leadership in intergroup contests gerald eisenkopf · 1 leadership in intergroup contests....

DISCUSSION PAPER SERIES IN ECONOMICS AND MANAGEMENT

Leadership in Intergroup Contests

Gerald Eisenkopf

Discussion Paper No. 18-12

GERMAN ECONOMIC ASSOCIATION OF BUSINESS ADMINISTRATION – GEABA

Acknowledgments:UrsFischbacherandmyformercolleaguesattheThurgauInstituteof Economics supported the planning of this project with multiple questions andsuggestions.DeboraGehringandtheresearchassistantsoftheLakelabattheUniversityof Konstanz provided excellent support by conducting the experiment. I gratefullyacknowledge financial support for this project from the DeutscheForschungsgemeinschaft(GrantEI983/3‐1).Allerrorsremainmyown.

LeadershipinIntergroupContests

GeraldEisenkopf

UniversityofVechta

Driverstr.22,

49377Vechta

E‐Mail:gerald.eisenkopf@uni‐vechta.de

April27,2018

I. Introduction.................................................................................................................................................2

II. DesignoftheIntergroupContestExperiment..............................................................................5

III. Predictions................................................................................................................................................7

IV. Results.....................................................................................................................................................10

V. Comparisonwithvoluntarycontributionmechanism(VCM)game.................................16

VI. Conclusions...........................................................................................................................................22

References...........................................................................................................................................................23

AppendixA–InstructionsforExperimentI.........................................................................................25

AppendixB–InstructionsforExperimentII........................................................................................28

1

LeadershipinIntergroupContests

Abstract:

The paper studies how leadership recommendations and leading‐by‐example shape

behaviorinintergroupcontests.Theexperimentalresultsshowthattheleaderisakey

driver of aggregate contest expenditure. Leaders increase their expenditure

substantially once they make recommendations to the followers. The specific

expenditure recommendations have a highly significant impact on the investments of

followers. The additional impact of leading by example is rather small. A second

experimentreplicatesthetreatmentsinanoncompetitivevoluntarycontributiongame.

It reveals a remarkable consistency in the leader‐follower‐relationship across the two

games despite significant differences in the impact of the treatments on leadership

behavior.

2

I. Introduction

Social scientists, and in particular economists, increasingly use experiments to study

leadership in groups (Zehnder, Herz and Bonardi, 2017). Experiments allow for a

random assignment of leadership roles (Huck and Rey‐Biel, 2006, Arbak and Villeval,

2011)andacontrolledvariationintheavailabilityofleadershipinstruments.1Thetask

fortheexperimentalleaderresemblesthechallengesof‘realworld’groupleaders.They

wanttoovercomecooperationproblemsamonggroupmembersinordertoimplement

mutuallybeneficialoutcomes.Therefore,experiments typically implementpublicgood

gamesorothervoluntarycontributionmechanismsthat imposeasocialdilemma.This

paper provides a novel approach and focuses on group leadership in intergroup

contests,i.e.asituationinwhichtwogroupswithmultiplememberscompeteforagiven

prize.

The behavioral analysis of leadership in intergroup contests does not just help

understandinghowfamouspeoplerisetoprominence,e.g.asgeneralsinawar,asteam

captains in sport tournaments or as successful managers in competitive markets.

Perhaps more importantly, intergroup contests have some specific characteristics

relative to voluntary contribution mechanisms that provide novel insights regarding

leadershipinstrumentandtherelationshipbetweenleadersandfollowers.

First, the incentive structure in intergroup contests is peculiar (see section 3 of this

paper, or, formore general theoretical considerations, Kolmar (2013)). Unlike typical

publicgoodgames, contestswithpredetermined,andstrictlypositive,prizesgenerate

an incentive to invest some resources for the benefit of the entire group. If all other

membersof the competinggroupsabstained fromanycontestexpenditure, aminimal

effortinvestmentbyonegroupmembercoulddecisivelychangetheoddsinfavorofthe

ownteam.

Second, increasingeffortsbysomegroupmembersdecrease the investment incentives

of the other group members if they have the same belief about the behavior of the

opposinggroup.Theseinvestmentsarestrategicsubstitutes.Hence,ifleaderscontribute

heavily to theirgroup’scause, theymay induce followers to lower theirowneffort. In

noncompetitivesocialdilemmas,theinvestmentsofonegroupmemberdonotaffectthe1 Note, that another strand in the literature experimentally investigates the personality traits andincentives,whichmotivate individuals to acquire or to delegate power (e.g. Fehr, Herz andWilkening,2013)

3

incentivesoftheothergroupmembers.Theinvestmentsbecomestrategiccomplements

ifthegroupmembershaveapreferenceforreciprocity,equityand/orfairnessconcerns

(Potters, Sefton and Vesterlund, 2005, 2007, Gächter, Nosenzo, Renner and Sefton,

2013). Because of the aforementioned peculiar incentive structure in intergroup

contests,suchpreferencesmustbestrongerforfollowerstoactaccordingly.

Third,groupmembersgenerate two typesofexternaleffects if theyprovideeffort for

theirgroup.Notonlydotheygenerateabenefittotheirfellowgroupmembers(asina

typicalvoluntarycontributionscheme).Theysimultaneouslyharmthemembersofthe

opposing group because the other group has a reduced chance towin the prize. This

negativeexternalityhasnomonetary incentiveeffectbut itcanfosterapreferencefor

winning (Mago, Samak and Sheremeta, 2013, Sheremeta, 2013) or parochial altruism,

i.e. when altruism towards one’s own group goes along with hostility towards the

opposing group (Abbink, Brandts, Herrmann and Orzen, 2012). In consequence,

contestants make rather large contributions to improve the odds of their own side

(Abbink, Brandts, Herrmann and Orzen, 2010, Sheremeta, 2015). Such seemingly

excessiveinvestmentsmitigatethesocialdilemmawithinthegroupand,therefore,limit

thescopeforleadership.

The paper also contributes to the understanding of the mechanisms of Leading by

Example (LbE) as an instrument of leadership. LbE implies that a group of followers

learns about the decision of their leader before they commit themselves in the social

dilemma. Several papers show that such LbE promotes cooperation in voluntary

contributiongames(e.g.Güth,Levati,SutterandVanDerHeijden,2007,Levati,Sutter

andVanderHeijden,2007,Gächteretal.,2013).Theyalsorevealthatgroupsperform

bestwhen ledbythosewhoarecooperatively inclined.DrouvelisandNosenzo(2013)

find that a shared group identity enhances this effect. Cartwright,Gillet andVanVugt

(2013) and Gächter and Renner (2014) identify how leaders shape the beliefs of

followersinthiscontext.

It is unclear whether LbE is still effective in circumstances that foster intra‐group

cooperation anyway. Therefore I study leadership instruments in a context in which

non‐binding investment recommendation allow for simple “cheap‐talk” coordination.

The literature does not provide clear insights on this issue. Pogrebna, Krantz, Schade

andKeser(2011)observethatnon‐bindingverbalstatementsofaleaderhaveasimilar

4

aggregateeffectlikeLbEwhileDannenberg(2015)reportsarelativelyloweffectofsuch

chatmessages.MeanwhileKoukoumelis,LevatiandWeisser(2012)showthatone‐way

communicationhasabeneficialimpactoncooperation.

The evidence derives from a laboratory experiment in which two groups with three

memberseachcompeteinaTullockcontest(Tullock,1980).2Inthebaselinetreatment

each groupmember canmake a private investment in order to increase her group’s

chance of winning the prize. In the second treatment, one randomly chosen group

memberineachgroup,the ‘leader’,recommendsacontributionlevelbeforetheactual

decision.The third treatment induces leadingbyexample.The leader recommendsan

investmentlevelanddecidesaboutherowncontribution.Theothergroupmembers,the

‘followers’, see both the recommendation and the actual investment decision of the

leaderwhentheydecideabout theirowncontribution. Inordertoobtainabehavioral

benchmark,Ireplicatethetreatmentsinasecondexperimentinwhicheachgroupfaces

asocialdilemmainthecontextofanoncompetitivevoluntarycontributionmechanism

(VCM).

Theresultsshowthatfollowersdonotfree‐rideontheinvestmentsoftheleaders.They

also reveal somedifferences in investment levels across the treatments.However, the

leadersarethemaindriversof thiseffect.Theytendtounderinvestbut increasetheir

expenditure substantially once theymake recommendations to the followers. Leading

by example, i.e. the visible ex‐ante investment commitment of the leader, has no

discernible additional impact on the investment level and a small positive impact on

followership.

Thesecondexperiment shows that thebehavioraldifferencesbetween the twogames

are remarkably small, starting with the observation that they induce the same

investments in the baseline treatmentswithout recommendations. The key difference

between the two games is the observation that the VCM induces leaders to increase

expenditure more strongly than in the inter‐group contest once they make

2 The Tullock contest is arguably themost widely usedmodel for the experimental study of conflicts(Abbink,2010,Dechenaux,KovenockandSheremeta,2012,Kimbrough,LaughrenandSheremeta,2017).Thegroupmemberscaninvestresourcesinordertoincreasetheprobabilitytowinaprize.Anyincreaseininvestmentsimultaneouslyreducestheprobabilityoftheopposinggrouptowintheprizeinthespecificround.

5

recommendations. This extra‐large increase in investments does not affect the

comparativestaticsoffollowership.

The paper now proceeds as follows. The next sections explain the design of the

intergroupcontest,derivethebehavioralpredictionsandpresenttheresults.SectionV

introducesthevoluntarycontributionmechanismsandcomparesthetwoexperiments.

SectionVIprovidestheconclusions.

II. DesignoftheIntergroupContestExperiment

In the experiment two groups competed against each other in a Tullock contest. The

experiment lasted for 20 rounds, each round the group faced a randomly chosen

opponent.Agroupconsistedof threeplayers,one leaderand two followers,whokept

theirrolesthroughouttheentireexperiment.3Table1summarizesthesequenceofthe

stagegameandthetreatmentdifferences.Thegamedidnotvaryacrosstheroundsina

specifictreatment.

3AppendixAprovidesanEnglish translationof theexperimental instructions (orginal inGerman).Theinstructions did not mention terms like leadership or followers and used neutral labels, referring toplayersA,BandC(theleader).Thisprocedureshouldminimizedemandeffectsthatbesetmanyappliedexperimentalstudies(SturmandAntonakis,2015).Iusedapartner‐matchingprotocolwhichimpliesthatthegroupcompositiondoesnotchangeacrossrounds.

6

Table1:TheDesignofaroundintheExperiment

Step Baseline Recommendation LeadingbyExample

(LbE)

1 Eachplayergetsanendowmentof100points

1a Leadermakesanon‐bindinginvestment

recommendation

1b Leaderdecidesabout

investment

2

Followerslearnaboutthe

recommendation

Followerslearnabout

therecommendationand

theleader’sinvestment.

Leaderandfollowersdecideaboutinvestment Followersdecideabout

investment

3

Allplayerslearnwhetherthegrouphaswontheprize.

Leaderslearnabouttheindividualinvestmentsofthefollowersandthe

aggregateinvestmentsoftheothergroup.

I now explain the game in a round in the Baseline Treatment in greater detail.

Afterwards,Idescribethedifferencesbetweenthetreatments.

BaselineTreatment

Each player received an endowment of 100 points in a round, with 120 points

exchanginginto1€.Theplayercouldkeepthepointsinaprivateaccountorinvestthem

inordertoenhancethechancesoftheowngroupintheintergroupcontest.Thegroups

competeforaprizeof300points.Irrespectiveoftheindividualinvestments,eachgroup

member receives 100points if her groupwins. Thewinning probability of a group is

determined by its members’ investments relative to aggregate investment in both

groups.At theendofaround, the followers learnabout theirownpayoff, i.e.whether

thegrouphaswontheprize.Theleadersalsoreceiveinformationabouttheindividual

investmentsofgroupmembersandtheaggregateinvestmentsoftheopposinggroup.

7

RecommendationTreatment

In the Recommendation Treatment the leader makes a non‐binding investment

recommendation toher followers.All groupmembers see this recommendationwhen

theymaketheirsubsequentinvestmentdecision.

Leading‐by‐ExampleTreatment

IntheLeading‐by‐ExampleTreatmenttheleaderalsomakesanon‐bindinginvestment

recommendation to her followers. Afterwards the leader makes her own investment

decisions.Thefollowersseetherecommendationandtheactualcontestexpenditureof

theleaderwhentheymaketheirsubsequentinvestmentdecision.

III. Predictions

In this section I present a set of competing hypotheses. The first set derives from

standard game theory assuming common knowledge that all actors are rational and

wanttomaximizetheirownpayoff.

Thestagegameisacontestbetweentwogroups,1and2.Eachgroupincludesaleader

( , with ∈ 1; 2 ) and two followers ( and ). The groups compete for a prize

0, thewinninggroupsdividestheprize inequalsharesamong its threemembers.

Each group member receives an endowment 0 and can spend 0 to

enhance thewinning probability of her group. Thewinning probability of a group in

Tullock contest is determined by the members’ investments relative to aggregate

investmentinbothgroups.

Now we study the payoff function of a risk‐neutral follower in group 1. The payoff

increasesintheendowment aswellastheproductofthewinningprobabilityandthe

shareof theprize . Itdecreases in thecontestexpenditure.The followerchooses the

expendituretomaximizetheexpectedpayoff

max3

,

with denoting the investments of leaders and followers in the

first group and for the second group. A transformation of the

resulting first order condition yields 1, and accordingly for the other

8

group, 1.Together,thetwooptimalityconditionsimplythatbothgroups

makethesameaggregateexpenditure .Theresultingsimplificationofthefirst

optimalityconditiongivesus

12

And,becauseof ,weobtaintheinvestmentofthefollower

12

Thisresultshowsthatthe investmentsof thegroupmembersarestrategicsubstitutes

1 ,which implies theaforementioned incentiveagainst leadingbyexample.

There is an optimal aggregate best response to the behavior of the opposing group.

Whatevertheleaderprovidestothisbestresponsedoesnothavetobeprovidedbythe

followers. If the leaders do not provide any investments, the followers make all the

investments.Followersshouldreducetheirinvestmentsiftheyseeahighinvestmentof

the leader.Notealso, that the leader’srecommendationsareactually irrelevant in this

context.

Wegetmultipleequilibriawithingroupsthatshareonecrucialcharacteristics,namely

theaggregateinvestmentofallgroupmembersis .With 300

points,thepredictedaggregategroupexpenditureis25points.

Hypothesis1(commonknowledgeaboutpayoffmaximizingpreferences):

a) Aggregategroupexpendituredoesnotdifferacrossthetreatments.

b) IntheBaselineandtheRecommendationsTreatments,theinvestmentsofleaders

andfollowersdonotcorrelatewitheachother.

c) IntheLeadingbyExampleTreatmenttheinvestmentsofthefollowersdecrease

withincreasinginvestmentsoftheleader.Leaderswillinvestlessthanfollowers

inthistreatment.

Thesehypothesesarenotinlinewithanintuitiveunderstandingofleadership.Leading

by example as a concept implies that leadership behavior sets a standard the others

shouldfollow.Theyalsocontradicttwowellestablishedpatternsaboutdecisionmaking

in intergroup‐contests and the leader‐follower relationship in noncompetitive

9

environments. First, we know that group members make seemingly excessive

investments in competitive environments (Abbink et al., 2010, Abbink et al., 2012,

Sheremeta,2015).Torationalizethisbehavior,Magoetal.(2013)incorporatea‘joy‐of‐

winning’ parameter in their model. Second, leadership studies in noncompetitive

environmentsgames(e.g.Güth,Levati,SutterandVanDerHeijden,2007,Levati,Sutter

and Van der Heijden, 2007, Gächter et al., 2013) and seminal theoretical papers on

conditional cooperation (e.g. Levine, 1998, Fehr and Schmidt, 1999, Falk and

Fischbacher,2006)showthatpeopleadjusttheirbehaviortotheobserveddecisionsof

othergroupmembers,inparticularafirstmovinggroupmember.

ToincorporatetheseobservationsIextendtheutilityfunctionofafolloweringroup1

with an additional parameter , . Again, I assume common knowledge that the

parameterdoesnotdifferbetweentheparticipantsinaspecificcontest

max3

,

The new parameter depends on the treatment T and increases in the (assumed)

investment of the leader (with | 0 0and , ,

, 0). It resembles the joyof‐winning‐parameter inMagoetal. (2013)as it

impliesanonmonetaryadditionalbenefitontopoftheprizeifthegroupissuccessful.

Theparameteralscontainsareciprocalelementbecauseitincreasesintheinvestment

of the leader. The assumed differences between the treatments in the comparative

staticstakeintoaccountthattheLeading‐by‐ExampleTreatment,at least,removesthe

uncertainty about the actual behavior of the leader. The transformed optimality

conditionisnow

3, 1

The aforementioned common knowledge assumption ensures homogenous aggregate

investmentsatthegrouplevelandweobtainthefollowinginvestmentofthefollower.

12,4

10

The analysis of the comparative statics reveals that the investments of the group

members are no perfect strategic substitutes anymore , 1 . The

investmentsofthefollowersincreaseintheinvestmentoftheleaderifthechangeinthe

newparameterissufficientlyhigh.

Hypothesis2:

a) Aggregate contest expenditure per group is ordered as follows across the

treatments:

, , ,

b) The correlations between the investments of leaders and followers increase

acrossthetreatmentsinthefollowingorder

0 , , ,

IV. Results

Procedure

Thedataweregathered inninesessions, three foreach treatment,witha totalof216

subjects. All sessions took place in autumn 2016 at the Lakelab at the University of

Konstanz.Subjectswerestudents fromtheUniversityofKonstanzwhowererecruited

with the software “ORSEE” (Greiner, 2015). To gain more independent observations,

eachsessionwasdivided into twodifferentmatchinggroupsof fourgroupseach.The

opposing groupwas always chosen from the samematching group. The experiments

were computerized with the software “z‐Tree” (Fischbacher, 2007). Each subject

participated in one of the treatments only. They received written instructions and

comprehension questions that had to be answered correctly before the experiment

couldstart.AnEnglishtranslationof the instructions is included inAppendixAofthis

paper.Thesessionslastedapproximately50minutesandsubjectsreceivedonaverage

about 19 Euro (about 21 US Dollars in 2016). All subjects received their payment

privatelyattheendoftheirsession.

DescriptiveStatistics

Table2showstheleaders’averageinvestmentrecommendationsandtheactualcontest

expenditureofbothleadersandfollowersinthethreetreatmentsacrossthe20rounds.

11

Thefollowingcomparisonsrelyongroupaveragesacrossrounds,usingWilcoxonrank‐

sumandsigned‐ranktests.

Table2:Investmentrecommendationsandactualcontestexpenditureofleadersand

followers(standarddeviationsinparenthesis)

Baseline Recommendations LeadingbyExample

(LbE)

Leader

recommendations‐‐‐ 54.28(14.82) 46.06(16.44)

Leaderinvestments 27.29(19.61) 41.17(17.33) 39.43(16.13)

Follower

investments33.63(13.50) 42.04(16.32) 36.31(14.88)

Npercell:24Leaders/48Followers

Themain impression is that leaders reactmore strongly to the treatment differences

than followers do. The leaders’ investments are significantly higher in the

Recommendations andLeading‐by‐Examples treatments than inBaseline (p= .03 and

.01).Leadersalsoinvestinsignificantlylessthanfollowersinthebaselinetreatment(p=

.16, according to theWilcoxon signed‐rank test)but significantlymore if they leadby

example(p=.02,accordingtotheWilcoxonsigned‐ranktest).Meanwhile,thefollower’s

investmentsincreaseiftheleaderjustmakesarecommendation(p=.053,accordingto

theWilcoxon rank‐sum test) but they are not higher in the LbE treatmentwhen they

alsoobservetheleader’sactualinvestmentdecision.

Furthermore leaders inflate recommendations if theydonothave to reveal theirown

decisions. The leaders’ recommendations are higher in the Recommendations

TreatmentthaninthenLeading‐by‐ExampleTreatment(p=.08,accordingtotherank‐

sum test). They are also significantly higher than leader efforts in that treatment

(Wilcoxonsigned‐ranktest,p<.01)whiletheyarenotintheLbETreatment.

Leaders

Now I study the treatment differences in greater detail. The first focus is on the

investmentoftheleaders.TheestimationsinthefirsttwomodelsinTable3confirmthe

significantly lower investments in the Baseline Treatment. The Recommendations

12

Treatmentservesasabenchmarkinthesemodels.Model2includesadditionalcontrol

variableswhich increase theexplainedvariancebuthavenoqualitative impacton the

treatment comparisons. They reveal a significant decline in investment over time

(Round t, see also Figure 1) and a strong persistence of behavior across rounds

(Investment t‐1). Model 3 estimates the statistical relationship between the leaders’

recommendationsandtheirowninvestmentsinLbEandRecommendationTreatments.

This relationship ishighlysignificant. Interestingly, itdoesnotdifferbetween the two

treatments even though the followers cannot identify in the Recommendations

TreatmentwhethertheLeaderstickstoherownadvice.

Table3:OLSEstimationsonTreatmentDifferencesinLeaderInvestments(with

RecommendationsTreatmentasreference)

Dep.Var:

InvestmentLeader

Model1 Model2 Model3

(w/oBaseline)

BaselineTreatment ‐13.881** (5.037) ‐6.107** (2.784)

LeadingbyExample

Treatment‐1.742 (4.554) ‐.861 (2.460) 2.030 (5.028)

Leaderrecommendation .481*** (.062)

LbE×Recommendations .021 (.128)

Roundt(1‐20) ‐0.532** (0.100) ‐.359*** (.089)

Winnert‐1 ‐.923 (1.211) ‐.268 (1.205)

Investmentt‐1 0.547*** (0.061) .390*** (.105)

Constant 41.173*** (3.249) 24.407*** (4.164) 2.483 (4.154)

R² 0.051 0.353 .525

N(obs/MatchingGroup) 1440/18 1368/18 912/12

Inparentheses:standarderrorsclusteredatthematchinggrouplevel.Eachmatchinggroupincludedfourgroupsthatwererandomlymatchedintocontestsacrosstherounds.***:p<.01;**:p<.05;*:p<.1.

13

Figure1:InvestmentsandRecommendationsofLeadersacrosstreatmentsandovertime.

Followers

In Table 2, the seemingly small differences of the followers’ investments across the

treatments suggested that leadership has a rather limited impact in the experiment.

However,ananalysisofthebehavioralrelationshipwithingroupsrevealsthatthisisnot

the case. Table 4 shows a increase in the correlation between leader and follower

investments if leaderscanmakearecommendation.Thiscorrelation increasesagain if

the leaders lead by example. Unsurprisingly, the followers focus their decision more

stronglyontheleader’sinvestmentthanherrecommendation.

0

25

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

average

lead

er Inve

stments (in points)

Rounds

Leaders Baseline Leaders Recommendations Tr

Leaders LbE Recommendations Rec Tr.

Recommendations LbE Treatment

14

Table4:CorrelationsbetweenRecommendationsandInvestmentsacrosstheTreatments

BaselineTreatment Leader

investments

Follower

investments

Leaderinvestments 1 .122

Followerinvestments 1

RecommendationsTreatment Leader

recommendations

Leader

investments

Follower

investments

Leaderrecommendations 1 .576 .548



LeadingbyExampleTreatment Leader

recommendations

Leader

investments

Follower

investments

Leaderrecommendations 1 .652 .606



Table 5 explores these correlations in greater detail. Its models estimate the

investments of the followers and their statistical relationshipwith the investments of

the leader across the treatments. Again, the Recommendations Treatment serves as

reference.Model1showsthatalltreatmentdifferencesareinsignificantifwecontrolfor

theinvestmentoftheleader.Model2comparesthestatisticalrelationshipbetweenthe

investmentsoftheleaderandthefollowersacrossthetreatments.Thisrelationshipisat

its lowest in the Baseline Treatment (in which it is insignificant), increases in the

RecommendationTreatments(inwhichtheleadersrecommendationsprovideacausal

link between the two investments) and has the highest coefficient in the Leading by

ExampleTreatmentwhereonecanclaimaclearcausalimpactofleadershipinvestments

onthoseofthefollowers.Model3includesadditionalcontrolvariables.Thecoefficients

regarding the statistical relationship of the investments in the different treatments

becomesmallerbutremainsignificant.

15

Table5:OLSEstimationsontheRelationshipbetweentheInvestmentsofLeadersand

Followers(withRecommendationsTreatmentasReferenceTreatment)

Dep.Var:

Investment

Follower


InvestmentLeader .548*** (.114) 0.529*** (.124) .310*** (.080)

Baseline

Treatment

‐.794 (4.646)7.112 (8.548) 8.104* (3.860)

Baseline×

InvestmentLeader

‐.299* (.161) ‐0.273*** (0.078)

Leadingby

Example

Treatment

‐4.770 (4.045) ‐18.808** (7.857) ‐7.950** (3.423)

LbE×Investment

Leader

0.355** (.152) .140* (.073)

Roundt(1‐20) ‐0.148* (.079)

Winnert‐1 ‐1.122 (1.303)

Investmentt‐1 0.591*** (.044)

Constant 19.470*** (5.648) 20.240*** (6.615) 6.610** (3.411)

R² .097 .117 0.430

N(obs/matching

group)2880/18 2880/18 2736/72

Inparentheses:standarderrorsclusteredatthematchinggrouplevel.Eachmatchinggroupincludedfourgroupsthatwererandomlymatchedintocontestsacrosstherounds.***:p<.01;**:p<.05;*:p<.1.

The aforementioned results contradict some key predictions derived from economic

theory. In particular, they show that the investments of leaders and followers are

strategic complements.We also observe some differences in investment levels across

the treatments.However, the leaders are themaindrivers of this effect. They tend to

underinvestintheBaselineTreatmentbutincreasetheirexpendituresubstantiallyonce

theymake recommendations to the followers. Leading by example, i.e. the visible ex‐

anteinvestmentcommitmentoftheleader,hasnodiscernibleimpactontheinvestment

levelandasmallpositiveimpactonfollowership.

16

V. Comparisonwithvoluntarycontributionmechanism(VCM)game

This section discusses whether the preceding results are the result of a peculiar

characteristicoftheinter‐groupcontestorwhethertheyreflectmoregeneralaspectsin

the relationship between leaders and followers. Hence, I replicate the experimental

designinthecontextofavoluntarycontributionmechanism(VCM)asithasbeenused

intheexperimentalliteratureonleadershipsofar(Güthetal.,2007,Levatietal.,2007,

Gächteretal.,2013).

DesignandProcedure

This second experiment also lasted for 20 rounds, using a partner‐matching protocol

throughout the experiment. Again, each group consists of three randomly chosen

players, one leader and two followers who kept their roles throughout the entire

experiment. Each player received an endowment of 100 points in a round, with 120

points exchanging into 1 €. The player could keep the points in a private account or

invest them inorder to enhance thewelfareof all groupmembers. More specifically,

onepoint invested impliedamarginalper‐capita return foreachgroupmemberof .5.

pointsandaggregatereturnof1.5points.Hence,itisefficienttoinvestallpointsbutan

individual who focuses just on her own payoff will not invest any point. The

Recommendation and the Leading by Example Treatments proceeded as described

above.Attheendofaround,thefollowerslearnedabouttheirownpayoff.Theleaders

also received information about the individual investments of group members. This

secondexperimentwas conductedalsoat theUniversityofKonstanz inMayand June

2016 with 120 students from the same subject pool. The smaller sample size also

reflects thatgroups constitute truly independentobservations in this experiment.The

proceduralaspectswerethesameasinthefirstexperiments.

DescriptiveStatistics

Table6summarizestheresultsofleadershipinthevoluntarycontributionmechanism.The

RecommendationsandtheLeadingbyExampleTreatmentstreatmentsseeaparticularly

strong increase in contest expenditure. The followers’ investments are higher in

RecommendationsandLbEthaninbaseline(p<.01andp=.047,respectively;seealso

Figure2),andsoaretheinvestmentsoftheleaders(bothp‐values<.01).Interestingly,

recommendationsaresignificantlyhigherthanleadereffortsinbothtreatments(p=.01

and.03,respectively).

17

Table6:Investmentrecommendationsandactualcontestexpenditureofleadersand

followersintheVCM(standarddeviationsinparenthesis)

Baseline Recommendations LeadingbyExample

(LbE)

Leader

recommendations‐‐‐ 81.66(13.89) 73.34(21.84)

Leaderinvestments 27.56(14.94) 65.47(26.59) 67.33(25.75)

Follower

investments31.41(14.00) 65.40(25.50) 57.35(30.44)

N(leader/follower) 16/32 8/16 8/16

Figure2:InvestmentsandRecommendationsofLeadersacrosstreatmentsandovertime

intheVCM

Figure3showsthatthetwoexperimentscaneasilybecomparedbecausebothBaseline

Treatmentsyieldsimilarinvestmentlevelsofleadersandfollowersinbothexperiments

0

25

50

75

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

average

lead

er Inve

stments (in points)

Rounds

Recommendations Rec Tr. Recommendations LbE Treatment

Leaders Baseline Leaders Recommendations Tr

Leaders LbE

18

(The rank‐sum tests yields p = .47 for the followers and p = .72 for the leaders).

Furthermore,otherbehavioralpatternspersistacrossthegames.Forexample,follower

investmentsarehigher(insignificantly) thanthoseof leaders inbaseline,donotdiffer

fromtheminRecommendations,andarelowerinLbE(Signed‐ranktestP=.01).

Figure3:InvestmentsandRecommendationsofLeadersacrosstreatmentsandovertime

intheContestandtheVCM

Leaders

The estimations documented in Table 7 show that the Leaders’ investments increase

oncetheyhavetomakerecommendationstothefollowers(Model1).Theinvestments

alsocorrelatesignificantlywiththeirownrecommendationsirrespectiveofwhetherthe

followersareinformedabouttheirleader’sinvestmentsornot.(Model2)Againonecan

observeasignificantdeclineininvestmentovertime(Roundt)andastrongpersistence

ofbehavioracrossrounds(Investmentt‐1).

0

20

40

60

80

100

BaselineContest

Baseline VCM Rec. TreatmentContest

Rec. TreatmentVCM

LbE TreatmentContest

LbE TreatmentVCM

(recommended) contest exp

enditure (in points

Leader recommendations Leader investments Follower investments

19

Table7:LeaderInvestmentsintheVCM(withRecommendationsTreatmentasReference

Point)

Dep.Var:

InvestmentLeader

Model1 Model2

BaselineTreatment ‐14.920*** (5.305)

LeadingbyExample

Treatment1.725 (5.065) 15.614 (11.777)

LeaderRecommendation .607*** (.186)

LbE×Recommendation ‐.117 (.189)

Roundt(1‐20) ‐.569*** (.134) ‐0.643*** (0.203)

Investmentt‐1 .608*** (.073) 0.442*** (.134)

Constant 30.879*** (7.616) ‐7.086 (5.560)

R² 0.576 0.627

N(obs/MatchingGroup) 608/32 304/16

Inparentheses:standarderrorsclusteredatthematchinggrouplevel.Inthefirstexperimenteachmatchinggroupincludedfourgroupsthatwererandomlymatchedintocontestsacrosstherounds.Inthesecond,eachgroupconstitutedamatchinggroupbecausetheexperimentdoesnotallowforinteractionbetweengroups.***:p<.01;**:p<.05;*:p<.1.

Table8studiesthedifferencesintheoutcomesacrossthetwoexperiments.Bothmodel

showsthattheVCMyieldssimilarcomparativestaticsregardingleadershipbehavioras

theintergroupcontests.However,Model1alsoconfirmsthatthedifferencebetweenthe

investments of leaders in the Baseline and Recommendation Treatments is much

strongerintheVCMthanintheintergroupcontest.

20

Table8:AComparisonofLeaderInvestmentsacrosstheTwoExperiments(with

RecommendationsTreatmentasReferencePoint)

Dep.Var:

InvestmentLeader

Model1 Model2

BaselineTreatment ‐5.862** (2.522)

LeadingbyExample

Treatment‐.816 (2.284) 2.107 (4.472)

LeaderRecommendation .474*** (.058)

LbE×Recommendation .018 (.120)

Vol.ContributionMech. 10.176** (4.520) ‐11.551 (8.181)

VCM×Recommendation .154 (.140)

VCM×Baseline ‐10.727** (5.002)

VCM×LbE 2.560 (5.989) 12.760 (11.819)

VCM×LbE×

InvestmentLeader ‐.123 (.211)

Roundt(1‐20) ‐.544 (.080) ‐.427*** (.085)

Investmentt‐1 .566 (.047) .403*** (.082)

Constant 23.290 (3.239) 2.878 (3.468)

R² .462

1976/50

.621

N(obs/MatchingGroup) 1216/28


Followers

Table9nowstudiestherelationshipbetweentheinvestmentsofleadersandfollowers

inthissecondexperimentingreaterdetail.Likemodels2and3inTable5,itestimates

theinvestmentsofthefollowersandtheirstatisticalrelationshipwiththeinvestments

of the leaders across the treatments. The Recommendations Treatment serves as a

benchmark.Model1showsthesignificantrelationshipbetweentheinvestmentsofthe

leaderandthefollowers.ThisrelationshipissignificantlystrongerthanintheBaseline

Treatment but (insignificantly) weaker than in the Leading by Example Treatment.

Model 2 includes the aforementioned control variables which increase the explained

21

variance but have little qualitative impact on the results. Model 3 finally provides a

combinedestimationacross the twoexperiments. Its results show that thequalitative

results regarding the leader follower relationships are the same in both experiments.

Noneofthedifferencesbetweentheenvironmentsisevenapproximatelysignificant.

Table9:OLSEstimationsontheRelationshipbetweentheInvestmentsofLeadersand

FollowersintheVCM(withRecomm.TreatmentasReferencePoint)

Dep.Var:

InvestmentFollower


InvestmentLeader 0.673*** (0.146) 0.360*** (0.088) .290*** (.074)

BaselineTreatment .216 (11.887) 1.939 (7.461) 7.802** (3.567)

Baseline×

InvestmentLeader‐0.314* (0.170) ‐0.240** (0.103) ‐.267*** (.073)

LeadingbyExample

Treatment‐22.999* (11.955) ‐11.961** (8.140) ‐7.296** (3.208)

LbE×InvestmentLeader 0.203 (0.167) 0.099 (0.111) .126* (.070)

Vol.ContributionMech. 3.717 (8.861)

VCM×Investment

Leader ‐.032 (.126)

VCM×Baseline ‐6.965 (9.246)

VCM×Baseline×

InvestmentLeader .097 (.151)

VCM×LbE ‐1.876 (14.482)

VCM×LbE×

InvestmentLeader ‐.048 (.193)

Roundt(1‐20) ‐0.422*** (0.122) ‐.231*** (.065)

Investmentt‐1 0.474*** (0.055) .612*** (.038)

Constant 21.326* (11.673) 15.197* (8.186) 6.877*** (3.273)

R² 0.510 0.626 .502

N(obs/MatchingGroup) 1280/32 1216/32 3952/50


22

Overall, the results show that the behavioral differences between the two games are

remarkably small. This holds in particular for the followers. The impact of leading by

example, i.e. the visible ex‐ante investment commitment of the leader, is almost

negligible in both experiments. The key difference between the two games is the

observationthattheVCMinducesleaderstoincreaseexpendituremorestronglythanin

the inter‐group contest once theymake recommendations.This additional investment

increasedoesnotaffectthecomparativestaticsoffollowership.

VI. Conclusions

This paper studied leadership in intergroup contests, comparing the results with

evidence from leadership in a noncompetitive social dilemma. Despite meaningful

differences in the incentive structure and in aggregate behavior the results identify

remark stable behavioral patterns in the leader‐follower relationship across the two

games.Inbothcontexts,theresultsshowsimilarcorrelationsbetweentheinvestments

of leadersand followers across the treatments. Intergroup contestsdonot exhibit the

negativecorrelationbetweeninvestmentsof leadersandfollowersthatstandardgame

theory suggests. Furthermore, the environments are all characterized by

overinvestments relative to standard. The most relevant difference between the two

gamesderivesfromtheobservationthatthetreatmenteffectsonaggregateinvestment

arestrongerinthevoluntarycontributionmechanismthanintheintergroupcontests.In

thelatterenvironmentleaderscoordinatethebehaviorofthefollowersbuttheydonot

risesignificantlywhichsuggestsamorelimited,butnotnegligiblescopeforleadership

inintergroupcontests.

The paper also contributes to the understanding of the mechanisms of Leading by

Example(LbE).ItwasunclearwhetherLbEisstilleffectiveincircumstanceswhennon‐

binding investment recommendations by the leader already allow for simple “cheap‐

talk”coordination.Bothexperimentsshowthatthisadditional impactofLbEis indeed

insignificantlysmall.Thefactthatleadersmaynotfollowtheirownrecommendationsif

theydonotleadbyexampledoesnotshapethebehaviorofthefollowersdecisively.

These insights suggest that the leader‐follower‐relationship is stable across decision

makingcontexts.Leaderscancoordinatefollowerstovariouslevelsofcooperationinall

23

environments. Inallcontexts,thesuccessofleadershipthereforecruciallydependson

thecourageoftheleadertogoforhighinvestmentsforthecommoncause.

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AppendixA–InstructionsforExperimentI

TheseinstructionshavebeentranslatedfromGerman.Allsubjectsinatreatmentreceived

the same instructions. Differences between the instructions across the treatments are

highlighted.Numerical examplesandOn‐Screen control questionsarenot included.The

experimentstartedonceallsubjectshadansweredallcontrolquestionscorrectly.

Welcometothiseconomicexperiment.

Yourdecisionsandthedecisionsoftheotherparticipantswillaffectyourpayoff.Hence,

it is important that you read these instructions carefully. Please contact usbefore the

26

experimentstartsifyouhaveanyquestion.

Pleasedonottalkwiththeotherparticipantsduringtheexperiment.

Otherwisewemightexcludeyoufromtheexperimentandanysubsequentpayment.

Duringtheexperimentswealwaystalkaboutpointsthatdetermineyourincome.Atthe

end of the experimentwe convert all points into Euros, using the following exchange

rate.

120points=1Euro

Yougetyourpaymentsat theendof theexperiment in cash.Nowweexplainyou the

experimentindetail.

ExperimentalSetup

At the start of the experiment you will form a group with two randomly chosen

participants.Therearethreeteammembers,A,B,andC.ParticipantChasaspecialrole

whichwedescribebelow.Youwilllearnatthestartoftheexperimentwhetheryouare

A, B, or C. During the experiment your group will meet another group of similar

composition.Ineachyouwillmeetanotherrandomlychosengroup.

The experiment has 20 rounds. The composition of your group will not change over

theserounds.Ineachround,yourgrouportheothergroupcangetaprizeof300points.

The probability of success of your groupdepends on the inputs of itsmembers. Each

groupmembergets100points irrespectiveof thepersonal input if thegroupgets the

prize.

Atthestartofeachroundeachparticipantgets100points.Anyparticipantcanusethese

points as inputs (from 0 to 100). All points not invested will be added to the

participant’sprivateaccount.

Once the participants have decided about their inputs, these investments will be

summed up. The success probability of your group depends on the ratio of its

investmentsrelativetotheinvestmentsoftheothergroup.

Thecomputeraddsuptheinputswithinateam.Thesuccessprobabilityisderivedfrom

the ratiobetweenyour team’s inputand the sumofboth teams’ inputs. Ifboth teams

27

investthesameamountthesuccessprobabilityis50%foreachteam.Thisalsoholdsif

both teams invest 0 points. If one team makes a higher investment the success

probability isalsohigher.However, it isnotguaranteed that the teamwith thehigher

investmentalsowinstheprize.Morespecificallytheformulaforthesuccessprobability

isasfollows:

SuccessprobabilityInputofyourteam

Inputofyourteam Inputoftheotherteam

Theincomeofanygroupmemberisdeterminedasfollows:

Payofffromtheprivateaccount(=100‐Investment)

+100points(ifthegroupwinstheprize.)

=totalpayoff

ParticipantC

ParticipantChasaspecialroleintheTeam.

BaselineTreatment Recommendation

Treatment

Learning‐by‐ExampleTreatment

‐‐‐

Participant C can suggest the other group members how

many points to use as input. Both A and B get the same

recommendation. A and B can never exchange information

amongthemselves.

‐‐‐ ‐‐‐

PlayerCthendecidesabouther

own input.ParticipantsAandB

learn about this input before

theymaketheirowninvestment

decision.

At the end of a round each participant receives information aboutwhether the own

grouphasreceivedthe300points.OnlyparticipantClearnsabouttheactualinputsofA

andBandtheaggregateinputsoftheothergroup.

- NumericalExamples‐

28

Timeline

Oneroundproceedsasfollows

1. Youget100points.

2. RecommendationsandLbETreatments:InputrecommendationbyparticipantC.

3. LbETreatmentonly: InputdecisionofparticipantC.The investedpointswillbe

withdrawnfromthe100point(onlyin)

4. Inputdecisions

Baseline andRecommendationTreatments: All participants decide about

theirinputs.Theinvestedpointswillbewithdrawnfromthe100point

LbETreatment:TheparticipantsAandBlearnabouttheinputofC.They

decideabouttheirinputs.Theinvestedpointswillbewithdrawnfromthe

100point

5. DistributionofthePrize.ParticipantClearnsabouttheactualinputsofAandB

andtheaggregateinputsoftheothergroup.

Theexperimenthas20roundsthatallproceedasmentionedabove.Youwillremainin

the same group throughout the entire experiment.Wewill add up all earned points,

exchangethemintoEuroandpaythemtoyouattheendoftheexperimentincash.

AppendixB–InstructionsforExperimentII

TheseinstructionshavebeentranslatedfromGerman.Allsubjectsinatreatmentreceived

the same instructions. Differences between the instructions across the treatments are

highlighted.Numerical examplesandOn‐Screen control questionsarenot included.The

experimentstartedonceallsubjectshadansweredallcontrolquestionscorrectly.

Welcometothiseconomicexperiment.

Yourdecisionsandthedecisionsoftheotherparticipantswillaffectyourpayoff.Hence,

it is important that you read these instructions carefully. Please contact usbefore the

experimentstartsifyouhaveanyquestion.

Pleasedonottalkwiththeotherparticipantsduringtheexperiment.

29

Otherwisewemightexcludeyoufromtheexperimentandanysubsequentpayment.

Duringtheexperimentswealwaystalkaboutpointsthatdetermineyourincome.Atthe

end of the experimentwe convert all points into Euros, using the following exchange

rate.

120points=1Euro

Yougetyourpaymentsat theendof theexperiment in cash.Nowweexplainyou the

experimentindetail.

ExperimentalSetup

At the start of the experiment you will form a group with two randomly chosen

participants.Therearethreeteammembers,A,B,andC.ParticipantChasaspecialrole

whichwedescribebelow.Youwilllearnatthestartoftheexperimentwhetheryouare

A,B,orC.Theexperimenthas20rounds.

Atthestartofeachroundeachparticipantgets100points.Anyparticipantcanusethese

points as inputs (from 0 to 100). All points not invested will be added to the

participant’sprivateaccount.

Once the participants have decided about their inputs, these investments will be

summedup.Thelabmanagerincreasesthissumby50%anddistributesallthesepoints

equallyamongthegroupmembers.

Allgroupmembersbenefit inthesamewayfromyour investmentasyoubenefit from

theinputsoftheothergroupmembers.Theincomeofanygroupmemberisdetermined

asfollows:

Payofffromtheprivateaccount(=100‐Investment)

+payofffromtheinputs(=0,5sumofallinputs)

=totalpayoff

ParticipantC

30

ParticipantChasaspecialroleintheTeam.

BaselineTreatment Recommendation

Treatment

Learning‐by‐ExampleTreatment

‐‐‐

Participant C can suggest the other group members how

many points to use as input. Both A and B get the same

recommendation. A and B can never exchange information

amongthemselves.

‐‐‐ ‐‐‐

PlayerCthendecidesabouther

own input.ParticipantsAandB

learn about this input before

theymaketheirowninvestment

decision.

Attheendofaroundeachparticipantreceivesinformationabouttheownpayoff.Only

participantClearnsabouttheactualinputsofAandB.

- NumericalExamples‐

Timeline

Oneroundproceedsasfollows

1. Youget100points.

2. RecommendationsandLbETreatments:InputrecommendationbyparticipantC.

3. LbETreatmentonly: InputdecisionofparticipantC.The investedpointswillbe

withdrawnfromthe100point(onlyin)

4. Inputdecisions

a. Baseline andRecommendationTreatments: All participants decide about

theirinputs.Theinvestedpointswillbewithdrawnfromthe100point

b. LbETreatment:TheparticipantsAandBlearnabouttheinputofC.They

decideabouttheirinputs.Theinvestedpointswillbewithdrawnfromthe

100point

5. Distribution of the payments. Participant C learns about the actual inputs of A

andB.

31

Theexperimenthas20roundsthatallproceedasmentionedabove.Youwillremainin

the same group throughout the entire experiment.Wewill add up all earned points,

exchangethemintoEuroandpaythemtoyouattheendoftheexperimentincash.

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