding performance components. WORKMATE simulates, by adjusting tasks, initiating relationships among workers, conducting on the job training, and motivating the virtual team. Second, WORKMATE may also be used as a platform for analysing organisational problems. By putting the self-organising processes that WORKMATE is able to generate into a organisational context with constraints related to structure, space, and time, WORKMATE will be able to analyse organisational processes and bottlenecks. It may answer questions like why a self-managing team is not self-managing. Is it because of the implementation or doesn’t the organisation need such teams? These questions are not new, but WORKMATE may give a new perspective on the answer. Especially a combination of a behavioural model such as WORKMATE with traditional simulation models for organisational processes such as logistic models, is able to analyse an interesting and useful combination of variables.

8.3 Validation of the Model To what extent does WORKMATE really describes what it clams to do? What is the validity of the model and, consequently, the results? Holland (1998) distinguishes three ways in which scientific models can be validated. The first and most traditional way states that models are validated through the correctness of their predictions about the world device (cited from Holland, 1998, p241). When looking at my study, I must conclude that my model is not validated in this sense. Although the theories and frameworks that served as input for the model were empirically validated, both the processes and the outcomes of the model were not. At the most I might conclude that my simulation processes and outcomes mimic real life phenomena, but I did not cross-validate my findings in real life settings. However, such a comparison could easily lead to a number of problems. For instance, both the simulation model and the empirical model could be based on stochastic factors or the simulation data is correct but the empirical data, being gathered with methods having their own validation difficulties, is not (for an overview of problems related to empirical validation, see Gilbert & Troitzsch, 1999, p. 22). This does not mean that we should not try to relate simulation experiments to empirical studies. On the contrary, although simulation studies are useful to comprehend the complex coherence of variables regarding organisational processes, ultimately, without being related to empirical studies, their scientific value will be limited.

The study of self-organising processes of task allocation can be empirical validated to some extent, for instance with experimental task groups. However, the study of complex social systems implies that simulated processes may develop in another direction as in empirical data because small effects at the micro level may result in large consequences at the macro level. This implies that outcome validation is only possible if the empirical data shows ‘stylised facts’ (e.g. Jager & Mosler, subm.). Stylised facts are robust empirical effects that have been identified in a number of examples. Validation of a simulation model consists of reproducing these effects. However, in more complex conditions empirical outcomes may vary too much to


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generate any stylised facts at all. Moreover, if a limited set of empirical outcomes is available, simulation outcomes are impossible to validate against such unstable outcomes. Nevertheless, it may very well be the case that the same underlying behavioural mechanisms are responsible for these outcomes. Hence we can imagine that process validation is possible.

But, as I stated before, this is not the only reason that cross validation of the outcomes of the experiments is more difficult to accomplish (see Gilbert & Troitzsch, 1999, p. 22). Therefore, although process validation would have been possible within the time horizon of a PhD-project, I choose to describe an overview of simulated self-organising processes under different conditions, generating different hypotheses about real life processes.

The second way to validate theoretical models serves as a demonstration that something is possible, as in Neumann’s demonstration that a machine is able to reproduce itself. Here validation occurs when a dynamic model works as claimed, as when validates a patented device (cited from Holland, 1998, p241) This type of validation resembles the verification stage of simulation research that Gilbert & Troitzsch (1999) describe. Indeed, as I described in chapter 3, I checked whether or not WORKMATE did what it has supposed to do. With regards to this way of validating, I dare to conclude that my model serves as a demonstration that with respect to self-organising processes of task allocation, simple agents at the micro level are able to produce complex behaviour at the macro level. The emergence of task rotation, the role of motivation concerning the results of the task dynamics experiments, and the decrease of performance concerning the experiments with newcomers, are clear examples of this. Therefore, I demonstrated that WORKMATE is able to simulate self-organising processes of task allocation.

Third, models may generate ideas about a complex situation, suggesting where to look for critical phenomena. Here, validation is in the cogency and relevance of the ideas they produce (Holland, 1998, p241). This way of validation is related to the model suggesting ideas about the importance of task allocation processes. My experiments produced a systematic description of endogenous and exogenous variables involved. This description generates hypotheses concerning important variables of group dynamical processes and how they are related to each other.

8.4 Strength, Weaknesses and Future Research In chapter one I discussed the discrepancy between the model as described in chapter two and the series of experiments I conducted as described in chapter three, four, five, and six. Whereas the model involved different components of task complexity, I only studied the effect of one, i.e. task variety. Furthermore, the model proposed both individual and social components that affect the task allocation process. However, I only studied the individual components. On the basis of this discrepancy I now formulate ideas for further research. Following the model, I mention task interdependence and social components such as power and attraction. Task interdependence refers to the way the parts of a task are related (e.g. Thompson, 1967) and its consequences for human behaviour. It is an important subject of empirical study


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within the area of group dynamics (e.g. Van der Vegt & Van der Vliert 2005). Moreover, it is an important component that determines the task allocation process. Because of this, computer simulation experiments may be used to systematically describe the underlying processes regarding the empirical data. Moreover, empirical data may validate the processes and outcomes of the computer simulation experiments. With respect to self-organising social processes of task allocation, the social components of power and attraction are needed to describe the dynamics concerning group formation. Only studies concerning these social components will justify the relation with Hebb’s rule that I stated in the introduction. Especially the concept of ‘structural learning’, i.e. altering the social structure, can only be studied with the use of social components.

The future research issues that I mentioned above are a logical consequence of the model that I highlighted in chapter two, and its discrepancy with the experiments that I conducted and described in this thesis. Other future research that I mention here can be divided into two parts, a part that formulates research within the structure of the conditions of self-organisation that I used in the former sections and a part that focuses on the realism of the model.

As I stated in the conclusions section, the relation between requisite variety and group dynamical processes needs more research. The experiments on task dynamics and groups of specialists and generalists that I have described in chapter five indicated that especially the generalists did not behave according to the law of requisite variety. Because the generalists were only generalists with respect to their original task and not with respect to the new tasks, they were not flexible enough to cope with task dynamics. A logical continuation of these experiments would imply experiments with generalists having larger sets of skills. A second way of exploring the relation between conditions of self-organisation and group dynamical processes is to focus on the condition of minimal critical specifications. Although chapter three indicated interesting results, the use of ‘real’ critical specifications may help to relate the simulation results to empirical findings. These critical specifications can be related to structure, such as formal and informal networks, space, such as spatial distance to potential co-workers, or rooms and corridors, and time, such as deadlines, nine-to-five jobs, or shift-work. However, organisations do not only limit self-organising processes, but may facilitate them as well, for instance, by operating as an information buffer with respect to learning, especially in the case of turnover (e.g. Levine et al., 2005).

In general, in this thesis I have been given the concept of learning only little attention. In the introduction I stated the relevance concerning the distinction between individual learning and structural learning. However, I did not explore its consequences for, for instance, the transactive memory system (TMS). TMS is a collective memory system for encoding, storing, retrieving, and communicating group knowledge (e.g. Brandon & Hollingshead, 2004). Therefore, future research can elaborate on the relation between TMS and structural learning. Furthermore, I did not explore the relation between the condition of ‘double loop learning’ and self-organising processes because in my experiments the environment, i.e. the task, was an independent variable. What holds for the condition of minimal critical specification also applies for the condition of double loop learning: with a more advanced definition, the condition not only serves as an


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independent variable, but indicates more complex mutual interactions either between critical specifications and self-organising processes or task/environment and double loop learning.

With regards to the realism of the model, I will now shortly focus on three variables: motivation, the task itself, and time. In the model, these variables show weaknesses that I would like to discuss. In the original model, motivation is independent of the task. However, one might state that each task contains elements that everyone likes or dislikes. Therefore, motivation being a combined outcome of both agent and task characteristics may result in more realistic dynamics. Further, with regards to the task, in chapter six I stated that a division into for instance operational and control parts would influence the task allocation process (see also Rice, 1976). Finally, the way I implemented the component of time is rather primitive. Although the time the agents need to perform a single cycle determines their performance, no matter how big their differences are, they all start and finish together. It is merely evident that a more realistic description would generate more sophisticated results.

Certainly, it is not difficult to come up with more ideas to implement into a computer simulation model. It is far more difficult to keep the model simple. Yes, I could enhance the agents with personality characteristics (see Zoethout & Molleman, 2000) and it is possible to model some cognitive abilities to let task allocation rules emerge in order to facilitate the task rotation process. Social components such as team size (e.g. Molleman 2005), commitment, team cohesion and coordination costs (e.g. Cohen, Ledford & Spreitzer 1996) would indeed cause the model to resemble reality in greater detail, including - to phrase Bonini again – its incomprehensibility. All these ideas, including the importance of empirical validation, suggest that the studies that I described in this thesis may only form a first step for future simulation studies. I already mentioned different research lines. They vary from elaboration of the simulation model to empirical validation and adjustment. Furthermore, the further development of a formalised behavioural model may contribute to other management disciplines, for instance by creating an artificial organisation, either for scientific or for practical use.

8.5 Finally I started this thesis with the question how humans organise themselves. Have I been able to answer this question in this thesis? By all means, no! The question that I started with is too fundamental to answer fully within the scope of a PhD-project. At the best I started with an introduction of describing some basic principles and mechanisms of self-organising behaviour related to task allocation and task performance. This introduction may only serve as a first step towards a better understanding of self-organising human behaviour. This means that I am not able to present definite conclusions. But does this mean that scientists in general should not try to comprehend fundamental issues in the first place? I think not. Every discipline, including management science, has its roots in its own fundamental questions. And what is the use of a question if nobody tries to answer it? Besides, fundamental issues serve as a shared bedrock that integrates the different perspectives within a study such as management science that is both multi-disciplinary and applied. This integration is


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needed as a counterpart for the logical specialisation that applied research brings about, because without it, a discipline would end up as an incoherent collection of various research topics. On the other hand, a discipline that only studies fundamental issues may loose its contact with reality. With respect to my study, this means that the development of applications, for instance as a described above, would be beneficial for both theory and practice.

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URLs:

AAMAS, Autonomous Agents and Multi-Agent Systems, Springer, the Netherlands, URL:

<http://www.springerlink.com/(5urrtr45fiupuv2d4mlr5l55)/app/home/journal.asp?referrer=parent&backto=linkingpublicationresults,1:102852,1>

CMOT, Computational & Mathematical Organization Theory, Springer, the Netherlands, URL:

<http://www.springerlink.com/(ebxiyzr40hzop055blvpdg45)/app/home/journal.asp?referrer=parent&backto=linkingpublicationresults,1:102865,1>

JASSS, The Journal of Artifical Societies and Social Simulation: an inter-disciplinary journal for the exploration and understanding of social processes by means of computer simulation, URL: < http://jasss.soc.surrey.ac.uk/JASSS.html>

SIMPAT, Simulation Modelling Practice and Theory, Elsevier, URL:

<http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=7295&_auth=y&_acct=C000024219&_version=1&_urlVersion=0&_userid=1256546&md5=da15eed501ef6c381fecf7df0b926464 >

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Appendix I Relevant Computer Code

Allocation Procedure TSystem.Allocate(rounde:integer); var s,count:integer; begin count:=0; InitialChoice; repeat for s:=0 to Agent[0].NrOfSkills-1 do begin if Agent[0].Skill[s].Active=True AND Agent[0].Skill[s].Available=True then begin ModifyInitialChoice; if (NrOfAgentsWithSameHighestSkill(s) > 0) then begin while ParForm.Task.AvailableActions(s)< NrOfAgentsWithSameHighestSkill(s) do begin RemLowestAgent(s,LowestAgent(s)); if ParForm.InflCheckBox.Checked=True then begin count:=count+1; ParForm.CountEdit.Text:=IntToStr(count); ShowMessage('Influence'); end; end; ActionToAgent(s,rounde); end; end; end; until(AvailableAgents=0)or(ParForm.Task.NrOfTaskUnitsAllocated=ParForm.Task.NrOfTaskUnits); end; procedure TSystem.ActionToAgent(s,rounde:integer); var a,c:integer; RoundAgent:string; begin for a:=0 to NrOfAgents-1 do begin if (Agent[a].Skill[s].Choice=True) AND (Agent[a].Free=True) then


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begin c:=ParForm.Task.FirstAvailableCycle(s); if c< ParForm.Task.NrOfCycles then begin Agent[a].Free:=False; ParForm.Task.Taskunit[c,s].Open:=False; ParForm.Task.NrOfTaskUnitsAllocated:= ParForm.Task.NrOfTaskUnitsAllocated+1; if ParForm.AllCheckBox.Checked=True then begin RoundAgent:=IntToStr(rounde+1)+ ' / '+IntToStr(a+1); ParForm.TTaskFrame.TaskGrid1.Cells[c+1,s+1-tvar]:=RoundAgent; end; end; if ParForm.Task.AvailableActions(s)= 0 then Agent[0].Skill[s].Available:=False; end; end; end; Main Process procedure TSystem.Start; var k,NrOfTasks,rounde:integer; begin remcounter:=0; NrOfTasks:=StrToInt(ParForm.NrOfTasksEdit.Text); tvar:=-ParForm.Task.NrOfVariation; ///handig bij loop waar tvar:=tvar+ Task.NrofVariation IntTimeTotToZero; TotalTimeToZero; for k:=0 to NrOfTasks-1 do begin WTimeTotToZero; tvar:=tvar+ParForm.Task.NrOfVariation; if tvar>(StrToInt(ParForm.NrofSkillsEdit.Text))then tvar:=tvar- StrToInt(ParForm.NrofSkillsEdit.Text); NextTask(k); rounde:=0; while (ParForm.Task.NrOfTaskUnitsDone< ParForm.Task.NrOfTaskUnits) do begin InteractionTimeToZero; WorkTimeToZero; if ParForm.CycleCheckBox.Checked=TRUE then begin ShowMessage ('New Round'); ParForm.Edit2.Text:=IntToStr(rounde+1); ParForm.ShowStatesAgents; end; if ParForm.AgVarCheckBox.Checked=True then Turnoverfit(rounde);//TurnoverNewComerLow(rounde); if ParForm.AllocationRadioGroup.ItemIndex =0 then Allocate(rounde+k*ParForm.Task.NrOfRounds); if ParForm.AllocationRadioGroup.ItemIndex =2 then Generalise(rounde+k*ParForm.Task.NrOfRounds); if ParForm.AllocationRadioGroup.ItemIndex =1 then Specialise(rounde,k);

Appendix I: Relevant Computer Code

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Perf(rounde+k*ParForm.Task.NrOfRounds,k); rounde:=rounde+1; SysIntTimeTot:=SysIntTimeTot + SysIntTime; WorkTimeTot:=WorkTimeTot+ WorkTime; end; ParForm.WorkTimeGraph[k,NrOfAgents]:=WorkTimeTot; TotalTime:=TotalTime+WorkTimeTot; ParForm.WorkTimeGraph[StrToInt((ParForm.NrOfTasksEdit.Text))+ 1,ParForm.System.NrOfAgents]:=TotalTime; ParForm.WorkTimeGraph[k+1,ParForm.System.NrOfAgents+1]:=TotalTime; ParForm.ShowStatesAgents; end; end; Performance procedure TSystem.Perf(rounde,k:integer); var a: integer; begin for a:=0 to NrOfAgents-1 do begin if Agent[a].Present=True then Agent[a].Perf(rounde,k,a); ParForm.PerfGraph[rounde+1,a]:=Agent[a].WorkTime; //graphic van agent ParForm.WorkTimeGraph[k,a] :=Agent[a].WorkTimeTot; ParForm.WorkTimeGraph[StrToInt(ParForm.NrOfTasksEdit.Text)+1,a]:= Agent[a].TotalTime; if Agent[a].WorkTime>WorkTime then WorkTime:=Agent[a].WorkTime; end; ParForm.PerfGraph[rounde+1,NrOfAgents]:=WorkTime; //graphic van system end; procedure TAgent.Perf(rounde,k,a:integer); var s: integer; begin for s:=0 to NrOfSkills-1 do begin if (Skill[s].Choice = TRUE) AND (Skill[s].Active = TRUE) then ChoiceTrueActiveTrue(rounde,k,a,s); if (Skill[s].Choice = FALSE)AND (Skill[s].Active = TRUE)then ChoiceFalseActiveTrue(rounde,a,s); if Skill[s].Active = FALSE then ActiveFalse(rounde,s); end; WorkTimeTot:=WorkTimeTot+WorkTime; TotalTime:=TotalTime+WorkTimeTot; end; procedure TAgent.ChoiceTrueActiveTrue(rounde,k,a,s:integer); var c:integer; RelMot,RelExp:real; RoundAgent:string; begin RelMot:=(1-Skill[s].ExpMotRate)*(Skill[s].Motivation/Skill[s].MotMax);


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RelExp:=Skill[s].ExpMotRate*(Skill[s].Expertise/ Skill[s].ExpMax); c:=ParForm.Task.FirstCycleToDo(s); if c<ParForm.Task.NrOfCycles then begin ParForm.Task.TaskUnit[c,s].Done:=True; RoundAgent:=IntToStr(rounde+1)+ '/'+IntToStr(a+1); ParForm.TTaskFrame.TaskGrid1.Cells[c+1,s+1-tvar]:=RoundAgent; ChartForm.AllocationGrid.Cells[c+1+k*ParForm.Task.NrOfCycles,s+1]:=RoundAgent; ParForm.Task.NrOfTaskUnitsDone:= ParForm.Task.NrOfTaskUnitsDone+1; if ParForm.PerfCheckBox.Checked=True then ShowMessage('Performed'); Skill[s].Used[rounde]:=TRUE; //// Skill[s].WorkTime:= StrToInt(ParForm.DurEdit.Text)/(RelMot+RelExp); WorkTime:=WorkTime+Skill[s].WorkTime; //worktime agent=sum(worktime skills) Skill[s].Learning; Skill[s].BoredomRecovery; ParForm.ExpGraph[rounde+1,a,s]:=Skill[s].Expertise; ParForm.MotGraph[rounde+1,a,s]:=Skill[s].Motivation; Free:=True; end; end; procedure TAgent.ChoiceFalseActiveTrue(rounde,a,s:integer); begin Skill[s].Used[rounde]:=False;//// Skill[s].WorkTime:=0; Skill[s].Forgetting; Skill[s].BoredomRecovery; ParForm.ExpGraph[rounde+1,a,s]:=Skill[s].Expertise; ParForm.MotGraph[rounde+1,a,s]:=Skill[s].motivation; end; procedure TAgent.ActiveFalse(rounde,s:integer); begin Skill[s].Used[rounde]:=False;//// Skill[s].WorkTime:=0; Skill[s].Forgetting; Skill[s].BoredomRecovery; end; Influence procedure TSystem.SelfOrganisation(rounde,k:integer); begin InitialChoice; AllocateSelf(rounde+k*ParForm.Task.NrOfCycles); end; procedure TSystem.AllocateSelf(c:integer); var s:integer; begin for s:=0 to Agent[0].NrOfSkills-1 do begin if Agent[0].Skill[s].Active=true then


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repeat MakeEnvironment(s); if ParForm.ProcesBox.Checked= True then ShowMessage('Environment'); Influence(s); if SysIntTime>5000 then SameAs(s); //500 voor results simpatpaper ParForm.IntGraph[c+1]:=SysIntTime; //grafiek!! until CountIdoAgents(s)=1; end; FinalState(c); end; procedure TSystem.MakeEnvironment(s:integer); begin if CountIDoAgents(s)> 1 then MakeIEnv(s); if CountIDoAgents(s)=0 then MakeYouEnv(s); if ParForm.ProcesBox.Checked=True then ParForm.ShowStatesAgents; end; procedure TSystem.MakeIEnv(s:integer); var a1,a2,t:integer; I,Y:real; DiffII, DiffYouYou:real; begin for a1:=0 to NrOfAgents-1 do begin if Agent[a1].Skill[s].Choice=True then //agent begin I :=0; Y :=0; t:=0; DiffII:=0; DiffYouYou:=0; for a2:=0 to NrOfAgents-1 do begin if (a1<>a2) AND (Agent[a2].Skill[s].Choice=True) then //omgeving begin t:=t+1; I:= I + (Agent[a2].Skill[s].I); Y:= Y + (Agent[a2].Skill[s].You); DiffII :=DiffII+ Abs(Agent[a1].Skill[s].I -Agent[a2].Skill[s].I); DiffYouYou:=DiffYouYou+ Abs(Agent[a1].Skill[s].You-Agent[a2].Skill[s].You); end; end; if t=0 then t:=1; I:=I/t; Y:=Y/t; //gewogen gemiddelde van alle I's en Y's Agent[a1].EnvSkill[s].DiffII :=DiffII/t; Agent[a1].EnvSkill[s].DiffYouYou :=DiffYouYou/t; Agent[a1].EnvSkill[s].I := I; Agent[a1].EnvSkill[s].You:= Y; //Agent[a1].EnvSkill[s].Power:=t/10; Agent[a1].EnvSkill[s].Power:=1/10; Agent[a1].EnvSkill[s].Choice:=True; end; end; end; procedure TSystem.MakeYouEnv(s:integer); var a1,a2,t:integer; I,Y:real;


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begin for a1:=0 to NrOfAgents-1 do //agents begin I :=0; Y :=0; t:=0; for a2:=0 to NrOfAgents-1 do //omgeving begin if a1<>a2 then begin t:=t+1; I:= I + (Agent[a2].Skill[s].I); Y:= Y + (Agent[a2].Skill[s].You); end; if t=0 then t:=1; I:=I/t; Y:=Y/t; //gewogen gemiddelde van alle I's en Y's Agent[a1].EnvSkill[s].I := I; Agent[a1].EnvSkill[s].You:= Y; //Agent[a1].EnvSkill[s].Power:=t/10; Agent[a1].EnvSkill[s].Power:=1/10; Agent[a1].EnvSkill[s].Choice:=False; end; end; end; procedure TSystem.Influence(s:integer); var a:integer; begin for a:=0 to NrOfAgents-1 do begin if (CountIDoAgents(s)<>1) then begin Agent[a].RememberOldValues(s); //voor SameAs if Agent[a].Skill[s].Choice=True then Agent[a].InfluenceAgent(s); if CountIDoAgents(s)=0 then Agent[a].InfluenceAgent(s); if Agent[a].IntTime>SysIntTime then SysIntTime:=Agent[a].IntTime; end; end; end; procedure TAgent.InfluenceAgent(s:integer); begin if (Skill[s].Expertise>Skill[s].ExpThresh) then begin if EnvSkill[s].Choice = TRUE then WeDo(s, EnvSkill[s].DiffII); if EnvSkill[s].Choice = FALSE then YouDo(s,EnvSkill[s].DiffYouYou); if Skill[s].IntTime>IntTime then IntTime:=Round(Skill[s].IntTime); end; end; procedure TAgent.WeDo(s:integer; DiffII:real); begin Skill[s].I:= EnvSkill[s].Inhibit (EnvSkill[s].I, Skill[s].I, DiffII, Skill[s].Inhibition,EnvSkill[s].Power); Skill[s].You:= EnvSkill[s].Excitate(EnvSkill[s].I, Skill[s].You, DiffII, Skill[s].Excitation,EnvSkill[s].Power);


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Skill[s].Choice:= Skill[s].I>Skill[s].You; end; procedure TAgent.YouDo(s:integer;DiffYouYou:real); begin Skill[s].I:= EnvSkill[s].Excitate(EnvSkill[s].You,Skill[s].I, DiffYouYou, Skill[s].Excitation,EnvSkill[s].Power); Skill[s].You:= EnvSkill[s].Inhibit( EnvSkill[s].You,Skill[s].You, DiffYouYou,Skill[s].Inhibition,EnvSkill[s].Power); Skill[s].Choice:= Skill[s].I>Skill[s].You; end; function TEnvSkill.Inhibit(x,y,l1,l2,l3:real):real; begin Result:= y-(x*y*l1*l2*l3); end; function TEnvSkill.Excitate(x,y,l1,l2,l3:real):real; begin Result:= y + x*(1-y)*l1*l2*l3; end;

Samenvatting

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Deze vaardigheden beschrijf ik met behulp van twee variabelen: expertise geeft aan hoe goed een bepaalde vaardigheid wordt beheerst, en motivatie is bepalend hoe leuk de agents het vinden om een bepaalde vaardigheid te gebruiken c.q. een bepaalde action uit te voeren. Met behulp van de waarden van deze variabelen en een drempelfunctie wordt bepaald of de agents daadwerkelijk een bepaalde vaardigheid willen gebruiken. Op basis van deze uitkomst beïnvloeden de agents elkaar door middel van exciterende en inhiberende verbindingen. Met dit beïnvloedingsproces probeert elke agent zijn eigen voorkeur te handhaven door er voor te zorgen dat de andere agents een voorkeur krijgen die complementair is aan de eigen voorkeur. Dit leidt tot een taakverdeling op basis waarvan de taak wordt uitgevoerd. Het uitvoeren van de taak impliceert veranderingen van expertise en motivatie van de agents hetgeen dan weer kan leiden tot een herverdeling van de taak.

Het derde hoofdstuk behandelt de stap van het model naar het simulatieprogramma WORKMATE. Het geeft een geformaliseerde beschrijving van een leer– en vergeetfunctie die de dynamiek van de expertise bepalen en een verveling– en herstelfunctie op basis waarvan de motivatie verandert. Op basis van de expertise, motivatie en coördinatietijd wordt de prestatie van de groep agents bepaald: hoe hoger de expertise en motivatie, en hoe lager de coördinatietijd, hoe beter de prestatie. Verder zet ik in dit hoofdstuk uiteen hoe de beïnvloeding tussen de agents plaatsvindt. Naast de geformaliseerde beschrijving van het model beschrijft het hoofdstuk drie pilot-experimenten die bedoeld zijn als verificatie van het model en WORKMATE. Het eerste experiment beschrijft hoe de coördinatietijd tussen agents groter wordt naarmate de expertiseverschillen tussen de agents kleiner worden. Het tweede experiment relateert dit gegeven aan de mate waarin een taak in de tijd verandert en laat zien hoe taakverandering leidt tot een grotere coördinatietijd, terwijl specialisatie binnen een taak leidt tot een kleinere coördinatietijd. Het derde experiment gaat in op de wederzijdse invloed van verveling en taakuitvoering. Uit dit experiment blijkt dat onder bepaalde omstandigheden de agents in staat zijn om door middel van taakrotatie hun verveling te reduceren.

Het fenomeen dat taakrotatie vanzelf ontstaat onderzoek ik verder in het vierde hoofdstuk. Hier beschrijf ik hoe verschillende gradaties van zelforganisatie, rotatiefrequentie en verveling zijn gerelateerd aan de ontwikkeling van expertise, motivatie en prestatie en het wel of niet optreden van taakrotatie. De resultaten laten zien dat met de mogelijkheid tot taakrotatie een systeem beter presteert dan een systeem waarbinnen de agents zich slechts specialiseren in een afzonderlijke vaardigheid. Verder blijkt dat onder bepaalde omstandigheden een taak die leidt tot een grote mate van verveling soms toch beter wordt uitgevoerd dan een taak die leidt tot weinig verveling.

In het vijfde en zesde hoofdstuk bouw ik voort op de kennis die ik op basis van de voorgaande experimenten heb verkregen. Beide hoofdstukken behandelen de flexibiliteit van taakgroepen, waarbij hoofdstuk vijf ingaat op de wijze waarop een groep zich aanpast aan externe veranderingen en hoofdstuk zes zich richt op de wijze waarop een groep en een nieuwkomer zich aan elkaar aanpassen. De experimenten die in hoofdstuk vijf zijn uitgevoerd beschrijven de invloed van taakdynamiek op de prestaties van twee taakgroepen, specialisten en generalisten. Ik test de hypothese dat de prestatie van specialisten afneemt wanneer de taakdynamiek toeneemt, terwijl de

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Samenvatting Zelforganiserende processen van taakverdeling zijn ordeningsprocessen die binnen een groep mensen die een taak moet uitvoeren kunnen optreden zonder dat er een ander systeem is dat die ordening bepaalt. Deze ordeningsprocessen beschrijven voor een belangrijk deel hoe een groep mensen haar eigen gedrag organiseert en vormen hiermee een relevant bedrijfskundig onderzoeksobject. Zelforganiserende processen van taakverdeling zijn tegelijkertijd erg lastig te onderzoeken, onder andere vanwege de meetbaarheid van de processen en de complexiteit van de samenhang van de onderliggende variabelen. Daarom heb ik gekozen voor computersimulatie als onderzoeksmethode. Hierbij heb ik gebruik gemaakt van de multi-agent benadering waarbij de interactie van meerdere gelijksoortige agents op relatief eenvoudige wijze kan worden gemodelleerd. De agents stellen hierbij de individuen voor die gezamenlijk een taak uitvoeren. Binnen de multi-agent benadering kunnen twee stromingen worden onderscheiden, een stroming die zich bezighoudt met de cognitieve kenmerken van de agents en een stroming die zich vooral richt op de sociale interactie tussen de agents. In dit proefschrift wordt gepoogd beide stromingen te verenigen middels agents met zowel cognitieve als sociale kenmerken.

In het eerste hoofdstuk van het proefschrift schets ik de context waarbinnen ik de vraag hoe een groep mensen zijn eigen gedrag organiseert tracht te beantwoorden. Hierbij relateer ik het begrip zelforganisatie aan de bedrijfskundige literatuur en richt me hierbij met name op de vier randvoorwaarden voor zelforganisatie zoals geschetst door Morgan (1984). Vervolgens maak ik een vergelijking tussen organisaties en hersenen omdat de hersenen de meest bekende zelforganiserende systemen zijn. Daarnaast baken ik in dit hoofdstuk het uiteindelijke object van onderzoek, zelfsturende teams, af. Tot slot betoog ik waarom multi-agent simulatie is gebruikt in plaats van meer reguliere methoden zoals vragenlijsten, interviews of observatiestudies.

Het tweede hoofdstuk beschrijft het model dat ten grondslag ligt aan alle simulatiestudies die in het proefschrift worden beschreven. Het model beschrijft taakcomponenten en teamcomponenten die tezamen het taakverdelingsproces beïnvloeden. Drie taakcomponenten beschrijven de complexiteit van de taak: component complexity, i.e. het aantal vaardigheden dat nodig is om een taak uit te voeren, coordinate complexity, i.e. de wijze waarop de verschillende onderdelen van de taak aan elkaar zijn gerelateerd, en dynamic complexity, dat de mate aangeeft waarin een taak verandert in de tijd. In dit proefschrift besteed ik alleen aandacht aan component en dynamic complexity en laat ik coordinate complexity buiten beschouwing. In het model wordt een taak gerepresenteerd als een matrix van actions en cycles. Een action is een deeltaak waarvoor precies 1 vaardigheid nodig is om die uit te voeren. Het aantal cycles geeft aan hoe vaak een action moet worden uitgevoerd.

De teamcomponenten betreffen de agents waaruit het team bestaat. De eigenschappen van de agents kunnen worden onderverdeeld in individuele en sociale eigenschappen. De sociale eigenschappen zoals macht en attractie laat ik in dit proefschrift buiten beschouwing. De individuele eigenschappen betreffen de vaardigheden van de agents.


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generalisten juist dan beter zouden presteren. De resultaten ondersteunen deze hypotheses slechts gedeeltelijk omdat leer- en motivatie effecten het taakverdelingsproces op een veel complexere wijze beïnvloeden. Op basis hiervan concludeer ik dat afwezigheid van taakdynamiek weliswaar leidt tot specialisatie en een hoge taakdynamiek leidt tot generalisatie, maar dat in het algemeen de prestatie het hoogst is wanneer de dynamiek laag is. Daarnaast blijkt dat zonder taakdynamiek de specialisten duidelijk beter presteren dan de generalisten. Situaties met een hoge taakdynamiek bieden geen mogelijkheid om vaardigheden te ontwikkelen hetgeen de verschillen tussen specialisten en generalisten teniet doet en daarmee ook de verschillen tussen hun prestaties.

De experimenten met nieuwkomers in hoofdstuk zes beschrijven de prestaties van twee soorten taakgroepen, een groep waar onlangs iemand is uitgevallen en een groep die vanwege de werkdruk iemand extra nodig heeft. Voor beide groepen zijn condities getest met nieuwkomers die specialist of generalist zijn en een controleconditie zonder nieuwkomer. Hiermee heb ik de hypothese getest dat een groep die iemand extra nodig heeft vanwege de werkdruk beter presteert wanneer die nieuwkomer een generalist is. De groep die iemand extra nodig heeft omdat een voormalige medewerker is vertrokken zou het meest gebaat zijn bij een nieuwkomer die gespecialiseerd is in hetzelfde als de voormalige medewerker. Ik heb de ontwikkeling van de taakverdeling en prestatie bestudeerd, met expertise en motivatie als procesvariabelen. De resultaten ondersteunen de hypothesen slechts deels, aangezien zowel de specialisten als de generalisten alleen bijdragen aan een betere prestatie in de groep waarbij iemand is uitgevallen. Alleen in dit geval is er ruimte voor de nieuwkomer om te integreren in de groep zonder dat het taakverdelingsproces zo ernstig verstoord wordt dat dit ten koste gaat van de prestatie.

In hoofdstuk zeven beschrijf ik de conclusies die ik op basis van de experimenten heb getrokken en relateer deze aan de vier randvoorwaarden voor zelforganisatie zoals beschreven door Morgan (1984). Hierbij concludeer ik dat hoewel dit proefschrift er misschien slechts deels in is geslaagd een relatie te beschrijven tussen zelforganiserende processen van taakverdeling en de randvoorwaarden van Morgan, het niettemin succesvol is gebleken om deze processen te relateren aan gedragstheorie.

Tot besluit beschrijf ik in het discussiehoofdstuk achtereenvolgens de wetenschappelijke bijdrage van dit proefschrift, de bedrijfskundige bijdrage, de validatie van het model, de sterktes en zwaktes van het proefschrift, en ideeën voor toekomstig onderzoek. De wetenschappelijke bijdrage van dit proefschrift bestaat uit vijf onderdelen: het eerste onderdeel beschrijft dat mijn benadering kan worden gebruikt als platform om verschillende psychologische theorieën en modellen te integreren. Deze integratie kan bijdragen aan de ontwikkeling van de sociale en organisatiepsychologie. Ten tweede biedt het model dat in dit proefschrift is gebruikt een beschrijving die psychologisch realistischer is dan een aantal bestaande multi-agent modellen. Ten derde bieden de studies die hier zijn besproken een systematische beschrijving van onderliggende processen die in het dagelijks leven moeilijk meetbaar zijn. Ten vierde toont dit proefschrift aan dat zelforganiserende processen van taakverdeling uiterst relevante processen zijn om te onderzoeken. Ten vijfde heb ik niet

Samenvatting

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alleen relevante aspecten van groepsprocessen bestudeerd, maar tevens een instrument ontwikkeld om deze processen te onderzoeken.

De meest belangrijke bedrijfskundige bijdrage van dit proefschrift is de mogelijkheid die simulatiestudies bieden voor het formuleren van nieuwe theorieën: Het concept van zelforganiserende processen van taakverdeling biedt inzicht in een aantal fundamentele organisatieprincipes. Deze inzichten worden beschreven aan de hand van de relatie tussen de onderzoeksresultaten en de randvoorwaarden voor zelforganisatie van Morgan. Daarnaast biedt dit proefschrift een bijdrage op grond van de context waarbinnen het is ontstaan waarin computersimulatie deel uitmaakt van een veel grotere ontwikkeling met betrekking tot het gebruik van complexiteitstheorie en geavanceerde informatiesystemen. Deze ontwikkeling heeft tevens geleid tot een groeiende vraag voor computersimulatiemodellen, bijvoorbeeld in het veld van organisatieadvies.

De validatie van het model bespreek ik aan de hand van de drie door Holland (1998) geformuleerde manieren waarop modellen kunnen worden gevalideerd. De eerste en meest traditionele wijze gaat in op validatie door de empirie. Hoewel de modellen en theorieën gebruikt voor dit onderzoek wel empirisch gevalideerd zijn, zijn de processen en uitkomsten van het model dat niet. Ze vertonen weliswaar een bepaalde overeenkomst met de werkelijkheid, maar deze overeenkomsten zijn niet getoetst. De tweede validatiewijze beschrijft validatie door verificatie: vertoont het model dat gedrag waarvoor het is ontworpen? Hoofdstuk drie beschrijft de verificatie van het model. Hierin stel ik dat de agents niet alleen het gedrag vertonen dat in lijn ligt met de eigenschappen van het model, maar dat ze in interactie tevens in staat zijn emergente eigenschappen te ontwikkelen, zoals de eigenschap van taakrotatie. Validatie kan ook plaatsvinden door middel van het genereren van ideeën over complexe situaties. In dit proefschrift onderstrepen de systematische beschrijvingen van de endogene en exogene variabelen het belang om taakverdelingsprocessen als belangrijk onderdeel van groepsdynamische processen in teams te onderzoeken.

In het laatste deel van hoofdstuk acht beschrijf ik de sterktes en zwaktes van dit proefschrift en bespreek ik enkele mogelijkheden voor verder onderzoek. Allereerst ga ik in op de discrepantie tussen het uitgebreide model zoals beschreven in hoofdstuk twee en de onderzoeken in de hoofdstukken daarna. Op basis hiervan stel ik dat een aantal belangrijke elementen in dit proefschrift onderbelicht blijven en nog nadere uitwerking verdienen. Voorts beschouw ik een aantal uitdagingen om de beperkingen van het gebruikte model en de onderzoeksdesigns op een aantal punten verder uit te werken. Tot slot poneer ik een aantal nieuwe ideeën voor vervolgonderzoek. Hierbij stel ik uitdrukkelijk dat het in het bijzonder bij simulatieonderzoek vaak lastiger is een simpel model te hanteren dan een plausibele beschrijving van een gevarieerde werkelijkheid te geven.

Ik eindig dit proefschrift met de stelling dat binnen elke discipline ruimte moet bestaan voor fundamenteel onderzoek, ook al levert dit niet meteen bruikbare resultaten op.

university of groningen self-organising processes …...een proefschrift vergeleken met het baren...

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