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Advanced Review

Agent-based models in sociologyFederico Bianchi∗ and Flaminio Squazzoni

This article looks at 20 years of applications of agent-based models (ABMs) insociology and, in particular, their explanatory achievements and methodologicalinsights. These applications have helped sociologists to examine agent interactionin social outcomes and have helped shift analyses away from structural andaggregate factors, to the role of agency. They have improved the realism of themicro-behavioral foundations of sociological models, by complementing analyticmodeling and game theory–inspired analyses. Secondly, they have helped usto dissect the role of social structures in constraining individual behavior moreprecisely than in variable-based sociology. Finally, simulation outcomes havegiven us a more dynamic view of the interplay between individual behavior andsocial structures, thus promoting a more evolutionary and process-based approachto social facts. Attention here has been paid to social norms, social influence,and culture dynamics, across different disciplines such as behavioral sciences,complexity science, sociology, and economics. We argue that these applicationscan help sociology to achieve more rigorous research standards, by promotinga modeling environment and providing tighter cross-disciplinary integration.Recently, certain methodological improvements toward model standardization,replication, and validation have been achieved. As a result, the impact of thesemodels in sociology is expected to grow even more in the future. © 2015 WileyPeriodicals, Inc.

How to cite this article:WIREs Comput Stat 2015, 7:284–306. doi: 10.1002/wics.1356

Keywords: agent-based models; sociology; social norms; social influence;collective behavior; social networks

INTRODUCTION

Agent-based models (ABMs) are computer simula-tions of social interaction between heterogeneous

agents (e.g., individuals, firms, or states), embed-ded in social structures (e.g., social networks, spa-tial neighborhoods, or institutional scaffolds). Theseare built to observe and analyze the emergence ofaggregate outcomes.1,2 By manipulating behavioralor interaction model parameters, whether guidedby empirical evidence or theory, micro-generativemechanisms can be explored that can account formacro-scale system behavior, that is, an existing

∗Correspondence to: [email protected]

Department of Economics and Management, University of Brescia,Brescia, Italy

Conflict of interest: The authors have declared no conflicts of interestfor this article.

time series of aggregate data or certain stylizedfacts.3,4

The origins of ABMs in sociology can be tracedback to the pioneering contributions by James S. Cole-man and Raymond Boudon in the 1960s5–7 and thepublication of the first two volumes of The Journalof Mathematical Sociology in 1971. These includedtwo important articles by James M. Sakoda andThomas C. Schelling on segregation dynamics.8,9 Inthese contributions, studying social outcomes by mod-eling agent behavior and interaction in a computerwas considered an alternative to the functionalistic,hyper-theoretical, macro-oriented social system theo-ries that dominated sociology at that time.

However, it was only from the 1990s that ABMapplications reached a critical mass. This develop-ment was due to the increasing computing power andthe diffusion of the first open source ABM platforms.

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WIREs Computational Statistics Agent-based models in sociology

These platforms made explicit individual behaviormodels possible for the first time, without requiringexcessive computing skills by the modeler. Initial soci-ological applications in the late 1990s covered the fol-lowing areas: cooperation and social norms, diffusion,social influence, culture dynamics, residential ethnicsegregation, political coalitions, and collective opin-ions, to name but a few.10–14

All these applications demonstrated that com-putational models can look at the dynamic natureof social facts better than most other social scientificmethods. These include analytical equation–basedmodels, used in standard economics and game theory;statistical regression models, used in macro-sociology;and un-formalized, descriptive accounts, used inqualitative sociology. Due to mathematical restric-tions, standard game theory and analytical modelingcannot account for the irreducible heterogeneity ofsocial behavior or look at out-of-equilibrium socialdynamics, both of which are intrinsic to the ABMapproach. In this sense, the ABM approach is closerto behavioral game theory, which studies a varietyof preferences and motivations through experiments,rather than standard rational choice theory, wherehomogeneous individual selfishness is assumed. Whilevariable-based statistical models cannot easily dealwith micro-generative processes, which are key toABMs, descriptive, qualitative accounts cannot dis-entangle the effects of social networks and at thesame time look at space, time, and large-scale socialprocesses in the same way as ABMs can.

By reviewing the first wave of ABMs in sociol-ogy in the 1990s, Macy and Willer15 emphasized thatABMs are instrumental when the macro patterns ofsociological interest are not the simple aggregation ofindividual attributes but the result of bottom-up pro-cesses at a relational level. Time has progressed sincethis influential review and advances have been madeboth in the extent and scope of ABM applications, inthe number of sociological publications, and in theirmethodological rigor. This article aims to report onthese recent advances by considering examples, whichlooked at the importance of behavioral factors, casesthat tested the effect of structural factors, and mod-els that pointed to the dynamic interplay of individualbehavior and social structures.

The article is organized as follows. The fol-lowing paragraph looks at ABMs, which investigatedsocial norms in cooperation and competition pro-cesses among individuals in stylized interaction con-texts. This is one of the most vibrant ABM fields,where sociology and behavioral game theory have use-fully interacted.16 Their results showed the importanceof considering the fundamental heterogeneity of social

behavior, the subtle nuances of individual rationality,and the influence of social contexts in understandingaggregate behavior. They also showed that sociolog-ical relevance increases when the interplay betweenindividual behavior and social networks is looked atin a more dynamic, coevolutionary way.

The third paragraph looks at examples of ABMs,which investigated social influence mechanisms andthe influence of certain structural constraints on socialoutcomes, such as residential segregation, stratifica-tion, and collective opinions. These examples help usto understand that certain facets of the social structuremight influence social connections among individuals.As a result, they may have wider implications, includ-ing not only pressure toward social uniformity andconvergence but also persistence of diversity in cul-ture, norms, or attitudes. At the same time, they helpus to conceive the constructive role of the interplay ofbehavioral mechanisms and social structures in under-standing the emergence of collective phenomena.

Finally, in the conclusion, we summarize the keyfindings and discuss the methodological implications.

COOPERATION AND SOCIAL NORMS

Social life is rich with complex forms of cooper-ation between unrelated individuals that are chan-neled through social norms and institutions. Donatingblood, being a witness at a trial, or reviewing an arti-cle for a journal would not be possible if we werenot able to overcome the temptation of self-interestto benefit others with our own effort. Given that natu-ral and social selection tend to encourage competition,social norms and institutions must exist to providea context for cooperation. Understanding in whichcontexts and for what reasons individuals can col-lectively generate social welfare despite self-interestis one of the most important missions of socialscience.

We will look at the importance of certain socialmechanisms in promoting cooperation in hostile envi-ronments, where there is a conflict between individualself-interest and group outcomes. Examples of thesemechanisms could be direct and indirect reciprocity,reputation, social punishment, trust, and socialconventions. In this field, fruitful cross-fertilizationalready exists between behavioral game theory andABM sociological analysis of social norms, withinteresting extensions and modifications of stan-dard game theory. Here, simulations were used tocomplement problems of analytic tractability ofstandard game theory as well as for exploring depar-tures from its deductive, equilibrium-dominatedframework.

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Direct ReciprocityA key mechanism of social life is reciprocity, i.e., aform of conditional cooperation between related orunrelated individuals, which can be either direct orindirect.17 Direct reciprocity means that two individ-uals are expected to cooperate if the probability oftheir future encounter exceeds the cost/benefit ratioof the altruistic act at an individual level. In this case,it is likely that certain aspects of social structure canhave significant implications for cooperation as theyinfluence the probability of encounters between twoindividuals, and so the type of behavior they areexposed to.18

It is widely acknowledged that the embeddednessof agents in a spatial structure dramatically increasescooperation, as this determines a higher probabilityof encounter between correlated agents.19 An interest-ing problem is to understand whether this can alsohappen in non-spatially related structures. A goodABM example of this is a study by Cohen, Riolo, andAxelrod on an iterated Prisoner’s Dilemma20 (see alsoNowak and Sigmund21). They simulated a popula-tion of agents, who could cooperate or defect, recipro-cate their opponent’s behavior (i.e., cooperating withcooperators and defecting with defectors), and imi-tate the behavior of the highest fitted individual theyencountered (with some noise), thus learning behav-ioral strategies from the social environment. Theymanipulated the initial network topology that con-nected agents to each other, by testing random encoun-ters, spatial neighborhoods, small-world networks,and fixed networks. Results showed that even thesole persistence of interaction patterns from initiallyrandom encounters could make cooperation possiblebetween selfish agents as it preserves favorable condi-tions for direct reciprocity, e.g., cooperators interact-ing more frequently among each other and receivinghigher payoffs. This situation did not vary when agentbehavior was spatially correlated, i.e., spatial effectsexisted between neighboring agents (see also Axelrodet al.22).

Although important, these examples neitherassume a considerable influence of the social struc-ture in shaping individual behavior nor look at thesocial mechanisms that exist to help individuals pre-dict other agents’ behavior. If we consider that ourlife is mostly structured into social groups, it is prob-able that cooperation is influenced by group identity,so that we prefer to cooperate with in-group membersand are less fair with outsiders. Coherently, in manycircumstances, we tend to use tags or etiquettes (e.g.,color of skin, group dress style, or any other obser-vational trait) to predict behavior,23 which can evenmake us unconscious victims of stereotypes. The point

here is that group identity or tags could substitute ormagnify direct reciprocity.

Hales24 built an evolutionary model that showedthat cooperation could emerge in a mixed popula-tion of cooperators and defectors with randomly dis-tributed tags playing one-shot Prisoner’s Dilemmagames with in-group members. Results showed thatthe formation of same-tag local clusters, in whichcooperative groups eventually outperformed nonco-operative ones, could work even without assuming thememory of past experience, nor reciprocity-orientedstrategies. Hammond and Axelrod25,26 modeled apopulation of agents with different tags who coulddecide whether to cooperate or defect with in-groupand out-group agents. Without building in-groupfavoritism in the model, simulations showed thatthe evolution of cooperation in a spatial structurecould be sustained by the emergence of a domi-nant ‘ethnocentric’ strategy, that is, by which agentscooperated with in-group members and defected withoutsiders, through the formation of local clusters ofsame-tag agents. Recently, Bausch27 has questionedthe tag-driven nature of the results of Hammond andAxelrod, arguing that higher levels of cooperationmight even be obtained by simply constraining interac-tion and reproduction to occur locally, without mod-eling different tags and preferential cooperation.

While these examples examined the importanceof forward-looking strategies in repeated dyadicinteraction, cooperation may also emerge frombackward-looking strategies, with individuals capableof learning from past experience and adjusting theirbehavior dynamically. Building on previous work onstochastic learning algorithms,28 Macy and Flache29

built a series of models that included a variety oftwo-person cooperation dilemmas. Their resultsshowed that adapting backward-looking agents couldgenerate a self-reinforcing cooperative equilibriumbut only within a narrow range of intermediate levelsof the agents’ aspiration. Mutual defection was morelikely if agents had low or high aspiration levels as inthese cases the context made defection worthwhile,due to agent inertia (low aspiration) or individualdissatisfaction (high aspiration).

The situation can change if agents could exploitforms of interpersonal commitment against therisk of being cheated. In this respect, followingexperimental research about commitment in dyadicexchange, Back and Flache30 looked at the viabilityof committing—i.e., acting unconditionally coopera-tively with some partners who have previously provedto be reliable—against a wide spectrum of otherexchange strategies in a competitive environment.Results showed that commitment-based strategies



TABLE 1 The Impact of Referee Behavior on the Quality andEfficiency of Peer Review in Various Selective Environments (Ref 31,p. 4.3)

Scenario

Evaluation

Bias (%)

Resource

Loss (%)

Reviewing

Expenses (%)

75% of published submissions

No reciprocity 14.10 5.69 23.47

Indirect reciprocity 12.58 6.51 44.16

Fairness 13.14 7.48 40.61




Fairness 15.68 8.60 38.68




Fairness 19.52 8.32 38.29

In ‘No reciprocity’, the reliability of scientists as referees was random. In‘Indirect reciprocity’, referees were reliable if they had published as authors inthe previous round, otherwise they reciprocated rejection by being unreliable.In ‘Fairness’, referees were reliable if they had received pertinent evaluationswhen authors in the previous round, whether they had been published ornot. The opposite was true in case of impertinent evaluation. Evaluationbias measured the number of low quality articles that were published whenthey did not deserve to be. Resource loss measured the average number ofresources at the system level that were wasted because of unpublished authors,who deserved to be published, compared with the optimal solution, i.e.,when only the best authors were published. Reviewing expenses measuredthe percentage of resources spent by agents for reviewing compared with theresources invested by submitting authors.

are more viable than even tolerant versions of directreciprocity, as they allow agents to create wider andmore efficient exchange networks, while avoidingthe vicious cycle of ‘keeping the books balanced’,which makes reciprocity-based strategies vulnerableto cascades of mutual retaliatory defection.

It is worth noting that recent ABM studies haveanalyzed the impact of reciprocity also in peer reviewand found a possible negative side of reciprocity whensocial sanctioning is absent or weak. Squazzoni andGandelli31 modeled the strategic behavior of refereesin a population of scientists called on to act as authorsand referees during the peer-review process in differ-ent competitive publication environments. Scenarioswhere referees were randomly reliable (i.e., providingmore or less pertinent evaluation of author submis-sions’ quality) were compared with others in whichreferees could strategically reciprocate past experi-ence as authors by being more or less reliable withnew authors. Their simulations showed that if ref-erees’ reciprocity is not inspired by fairness (con-tributing to scientific progress as a public good), butonly by past publication or rejection when authors,peer review generates dramatic publication bias and

allocates resources inefficiently (see Table 1; see alsoThurner and Hanel32; Squazzoni and Gandelli33).

Indirect Reciprocity and ReputationIt is worth noting that individuals can also cooperateindirectly via third parties. In these cases, individu-als could expect future benefits by cooperating witha counterpart from other partners, e.g., other groupmembers, or by accessing or being subject to repu-tational information, e.g., cooperating with someoneestablishes good reputation that will be awarded byothers.34

Behavioral and evolutionary research hasrecently shown that the complex cooperation scaffoldsthat characterize social life seem to primarily dependon these complex forms of indirect reciprocity.17 Thishas interesting sociological implications as socialrelationships pass from a dyadic to a triadic formand network effects are also included. This can helpus to understand why social evolution involves theestablishment of generalized forms of social exchangeand large groups of unrelated individuals beyonddirect reciprocity motives.

In this respect, many ABM studies have lookedat the impact of reputation as a form of indirectreciprocity.35,36 These studies emphasized two impor-tant functions of reputation: learning (accessing infor-mation about unknown partners via third parties,which was not previously available and/or was toocostly) and social control37,38 (monitoring and pun-ishing norm violators through socially shared reputa-tional signals).

As regards to learning, Boero et al.39 developedan ABM calibrated on behavioral data gathered froma laboratory experiment where subjects were asked totake investment decisions in a simulated financial mar-ket characterized by asymmetries of information anduncertainty. Subjects had different investment options,which were more or less risky and could receive/sendinformation by/to others, so mimicking the formationand circulation of reputational information. Resultsshowed, firstly, that subjects followed three typesof behavior, coherent with behavioral game theoryfindings, i.e., always cooperating with others bysharing reliable information, reciprocating reliableinformation only with reliable partners, and cheatingby always providing unreliable information to others.Secondly, results showed that socially sharing reputa-tional information was beneficial for the explorationcapabilities of agents in situations of uncertainty,independent of the quality of the information shared.Finally, they showed that reputation (social sharingof personal evaluation, even if potentially biased) was



more effective than personal experience (formation ofan opinion on the counterpart in direct interaction) indetecting reliable information partners and reducingthe amount of false reputational information in thesystem.

With regard to social control, Conte andPaolucci40 developed a model that also distinguished‘image’ from ‘reputation’ and focused on social pro-cesses of reputation formation and transmission.They simulated a population of agents that followedheterogeneous behavior, i.e., self-interest, altruism,and norm compliance, in a social dilemma situa-tion and manipulated simulation scenarios to addsocially shared evaluation of other agents’ behavior.Results showed that by allowing individuals to sharethe social cost of sanctioning against self-interestedbehavior, reputation provided room for evolutionarystability of cooperation at levels hardly achievableby other mechanisms, e.g., direct reciprocity or cog-nitively sophisticated trustful partners’ detection.Furthermore, they found that the circulation of falsebad reputation tended to protect normative behaviormore than leniency (false good reputation) or silence.This work has influenced a large body of ABMresearch on reputation as a social control device forgroup behavior.41–43

Social PunishmentAnother form of indirect reciprocity is social pun-ishment. Indeed, while reciprocating bad behaviorwith a bad behavior in some circumstances can cre-ate the conditions for cooperation, social life is fullof examples of individuals bearing a personal costfor punishing wrongdoers, e.g., an individual report-ing misbehavior to the police to benefit a victim. Thisbehavior is called ‘strong reciprocity’ as it implies adirect reduction of payoffs imposed on the cheater atthe expenses of the punisher without direct reciprocalbenefits for the latter.44

Empirically inspired by the case of mobilehunter-gatherer groups in the Late Pleistocene, Bowlesand Gintis45 have developed an ABM where a popula-tion of agents played an n-player Prisoner’s Dilemmathat mimicked cooperation problems in hunting, foodgathering, and common defense without any central-ized institution. They explored a mixed population ofegoists, cooperators, and strong reciprocators. Due tothe presence of self-interested agents, group benefitscould be eroded by the fact that certain individualscould exploit the collaborative work of others withoutthemselves contributing. They found that the robust-ness of cooperation depended on the coexistenceof these behaviors at a group level and that strong

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FIGURE 1 | Coexistence of behaviors and shirking rate in a typicalsimulation run (Reprinted with permission from Ref 45, p. 21 Copyright2004 Elsevier Ltd).

reciprocators were functional in keeping the level ofcheating under control in each group (see the shirkingrate as a measure of resources lost by the group due tocheating in Figure 1). This was due to the fact that thehigher the number of cooperators in a group withoutreciprocators, the higher the chance that the group dis-banded due to high payoffs for shirking. This meansthat group structure may be the key to evolutionarysocial selection, even more than individual strategies(see also the test on the case of team collaboration inorganizations by Carpenter et al.46). This is a relevantfinding as it paves the way to consider whether socialselection can be multilevel, working not only at agenetic-individual level but also at a social group level.

These findings were extended by Boyd et al.47 tosituations of public punishment (i.e., the establishmentof an institution, which monitors people’s behaviorand punishes wrongdoers by exploiting economies ofscale). Their results showed that in the case of insti-tutional punishment also, the presence of a minimalfraction of strong reciprocators intrinsically motivatedby social norms to support institutional punishmentby paying fees and help social monitoring is instru-mental to maintain cooperation over time.

More recently, Andrighetto et al.48 built an inter-esting ABM based on experimental data in a pub-lic goods game similar to the previous examples,where punishment was combined with normative sig-naling. In this case, agents were called on to decidewhether to cooperate by contributing to the publicgood or defect by exploiting other agents’ contri-bution, punishing defectors, and sending signals toothers about the appropriate amount of contributionexpected (i.e., the norm). As it is a focal point forwhat others expect as an appropriate contribution,signaling could affect individual preferences. Their



simulations showed that punishment accompanied bynorm signaling can ensure more robust cooperationat a lower cost for the group than when acting alone.They also showed that punishment is more effectivewhen norm communication has already proved to beimportant for the perception of the norm by individu-als. This socio-cognitive approach has been followedby other ABM studies to examine the cognitive coun-terpart of social norms and the importance of socialcontexts. These provide normative meaning and sig-nals for individuals in typical social dilemmas, usingan interesting mix of ABM, experimental and qualita-tive methods.49–52

TrustIn many cases, we provide relevant information, time,or money to others when we trust that they will honorour help. However, in competitive environments andin situations of information asymmetry, distrust couldprevail given that the potential benefit of interactingwith others could be lower than the future cost ofbeing cheated. On the other hand, when interactionis between strangers, with no previous experience ofeach other, a set of communication signals or tagsmight exist. These in turn could help individuals toconvey and recognize the degree of trustworthiness ofa potential partner and thus risk cooperation. This isthe case of taxi drivers and their relationships withcustomers, brilliantly documented by Gambetta andHamill.53

In order to look at the emergence of trust amongstrangers, Macy and Skvoretz54 built a model in whichagents could decide whether to engage or not ina Prisoner’s Dilemma game by learning to displayor mimic and recognize actual or fake signals oftrustworthiness and eventually imitating successfulstrategies from others. They assumed that agentswere embedded in a social network structure withneighbors and strangers through strong and weakties, respectively. Couples were randomly paired witha probability correlated with the social distance ofagents. They tested the effect of different payoffs fornot engaging in a risky exchange (i.e., an exit option)and the degree of the agents’ network embeddedness.Results showed that cooperation between strangerscould emerge in the long run, due to less costly exitpayoffs that allowed agents to build clusters of trustfulrelationships locally that gradually diffused via weakties, depending on the level of agent embeddedness.

Following experimental studies on cross-culturaldifferences on trust and commitment,55 Macy andSato56,57 tested the effect of spatial mobility on theemergence of trust and cooperation in a simulated

population of learning agents. These played a repeatedversion of the Prisoner’s Dilemma with an exit optionand the possibility to choose to play with a neighbor ora stranger with different opportunity and transactioncosts. Simulations found a curvilinear effect of mobil-ity on trust. Indeed, the ability to detect trustwor-thy partners emerged only beyond moderate levels ofmobility, which allowed agents to meet other partners.In case of higher levels of mobility, trust decreasedbecause agents could not appropriately discriminatetrust anymore.

These studies indicate that one of the mainchallenges for cooperation in trust situations is thecapability of agents to detect trustworthy partnersand build stable forms of interaction around them.In this respect, some studies have looked at partnerselection in dynamic networks.58,59 The idea here isthat not only might individual behavior vary fromperson to person and within the same person overtime, but social networks are also constantly changing.This reflects new opportunities or constraints for aperson when connected with another one. Behaviorand networks can change dynamically in a complexregime of possibilities/constraints that could havedramatic implications for macro behavior.

Dynamic networks are also important factors inestablishing trust. Bravo et al.60 calibrated an ABMon experimental data on the behavior of real sub-jects in a repeated trust game. They compared scenar-ios where agents were embedded in exogenously fixednetworks (e.g., random, scale-free, and small-worldnetworks) and scenarios with endogenous networks,where agents could select their partners according toa simple happiness function. They found that coop-eration dramatically increases in dynamic networks.Trustworthy agents tended to cluster around emerg-ing cooperators, who had more ties and ensured higherprofit to their respective partners. On the other hand,‘bad apples’ tended to be isolated over time losingboth profit and opportunities for exchange. Further-more, while different initial network conditions didnot affect this endogenous dynamics (see Figure 2),with more cooperative agents benefiting from an expo-nential growth of number of ties independently of theinitial network constraints, the final network topol-ogy in case of initial random or regular networks wasdifferent (see Figure 3).

These results were confirmed experimentally inan iterated Prisoner’s Dilemma.61 It was also con-firmed in a model on a helping game where Chiang62

allowed agents to use information of network char-acteristics (e.g., the structural attribute of the nodes)to strategize whether to cooperate or not. The coevo-lution of behavior and network created a crystallized



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Dynamic2Couples

Dynamic2k10

40 60 80 100

Agent number

No.

of l

inks

FIGURE 2 | Average number of links per agent in the‘Dynamic2couples’ (initial random coupling and broken ties werereplaced by only one of the two formerly linked agents) and‘Dynamic2k10couples’ (the same but starting from a regular network ofdegree 10) scenarios (Reprinted with permission from Ref 60, p. 489Copyright 2012 Elsevier Ltd).

configuration where cooperators had more ties andachieved higher profit so that cooperation outper-formed defection over time.

This fact would indicate that social structure canendogenously generate role differentiation that may berelevant in generating conditions favorable to cooper-ation. For instance, Eguíluz et al.63 simulated a spatialPrisoner’s Dilemma model where diverse social rolesemerged from dynamic networks with ‘leaders’, i.e.,agents obtaining a large payoff, who were then imi-tated by many others, ‘conformists’, that is unsatisfiedcooperative agents, who keep cooperating and finally,

‘exploiters’, i.e., defectors who have a larger payoffthan the average obtained by cooperators. By endoge-nously converging toward a small-world topology, thenetwork achieved a strong hierarchical structure inwhich the leaders played an essential role in sustain-ing cooperation. On the other hand, they found thatonce disruptions affecting leaders were introduced, adynamic cascade was found, which propagated defec-tion throughout the network.

ConventionsSocial life is full of examples of social interactionwhere it is of mutual interest for individuals to con-verge toward a dominant behavior, rather than com-pete on certain rewards at stake. We have devel-oped certain habits or conventions, e.g., language,monogamy versus polygamy in marriage, a partic-ular dress code, that help us coordinate with eachother more or less efficiently. Once established, theseconventions can even be institutionally enforced, e.g.,traffic rules. The challenge here is to understand theorigins of these social artifacts, given that any coor-dination game may have multiple possible equilibria,no initial preferable options exist, and outcomes areextremely sensitive to initial conditions, path depen-dence, and increasing returns.64

In order to understand this, Hodgson andKnudsen65 modeled a population of agents ran-domly located in a 100 × 2 cell ring that had todecide whether to drive clockwise or counterclock-wise around a ring to avoid collision. Agents werecharacterized by a limited vision of space, inertia,and a habituation level, i.e., the tendency to repeatpast behavior. Their simulations showed that theconvergence of agents toward a right/left convention

Dynamic2Couples(a) (b) Dynamic2k10

FIGURE 3 | Networks after 30 rounds of a typical simulation run of the ‘Dynamic2couples’ (a) and the ‘Dynamic2k10couples’ (b) scenarios(Reprinted with permission from Ref 60, p. 488 Copyright 2012 Elsevier Ltd).



1.00

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FIGURE 4 | Convergence of the population on a shared conventionfor each habituation level and for different error probabilities (Reprintedwith permission from Ref 65, p. 29 Copyright 2004 Elsevier Ltd). Thehigher the convergence value, the larger the diffusion of any givenright/left convention.

is higher when the level of habituation increases, inde-pendent of the error at the agent-level when estimatingother agents’ behavior (see Figure 4). Furthermore,they confronted agents with different cognitive capa-bilities of monitoring the environment. They foundthat although habit had a positive effect on the emer-gence of conventions even for omniscient agents,the most striking influence was found when agentswere boundedly rational, thus showing how habitcan complement individuals’ cognitive limitations inachieving coordination at a collective level.

Epstein66 built a similar model to investigate thelink between the strength of a convention and thecognitive costs that individuals have to pay to decidewhat to do. He simulated a population of agents ina ring, similar to the previous example, which had aheterogeneous sampling radius (i.e., space of vision).They could observe other agents’ behavior within theirradius and could generalize global attributes by reduc-ing or extending the search process around it. Hissimulations showed that two conventions could coex-ist, with local conformity versus global diversity pat-terns. However, this required considerable cognitivecosts for intermediate agents, i.e., agents who contin-ued to shift from one convention to another one. Healso found that when a given convention equilibriumemerges, it feeds back to the agent-level by minimizingcognitive decision costs, and therefore a macro–microself-reinforcing path.

However, it is reasonable to presume that theemergence of conventions is also influenced by net-work effects, i.e., how agents are connected. Manystudies have examined the influence of exogenous net-work structures on the diffusion of conventions.67 Itis probable that, while engaged in coordination prob-lems, agents try to avoid those who behave differentlyand prefer relationships with agents similar to them-selves. The consequences of these endogenous mecha-nisms of the formation of a social environment wereexplored by Buskens et al.68 in a repeated coordi-nation game model. Here, agents were called on todecide which opinion to endorse and their payoffsdepended on the choices of other agents they weretied to. The authors examined the importance of ini-tial network conditions on the emergence of conven-tions. They found that the density of the network hada crucial impact on the final conventions’ equilibrium.The more segmented the network was, the higher thelikelihood that two groups with different conventionsemerged over time. This was due to the fact that cer-tain agents preferred to have ties with agents similarto themselves, rather than adapting their behavior todissimilar ones.

The importance of these endogenous networkformation mechanisms was also confirmed by Cortenand Buskens.69 Their findings from a repeated,multi-person coordination game model with networkembeddedness were tested in a laboratory experiment.Here, subjects played a coordination game with pay-offs depending on the choices of other neighboringagents while they could create, maintain, or breaktheir ties depending on a certain cost. Results showedthat agents were more efficient in terms of coordina-tion, where the initial networks were less dense andthey could endogenously adjust their networks.

Finally, it is worth noting that these results werealso empirically tested on a longitudinal survey aboutalcohol use among adolescents in 14 Dutch secondaryschools, conducted in 2003 and 2004. Here, alcoholuse was modeled as a risk-dominant inefficient behav-ior in a coordination game. Adolescents were moti-vated to align their behavior with that of their friendsto be approved socially.70 While initial alcohol usepropensity per class had a positive effect on averagealcohol use at a later stage, the initial network densitydramatically amplified this tendency.71

SOCIAL INFLUENCE

Individuals rarely make decisions in complete isola-tion of their social context.72 The influence of socialcontexts on individual decisions is something thatsupporters of rational choice theory often tend to



underestimate or conceive simply as information bias.However, in situations of uncertainty, the exposureto social signals from the behavior of other peoplemight influence our behavior, as we presume that oth-ers know more than we do. At the same time, in grouplife, we know that our behavior is a signal for otherswho are observing and judging us. This is particularlyimportant when the opinion of others can influenceour access to important resources, e.g., economic ben-efits and social approval.

When the decisions of individuals are notindependent but interdependent, choices do not sim-ply aggregate at the macro level. This makes anymicro–macro or macro–micro mapping potentiallymisleading if we do not consider the meso-levelbetween individual choices and social outcomes.For instance, macro patterns can be the result ofunintended consequences given that they do notreflect individual preferences but only interaction orpropagation effects.

Segregation PatternsA classic example of the analysis of social interdepen-dence is the famous Schelling’s segregation model.9

Here, a population of households of two groups, sayblack and white, was located in a two-dimensionalspace, characterized by regular neighborhood struc-tures, representing an idealized urban space. House-holds had a threshold preference about the group oftheir neighbors and could stay or move randomlytoward new locations in case the number of similarneighbors was below the threshold. Results showedthat even moderate preference for similar neighborscould tip a society into a segregated pattern. This wasdue to the interdependent nature of choices and theirspatial and temporal effect on changing the context.

Indeed, any household that reached its threshold andmoved out of its neighborhood reduced the numberof similar neighbors in the original neighborhood,leaving whoever was left closer to its threshold. Anymovement of households also changed the receivingneighborhood and indirectly also the neighborhoodsof the neighborhoods, thus triggering a cascade ofreactions toward an equilibrium of household distri-bution far from the original households’ preferences(see Figure 5).

If we only looked at the individual level, wecould predict macro segregation but with a moremixed residential distribution. If we only looked atthe macro level, we should presume the segregationalpreferences of households, which was not the case.This abstract model allows us to understand thatsocial context is typically a nexus of interdependence,e.g., the choice of A influences the choice of B,which influences the choice of C, and subsequentlythat of A again. This makes it difficult for anylinear micro–macro mapping (see also Sakoda8). Thisreminds us of the classic lessons of complex adaptivesystems theory: even with simple agent interaction,there is always a possible gap between individualchoices and aggregate processes so that looking onlyat individual levels, whether micro or macro, can leadus to draw illusionary conclusions.74

Thanks to its simplicity and ability to be gen-eralized, the Schelling’s model has contributed to aprolific stream of ABM research. Certain authorshave extended this original version by modifyingimportant model parameters, e.g., preference thresh-olds, search for new locations, intentional householdpreferences toward integration, size of the neigh-borhoods, or spatial network topologies.12,75–79

Gilbert80 examined the influence of certain socialattributes of neighborhoods, such as crime rate,

(a) (b) (c)

FIGURE 5 | Residential segregation in the NetLogo Schelling’s segregation model with household threshold preferences of similar neighbors at(a) 25%, (b) 33%, and (c) 50%.73



the neighborhoods’ perceived prestige, and certaineconomic constraints, by providing households withmore sophisticated cognitive processes of socialenvironment’s detection. Benito et al.81 provided anexperimental test of Schelling’s findings in a laboratoryexperiment. In all these cases, the original findingswere corroborated and this contributed to makeSchelling’s model a general example of the unintendedconsequences of individual choices in social situations.

In a recent article, Bruch and Mare82 startedfrom empirical evidence that indicated that individualstend to respond continuously to variations in the racialmakeup of their neighborhoods. They replicated theSchelling’s model, but assumed that households couldexperience a small increase in the desirability of theirlocation for each given percentage increase in the pro-portion of similar households in their neighborhood,thus removing the threshold shape of households’preference. Their results showed that linear functionpreferences could soften residential segregation.

In response to the model of Bruch and Mare,van de Rijt et al.83 examined the rules that determinedhow households moved when they were unsatisfied.They showed that in a multicultural population withintegrative preferences, threshold preferences at amicro level might help to prevent tipping, providedthat households made mistakes and moved to neigh-borhoods that did not necessarily correspond to theirpreferences. This presumed that they did not havecomplete information about the real composition ofthe new targeted neighborhood. They showed thatsegregation is likely to occur once agents have a clearpreference toward diversity, move to undesirableneighborhoods, or promptly react to the changes intheir neighborhood. On the contrary, once house-holds have a clear preference toward ethnicity, reactpromptly to their neighborhood’s changes and rarelymake mistakes in selecting their new neighborhood,integration is more likely. This indicates that theshape of preferences does not have unequivocal impli-cations, but rather that this depends on householdpreferences. It is worth noting that the importance ofthe contextual nature of preferences and the possibleheterogeneous nature of neighborhood composi-tion were also found in an empirical calibration ofSchelling’s model in Israel.84,85

More recently, Bruch86 calibrated a segrega-tion model by using empirical data on three citiesin the U.S., the Panel Study of Income Dynamicsand the 1980–2000 U.S. census data. She found thatincome inequality affects racial segregation. Giventhat higher between-group income inequality increasesthe salience of economic factors in residential mobil-ity decisions, she found that high-income blacks live

in whiter neighborhoods than they would otherwise,whereas poorer blacks are racially and economi-cally isolated. The focal mechanism is called ‘off-setting’: under sufficiently high levels of within-raceincome heterogeneity, increasing between-race incomeinequality can have opposite effects at the high andlow ends of the income distribution. Whether theseoffsetting processes cause a net increase or decreasein segregation depends on the relative size of the blackpopulation, the salience of racial versus economic fac-tors in residential mobility decisions, and the shape ofthe income distribution.

Finally, it is worth noting that Schelling’s find-ings have also been extended into policy and healthfields. For instance, Auchincloss et al.87 showed thatresidential segregation might play a role in deter-mining the diffusion of obesity and related illnessesin low-income families. By adding food price andpreferences and locating stores across the neighbor-hoods in the model, they showed that ceteris paribus,residential segregation alone could increase incomedifferential in diet, independent of the low-incomehouseholds’ food preferences. Negative implicationsof residential segregation were also found in publicgoods provision,88 income distribution,89 and qualityof schools and labor market.90

Cultural and Opinion DynamicsAlthough social influence would lead us to expecta dominant tendency toward convergence in collec-tive behavior, social systems often display persistentdynamics of cultural and opinion diversity. Minoritybeliefs or opinions tend to persist over time, indepen-dent of any social force pushing them toward unifor-mity. This is especially relevant when we observe thepersistence of collective misbeliefs and discriminatorystereotypes in certain societies or the impact of extrem-ist groups in politics.

Influenced by Latané’s social psychological the-ory of social impact,91 Nowak et al.92 modeled a pop-ulation of agents in a lattice with randomly assignedbinary values of an opinion variable and heteroge-neous levels of persuasiveness and supportiveness.These levels were defined, respectively, as the abil-ity to make out-group agents change their opinionand in-group agents to resist outsiders’ persuasive-ness. Agents changed their opinion value accord-ing to the relative impact of total persuasivenessor supportiveness exerted on them by other agents,weighted by their distance from the agent within thematrix. Simulations showed that, besides the emer-gence of a dominant opinion, the formation of stronglocal minority clusters prevented in-group agentsbeing influenced by the majority. This determined the



emergence of a polarized stable equilibrium, with localconvergence and global polarization of cultural traits,due to the high sensitivity of persuasiveness and sup-portiveness to structural embeddedness factors.

This avenue was further explored by Axelrod,13

who built a more sophisticated model to test the effectsof structural embeddedness, cultural heterogeneity,and interpersonal influence on convergence and polar-ization outcomes. Adaptive agents were modeled withheterogeneous cultural characteristics, defined as acombination of a fixed number of cultural features(e.g., language, religion, etc.), each taking n possi-ble trait values (e.g., English, German, Italian; Chris-tian, Muslim, etc.). Agents interacted with neighborswith a probability dependent on the number of iden-tical cultural features they shared. A mechanism ofinterpersonal influence was added to align one ran-domly selected dissimilar cultural feature of an agentto that of the partner, after interaction. The authormanipulated certain parameters of cultural hetero-geneity (number of features and number of traits) andstructural embeddedness (interaction range and envi-ronment size). Confirming previous studies, Axelrod’ssimulations showed that global convergence towarda single culture did not occur, despite interpersonalinfluence mechanism. Moreover, they showed that thenumber of emergent cultural groups positively corre-lated with the number of cultural features and neg-atively correlated with the interaction range. Thiswas because large-distance interaction amplified theeffect of interpersonal influence from the local to theglobal scale. However, cultural diversity was unex-pectedly found to negatively correlate with both thenumber of possible traits and the environment size.More recently, Klemm et al.93 found that culturalhomogeneity could eventually emerge due to low ratesof random cultural perturbations, which caused thecollapse of boundaries between otherwise dissimilarneighbors. Moreover, by looking at the coevolutionof network structure and agents’ partner selection,Centola et al.94 identified a certain size-dependentperturbation parameter region for which interpersonalinfluence and homophily prevented the evolution ofthe system into monoculture or unstable global cul-tural diversity. This in turn generated a stable, polar-ized global equilibrium.

However, the unrealistic narrowness of suchparameter region was pointed out by Flache andMacy,95 who found a stabilizing mechanism for theemergence of a bipolarized global equilibrium. Theyquestioned the assumption of the dyadic character ofsocial influence in favor of a multilateral model ofthat mechanism.96 Their results showed that multi-lateral interaction could be a more robust mechanism

for the persistence of cultural diversity, especially inlarge populations, as local clusters could better resistdeviant agent influence under conditions of perturba-tion, and eventually prevent it from spreading globally.

It is worth considering that the local convergenceand global diversity pattern can also be generatedwhen homophily or social influence is not expected toplay a crucial role. Combining standard game theoryand ABMs, Bednar and Page97 showed that certainstructural characteristics of cultural dynamics mightbe generated by purposive agents playing multiplegames without reacting to evolutionary pressures.Similarly, Bednar et al.98 showed that a certain levelof diversity could persist within local cultural clusters.By assuming that culturally heterogeneous agents,besides facing social pressure to conformity, also strivefor internal consistency among their own differentfeatures, they showed that global convergence couldemerge in the long run, yet allowed for an intermediatephase in which cultural heterogeneity persisted.

Social influence is also important for the for-mation and diffusion of political opinions, includ-ing the rise and propagation of minority politicalpositions. By extending previous studies on opiniondynamics,99,100 Deffuant et al.101 built a model inwhich a continuous opinion variable x (−1<x< 1)was distributed within a population of adaptiveagents. In this way, moderate and extreme positions ona political issue could be contemplated. Agents werealso equipped with an uncertainty value, negativelycorrelated with the level of the agents’ political radical-ism, following the assumption that radicals are moreconfident of their own opinions. Both opinion anduncertainty could change over time through interac-tion, so that agents randomly coupled and influencedeach other if their opinion distance was lower thana threshold, eventually leading to converging opin-ions. The agents’ influence negatively depended ontheir level of uncertainty. By manipulating the uncer-tainty distribution and the proportion of radicals inthe population, they showed that for low levels ofuncertainty, the influence of radicals was effective onlyon a small proportion of closer agents, eventually lead-ing to convergence around moderate levels. However,for high uncertainty levels, radicals prevailed, causingconcentration of opinion distribution either on a singleextreme or on both (bipolarization).

By adding a social network structure to theprevious model, Amblard and Deffuant102 showedthat extremists could exploit low connected networksbetter, as they could spread in local clusters and coexistwith the rest of the population. On the other hand,when connectivity increased around a critical value,the extremists were confined to peripheral regions by



core moderate agents. Furthermore, Deffuant103 com-pared different formal models of opinion and uncer-tainty across three network structures, pointing outthat extreme convergence was possible in certain net-work configurations, which favored the isolation ofclusters of moderates and permitted radicals to influ-ence other agents without being influenced in turn.

Polarization can be further influenced by thefact that in social life partner selection might bedriven by xenophobia.104 This implies that negativeinterpersonal influence could even exacerbate thistendency. In order to consider this, Macy et al.105

developed a model of adaptive agents with binarycultural states, which were embedded in a fully con-nected network of weighted undirected ties. Weights,w (−1<w< 1), incorporated information about thestrength and the valence (positive or negative) ofthe influence between agents in dyadic interaction,were randomly distributed among the ties, and couldevolve according to changes in the number of similartraits. By manipulating decision-making flexibilityand the number of cultural states, results showedthat a bifurcating network equilibrium emerged. Astable outcome toward homogeneity would not occurunless only positive valence of partner selection andsocial influence were assumed. In a development ofthis model, Flache and Macy106 tested the effect ofthe bridging role of ‘long-range ties’107 in fosteringcultural convergence, by allowing agents to createdynamic networks within different exogenous net-work structures. Results showed that long-range tiesdid generate cultural homogeneity but only wheninteraction was limited to positive selection and influ-ence. On the contrary, in cases of bivalent influence,long-range ties induced a polarized equilibrium.

By looking at the U.S. American public opinion,Baldassarri and Bearman108 investigated the bivalentnature of partner selection and social influence mech-anisms to explain the mismatch between perceivedand actual polarization at both local and global level.They modeled a population of agents with heteroge-neous opinions about multiple political issues, attach-ing different levels of interest to each of them, whosesign represented the opinion on them (either posi-tive or negative). Interaction partners were selectedwith a probability inversely depending on the per-ceived ideological distance between the agents. More-over, interaction directly depended on the absolutevalue of the interest level that agents attached to dif-ferent issues. Agents then interacted by focusing onlyon the issue in which they were most interested andcould then update their opinions. Simulation resultsshowed that bivalent selection and influence acrossmultiple issues caused clustered polarization in the

emergent interaction structure. However, the overalldistribution across multiple issues was not polarized,except for highly salient takeoff issues. This suggeststhat individuals’ perception of opinion homogeneityin local interpersonal networks emerges from grad-ual segregation of interaction partners around takeoffpolitical issues, despite the fact that individuals stillhave heterogeneous opinions about other issues.

Furthermore, it is probable that individualiza-tion mechanisms besides homophily-driven socialinfluence can affect collective dynamics, i.e., thetendency of certain individuals to increase theirown ‘uniqueness’ when their group starts to becomeovercrowded.109 For instance, Mäs et al.110 testedthe effect of individualization on cultural conver-gence by building a simple model with mechanismsof choice homophily and nonnegative social influ-ence. By assuming a noise parameter that imposedagents’ changes of opinion depending on other similaragents in the group, they showed that a phase ofstable clusters with diversity between and consensuswithin tended to emerge. In this same vein, Mäsand Flache111 developed and experimentally testeda model of homophily and social influence in whichagents interacted through the exchange of argumentsinstead of adjusting to each other’s opinions. Theirresults showed that interpersonal communicationgenerated a bipolarized equilibrium but only for highlevels of choice homophily.

This approach has also been applied to diffusiondynamics of innovation. Deffuant et al.112 extendedthe continuous opinion dynamic models by simulatingagents who held dynamic opinion values about theimpact of a particular innovation on society—i.e., itssocial value. Agents could collect and share informa-tion for the assessment of expected individual payoff,only when the social value was considered to behigh enough. Their results suggested that under theseconditions, innovations with overall high social valuebut low expected payoffs were more likely to succeedthan innovations with low social value but higherindividual benefits. Moreover, diffusion dynamicsare significantly influenced by at least a minority ofradical innovators.

More recently, Van Eck et al.113 developed anempirically grounded ABM to study the effects ofopinion leaders on the diffusion of innovation via nor-mative and informational influence. The basic con-cept was that agents could adopt innovation stemmingfrom either social pressure or social information aboutquality. A sample of free online game consumers wasused to calibrate the behavior and position of opinionleaders. Opinion leaders were situated in central posi-tions within the network. They were more prone to



adopt innovations, could assess the quality of a prod-uct better, and were also less permeable to normativeinfluence. By comparing network configurations withand without opinion leaders, the authors found a sig-nificant effect of opinion leaders on the rapid spreadof diffusion. This was because they could spread posi-tive information about the quality of the products andwere less likely to be affected by the normative influ-ence exerted by more conservative agents.

Collective BehaviorOur decision to join a social movement or spread acultural fad depends heavily on the effects of socialinfluence. This is because we are often influencedby observing other people’s behavior before decid-ing what to do. It is often difficult to understandempirically how certain collective behavior are pro-duced when individuals are subjected to social influ-ence without analyzing the effect of social structuralfactors, such as complex network configurations.

In this field, a seminal model was published byGranovetter,114 who analyzed the dynamics of a typeof collective behavior, such as a riot, by simulatingagents deciding whether to join it depending on thedecisions of other agents. Agents were modeled tomake a binary choice, according to an expected benefitdependent on a heterogeneously distributed thresholdvalue of how many agents were already participating.In a simulation scenario, he added the impact ofprevious decisions of relevant agents connected to theindividual. His results showed that whenever networkexternalities are added, collective behavior becomesextremely dependent on nonlinear dynamics, whichmakes it very difficult to predict macro behavior onsingle individual preferences.

Threshold models of collective behavior havealso been used to analyze innovation diffusion dynam-ics. By integrating Granovetter’s classic model witha network structural component, Abrahamson andRosenknopf115,116 looked at the differences in band-wagon effects due to certain network communica-tion properties. They found that bandwagon effectsin innovation diffusion within a network also dependon particular structural characteristics of nodes thatbridge core and peripheral components and the perme-ability of their boundaries. Furthermore, by weightingsocial influence with exogenously distributed opinionsabout the reputation of innovations, they showed thatbandwagon effects could override information abouttheir unprofitability, eventually leading agents to con-verge on inefficient practices.

Hedström117 relaxed Granovetter’s originalassumption of homogeneity of interpersonal influenceand added the more realistic dimension of spatial

embeddedness to this model. He assumed that agentswere more influenced by spatially closer connections.He used data on the extraordinarily rapid diffusion oftrade union organizations in Sweden between 1890and 1940 to test this model. Simulations showed thatthe spatial-based structures of social contacts couldexplain the empirically observed behavior.

A more complex model was elaborated by Kimand Bearman118 to explain the participation to socialmovements. Their model showed that there was noneed to assume agents’ irrationality to explain whyindividuals voluntarily engaged in collective actioneven when this was risky or costly. They simulatedthe interaction between agents with different interestlevels in providing a public good—from whose ben-efits no agents could be excluded—and the differentamounts of resources to produce it, which shaped adynamic network. Agents decided whether or not tocontribute according to the expected marginal ben-efit, which they calculated upon their interests, thecost of participation, and the amount of resourcesthey possessed. However, the agents’ interest in thegood varied either upward or downward dependingon whether their ties had previously contributed ordefected. By manipulating various structural parame-ters, simulations showed that a critical mass of highlyinterested agents situated in central network positions,even if guided by self-interest, could create a localdense cluster, which eventually neutralized the influ-ence of defecting agents. In particular, network densitywas more decisive to achieve this critical mass thanhigh concentration of resources.

Chwe119 proposed a model in which strate-gic agents chose to participate in a collective actiondepending on the expected number of participantsamong their neighbors. Consequently, expectations ofneighbors’ participation depended in turn on expec-tations of neighbors of neighbors’ participation andso on. The agents were assigned a fixed number ofpartners for the whole simulation cycle. By examiningthe effect of network transitivity on social influence,results showed that transitivity was particularly effec-tive in triggering bandwagon effects among agentswith low thresholds, as they could get informationfrom locally small and yet dense clusters. For agentswith high thresholds, however, weak ties were espe-cially important as they transmitted information abouta larger amount of agents.

Social InequalityIt is probable that social influence is responsiblefor a variety of dysfunctional collective patternstypically observed in macro quantitative sociology.These include inequality in educational opportunities,



social stratification, employment traps in the labormarket, and the coevolution of social and workplacesegregation.120

For instance, by looking at the labor market,Hedström and Åberg121 built an empirically calibratedABM to examine how social influence mechanismscan explain aggregate youth unemployment rates.Their hypothesis was that levels of unemploymentamong neighborhood peers had an effect on youthunemployment by lowering their expectations offinding a job, reducing the psychological costs ofbeing unemployed, and preventing outsiders access-ing insider information about job opportunities.Large-scale observational data on youth unemploy-ment in Stockholm between 1993 and 1999 were usedto calibrate the socio-demographic characteristics ofindividuals and the structural features of the neigh-borhood network clusters. Transition probabilities ofleaving unemployment were also estimated throughmaximum likelihood statistical modeling. The authorsassumed that agents decided to leave unemploymentaccording to their own socio-demographic character-istics, the unemployment rate in their neighborhood,and the tightness of the job market. Simulationsshowed that the combination of social influence andagents’ educational level provided the most strik-ing effect on the population’s rising unemploymentrate. Furthermore, the effect of social influence wascomparably higher than that exerted by the agents’educational level per se.

When looking at social stratification, it is likelythat there is a persisting effect of social originon educational attainment, which has traditionallybeen explained through rational choice approaches.122

Recently, Manzo123 proposed an ABM to improve therealism of standard rational choice models by intro-ducing a social influence mechanism within friendshipnetworks. Agents were assigned into four groups, rep-resenting background social classes. They were thenembedded in a small-world network and allowed totake decisions about transitions from an educationallevel to the next one. These decisions were basedon the evaluation of their own ability, the perceivedcost/benefit ratio, their probability of success in func-tion of their ability, and the effect of the overall socialinfluence exerted by others with whom they were tied.Simulation findings were tested against observationaldata about the French stratification of educationalchoices across social origin in 2003. Results showedthat only by considering a social influence mechanismcould the model generate outcomes sufficiently closeto the empirical data.

Another interesting field includes the study of theeffects of social influence on the reproduction status.

Analytical theories explain the emergence of statushierarchies caused as a result of a self-reinforcingprocess driven by the exchange of deference-conferring gestures (i.e., the attribution of a per-ceived quality evaluation). This amplifies the alreadyexisting qualitative differences between individuals.124

Recently, Manzo and Baldassarri125 tested the poten-tial inequality driving effect of social influence onstatus attribution mechanisms, by hypothesizing acounteracting effect of reciprocity in the exchangeof deference-conferring gestures. They modeled apopulation of agents with heterogeneously distributed‘quality’ values, assessing each other’s quality andexchanging deference gestures. In addition, theycould become biased by other agents’ behavior. Theagents interacted on the basis of status homophily,by selecting partners within an acceptable range ofstatus dissimilarity (corrected by a heterogeneouslydistributed ‘heterophily’ constant). They also assessedpartners’ quality, by considering the partner’s pre-viously acquired status, their own tendency to relyon social influence, and a noise value. Subsequently,the agents transferred a deference value to theirinteraction partners, which was equal to the part-ner’s perceived quality, unless the evaluating agenthad previously received less deference than expectedfrom the partner. In the latter case, according to aheterogeneously distributed parameter for sensitivityto reciprocity, the evaluating agent reciprocated thepartner’s previous unfair behavior by exchangingless deference. Status values were then calculatedfor each agent as the average deference received.The simulation results suggested that the interactionbetween the cumulative effects driven by social influ-ence and the counterbalancing effect of conditionaldeference exchange was sufficient to generate statushierarchies, which are qualitatively similar to thoseobserved in empirical research, that is, the increasinggap between actual quality and status asymmetry.Furthermore, if low-status agents were more proneto have mixed interaction with similar and dissimi-lar agents rather than high-status agents, outcomestended toward a ‘winner-takes-all’ status hierarchy.

Finally, Gabbriellini126 built an empiricallytested model of the emergence of status hierarchiesin task-oriented groups as the effect of a networkof precedence ties.127 He modeled the interactionwithin a disconnected network of agents, who couldparticipate in a discussion with other members byaddressing precedence claims in the hierarchy to allothers (i.e., asking everyone to accomplish a task).Agents’ participation depended log-linearly on theexpected consequences of their claim. Permanentprecedence ties were established with a probability



that partially depended on comparing agents’ exter-nal status values, which were activated accordingto a probabilistic value. He collected empirical dataon communication in an online task-oriented dis-cussion forum of a role-playing game community.His simulations showed that highly linear statushierarchies—similar to those observed—were due tothe higher participation of agents in communicationand the deference generated by mutual observation ofexternal status.

DISCUSSION AND CONCLUSIONS

This article presented a number of sociologicallyrelevant ABM studies that explain complex socialoutcomes as effects of agent interaction. Table 2summarizes the most important contributions andprovides a systematic overview on their main explana-tory achievements. These cases combine abstractmodels, which look at general mechanisms of socialphenomena, such as cooperation and social norms,with middle-range models where specific social puz-zles are analyzed, such as youth unemployment andeducation. Although the prevalence is for theoreticalapproaches, some empirical applications of thesemodels also exist, where important behavioral orstructural model parameters have been calibratedwith available or ad hoc–generated empirical data.In these cases, such models have been used to com-plement empirical data by manipulating certainparameters (e.g., complex social networks) thatwould be difficult to observe empirically,60 or usedto generate empirically tested hypotheses.69 In othercases, models have been used to reproduce certainmacro empirical regularity by a given theory.123,126

Although most sociologists shrink from abstract,formalized theories, these examples show that abstrac-tion can have a crucial role for theory building even insociology when it is guided by modeling. On the otherhand, empirically grounded studies are fundamentalto explain well-studied sociological puzzles and stim-ulate cross-methodological approaches with mutualbenefits between, for example, standard quantitativesociology and ABMs. Furthermore, this type of studyis pivotal in persuading traditional sociologists aboutthe advantages of this approach.

At a substantive level, these examples show thatexploring the fundamental heterogeneity of individualbehavior is of paramount importance to understandthe emergence of social patterns. Cross-fertilizationbetween experimental and computational research isa useful process. It shows us that by conflating theconcept of rationality with that of self-interest, asin standard game theory and economics, we cannot

account for the subtle social nuances that characterizeindividual behavior in social contexts. In this respect,Gintis129 suggested that we question the aprioristicassumption of common knowledge that lies behindstandard game theory. If we assume that individu-als are rational and self-interested as they perceivetheir counterparts to be, game equilibria of any socialor economic exchange can be predicted. The prob-lem here is that experimental research has repeatedlyfound that social outcomes are better explained if werecognize that people develop an ‘epistemic knowl-edge’ within the game based on implicit ‘shared mind’efforts. Culture, social norms, and learning as socialscaffolds for individual rationality make a wider setof behavior ‘rationalizable’, which would otherwise befar from standard self-interest (see also neuroscientificresearch on the positive role of emotions130).

Behavioral game theory could help exploredepartures from standard rational choice models.Furthermore, it can be used to understand socialnorms in well-controlled experimental scenarios,relevant for sociological research. By concentrat-ing on interaction situations where self-interest isexpected to prevail, we can understand the genesisof social norms, their dynamics in terms of fragilityor robustness, and the factors that could conditiontheir evolution. This is impossible if we assume thatindividuals have no individual autonomy (also thatof being self-interested) and thus passively internalizenorms by culture, education, or social conformism, asin many standard sociological accounts.

Interestingly, most ABM studies mainly look atthe self-organization of social groups around socialnorms and should not be seen as a naive exercise. Noone believes that institutions and top-down influencessimply do not exist. At the same time, the ABMapproach is not a bottom-up ‘market’ ideology. Byfocusing on micro–macro aspects, ABM studies canoffer relevant insights on how groups and communi-ties can coordinate and collaborate in our world. Thisis more and more fragmented into cultures, contextsand domains, and in constant evolution and change.This is to say, the ABM approach is also sociologicallytimely and can contribute to understanding socialchange.

These ABM studies show that, if we considersociety as an evolutionary system in constant changeand adaptation, the coexistence of different behav-iors and norms over time is instrumental to pro-mote and maintain social order. This means thatinstitutional policies, which typically assume that indi-viduals are self-interested, end up eliciting self-interestin people. This situation could actually worsen thelong-term sustainability of social systems for the



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following reasons: Firstly, they do not nurture diver-sity and heterogeneity of behavior; and secondly, theycan crowd out preexisting social norms and intrinsicmotivations.131 In these cases, ABM studies could beused to understand when incentives, regulations, andexternal institutional design can work, when socialnorms are beneficial and when institutions and socialnorms can work in synergy.

Moreover, these ABM studies can help us tounderstand the importance of social contexts evenwhen looking at individual behavior in a moremicro-oriented perspective. The role of social influ-ence and the fact that we are embedded in complexsocial networks have implications for the type ofinformation we access and the types of behavior weare exposed to. At the same time, individual behaviorhas a constructive role in endogenously shaping thesenetworks. While the literature on social networks typ-ically looks at structural factors, the ABM approachcan enrich the behavioral counterpart of these studies,providing a more dynamic picture of the interplay ofindividual behavior and networks. This could helpus to understand the evolutionary bases of networkstructures, ideally considering a complex set of recip-rocal influences between micro and macro levels.It is worth noting that this interplay is difficult tounderstand using standard social science approaches,given that a combination of qualitative and quan-titative factors must be considered simultaneously.Furthermore, simulations can provide a vivid pictureof space and time processes that might unfold over along time, also supporting intuitive understanding ofthe complexity of social systems.

Here, the advent of the big data movement andthe increasing convergence between data platforms invarious domains of social life (e.g., the public, pri-vate, and social sectors) could allow sociologists tohave fine-grained, large-scale data not only on indi-vidual choices but also on social network connectionsthat were impossible even to contemplate before. Byapplying sociologically informed computational mod-els to these multisource, layer data, we could reveal thecomplex mechanisms of social life in a globally inter-connected world.132

Finally, one of the most important sociologicaladvantages of ABMs is that they can help sociologiststo achieve more rigorous standards of theorizationand empirical analysis. ABM studies have developed aserious methodological debate on standards in orderto improve empirical calibration and validation ofmodels, model documentation and reporting, andmodel replication and test.133,134 Tools such as apublic repository of models have been developed(e.g., ABM Open: http://www.openabm.org/), where

researchers are asked to make models public so thatreplication and model extension are easier. This canincrease the cumulative findings and create the collec-tive dimension of any rigorous scientific endeavor.2

ABMs can promote a modeling attitude in soci-ology, including more disciplined theory building anda stronger ‘testing hypotheses’ experimentalist cul-ture (Box 1). Moreover, they can make sociology amore collective effort by undertaking the path fol-lowed by more mature disciplines. In this regard, itis worth noting that there is still a serious gap in

BOX 1

ABM PLATFORMS FOR SOCIOLOGISTS

Various software platforms are available forsociologists to build ABMs. The primary onesare open-source and have been constantlydeveloped by large user communities. Theyprovide researchers with specific developingtools, graphic user interface, and libraries toimplement various programming languages.Swarm was the forefather of all ABM platforms.It was developed in the early 1990s by an inter-disciplinary team at the Santa Fe Institute. Ithas implementations in Objective C and Java(http://www.swarm.org). Another popular plat-form is Repast (http://repast.sourceforge.net/),which was developed by a team at the Universityof Chicago and has implementations in vari-ous object-oriented languages, e.g., Java, C++,Microsoft .NET, and Python. It also allows GISprogramming and the creation of sophisticatedvisualizations. It is well documented and usedby a growing user community. Models with Javacan also be programmed with MASON (http://cs.gmu.edu/~eclab/projects/mason/), which wasdeveloped by a team from George MasonUniversity. Finally, developed by a team atNorthwestern University (Chicago, U.S.A.), Net-Logo128 (https://ccl.northwestern.edu/netlogo/)is currently the most famous ABM platform,although it is not based on an object-orientedprogramming language. It provides an inte-grated modeling environment based on its ownprogramming language, a dialect of Logo (aneducational programming language, originallydesigned to train youngsters). NetLogo can beideally considered as the best solution to startlearning ABMs as it is user-friendly, well doc-umented, and has a large set of ready-to-usemodels, including some of the classic studiesmentioned in this article. It is also the most com-monly used platform for educational purposes.


http://www.openabm.org/

http://www.swarm.org

http://repast.sourceforge.net/

http://cs.gmu.edu/~eclab/projects/mason/

https://ccl.northwestern.edu/netlogo/


computing skills in the education programs of soci-ologists at all levels, from Bachelors to PhD courses,and even in top institutions. We need to fill this gap inorder to equip a new generation of sociologists toward

cutting-edge, collaborative research. This is also essen-tial for sociologists to collaborate and compete withexternal experts, who are increasingly performing rel-evant sociological research.

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