k1Pj20icjwherethelasttermissummedover0ithenetworkneighborhoodACMSIGecomExchangesVol10No2June2011Pages38 61SSuriandDWattsorintheaveragecontributionsofgroupsde12nedbythenetwo ID: 822180
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4S.SuriandD.Wattscomesofinterest,suc
4S.SuriandD.Wattscomesofinterest,suchasaggregatelevelsofcooperation,plausiblydependonthestructureofthenetworkaswellasonthestrategiesoftheindividualsinthepopulation[Nowaketal.2010].Therearetwomainreasonstosuspectthatcooperationshoulddependonnet-workstructure.Therstreasonisthatmanytheoreticalmodelsofsocialdilemmasassumethatcooperationisconditional,inthesensethatanindividualwillonlycooperateontheconditionthatitspartnersarealsocooperating.ArguablytheclearestexampleoftheprincipleofconditionalcooperationisthecelebratedTit-For-Tatstrategy,whichhasconsistentlybeenshowntooutperformmoreexploita-tivestrategiesinarangeofsimulationstudies,inlargepartbecauseitperformswellwheninteractingwithothercooperativestrategies[Axelrod1984].Inaddition,relatedstrategieshavealsobeenproposedthatgeneralizetheideaofconditionalcooperationtomulti-playersettings[Watts1999;GlanceandHuberman1993],usuallybyspecifyingsomeformofthresholdrequirement|i.e.\IwillcooperateifatleastXofmyneighborscooperatedlastround,elseIwilldefect."Regardlessofthespecicsoftherule,theimplicationoftheseresultsfornetworksisthatnetworkscharacterizedbyhighlevelsoflocalclustering[WattsandStrogatz1998],meaningthatanindividual'sneighborsarealsolikelytobeneighborsofeach
other,oughttosustainhigheraggregatelevel
other,oughttosustainhigheraggregatelevelsofcooperationthanpopulationsinwhichindividualsarerandomlymixed[AxelrodandHamilton1981].Putanotherway,localreinforcementwouldimplythatwhenanindividual'sneighborsalsointeractwitheachother,theyareinabetterpositiontoreinforceoneanother'spro-socialbehavior,andsomaybeexpectedtoresist\invasion"bydefectingstrategiesbetterthanwheneachneighborinteractswithadi erentsetofothers.Thesecondreasontosuspectthatnetworkstructureshouldimpactcooperationisthatcooperationinnetworksmightbe\contagious".Specically,ifAisacon-ditionalcooperatorsurroundedmostlybycooperatingneighbors,Awillcooperatemore;butthenA'sincreasedcooperationmaycauseitsremainingneighborstocooperatemoreaswell.Theseneighborsmayinturncausetheirneighborstoco-operatemoreaswell,andsoon,leadingtoacascadeofcooperationthatsustainsitselfovermultiplesteps.Infact,recentlyithasbeenclaimedthatcooperationischaracterizedbya\threedegreesofin uence"rule[FowlerandChristakis2010],meaningthatanindividualwhoincreaseshisorherlevelofcooperationcanpos-itivelyimpactthecontributionofanindividualwhoisthreestepsremovedfromtheminthenetwork.Becausethenumberofindividualswhocanbereachedwithinthreedegreesofacooperatingindividualwillingeneraldependontheno
n-localstructureofthenetwork[WattsandStr
n-localstructureofthenetwork[WattsandStrogatz1998],thepresenceofsocialcontagionwouldimplythatnetworkfeaturesotherthanlocalclusteringshouldalsoimpactaggregatecooperationlevels.2.EXPERIMENTALDESIGNIncontrastwithstandardpublicgoodsgames,inwhichparticipants'contributionsaresharedamongmembersofthesamegroup,hereparticipantsarearrangedinanetworkandtheirpayo isonlya ectedbytheactionsoftheirneighbors.Tore ectthischange,players'payo saredenedbythefunctioni=ei�ci+ak+1Pj2�(i)cj,wherethelasttermissummedover�(i),thenetworkneighborhoodACMSIGecomExchanges,Vol.10,No.2,June2011,Pages3{86S.SuriandD.Wattsorintheaveragecontributionsofgroupsdenedbythenetworktopologiesovereachround.Thusweconcludethattopologydoesnotexertanoticeableimpactoncontributionsatanylevel:individual,group,oraggregate.Theabsenceoftopologicaldependencyofcontributionssuggeststhatoneorbothofthehypothesesoutlinedabove(reinforcementandcontagion)mustbewrong.Wethereforeconductedtwofurtherseriesofexperimentsdesignedtotestthereinforce-mentandcontagionhypothesesrespectively.Intherstseriesof30experimentswefollowedthesamedesignasabove,butwiththekeydi erencethatineachex-perimentfournodeswereselectedandtheircontributionswerealla
rticiallyxedeitherat10(the\coo
rticiallyxedeitherat10(the\cooperative"condition)or0(the\defection"condition)forallrounds.Thus,wewereabletestthereinforcementhypothesisbydirectlymeasur-ingthepositive/negativein uenceofunconditionalcooperators/defectorsontheirimmediateneighbors.Theseedplayerswerearrangedinordertocoverthenet-work,meaningthateachhumanplayerwasadjacenttopreciselyoneseedplayer(intherandomregularcase,aperfectcoverarrangementdidnotexistforthese-lectednetwork;thusacloseapproximationwasusedinstead).Anadvantageofthisarrangement,isthatallhumanplayersweresubjectedtothesameexperimentallymanipulatedin uence.Thepresenceofcooperatingseedsstimulatedconsistentlyhigheraggregatecon-tributionsfromtheremaining20players,whilethepresenceofdefectingseedshadtheoppositee ect.Possessingahigh(orlow)contributingneighborthereforedidincrease(ordecrease)theaveragecontributionlevels;thusoursubjectswereindeedbehavingasconditionalcooperators.Neverthelessthee ectoftheseedplayerswasnotconsistentlybiggerinthegraphswiththehighestclustering.Forexamplethee ectoftheseednodesinanetworkofdisjointcliques,whichhadthemaximumnumberoftrianglesincidentoneachnode,wasverysimilartothee ectoftheseedsnodesintherandomregularnetwork,whichhadfewerthan1/10thasman
ytrian-gles.Thisresultimpliesthattwonode
ytrian-gles.Thisresultimpliesthattwonodesthatformatrianglewithacooperating(ordefecting)seeddonothaveanappreciablylarger(orsmaller)averagecontributionlevelthentwodisconnectednodeswithacooperating(ordefecting)seedneighborincommon.Mutualreinforcementofthecontributionsamongtheneighborsofaseednodeislargelyabsent,whetherornotthereisanedgebetweentheneighbors.Next,inaseriesof20experimentsover2weeks,wetestedthecontagionhypoth-esisbykeepingthenumberofunconditionallycooperatingseedsconstantatfourpernetwork(wedidnotintroduceunconditionaldefectorsintheseexperiments),butconcentratingthemtogetherintotwoadjacentpairs.Thisarrangementofseedsexposedsomehumanplayerstotwounconditionalcooperatorsasimmediateneighbors,whileotherswerenotexposedtoanyseedsdirectly,butwereconnectedindirectlytotheseedsviaahumanintermediary.Ifpositivecontagionwerepresentinthenetwork,wewouldexpecttoseenodesatdistancetwofromtheseedsin-creasetheircontributionsrelativetotheall-human(i.e.noseeds)condition.Quitetothecontrary,infact,thetwo-stepneighborsofthecooperatingseedscontributedslightlylessthanthenodesinthecorrespondingnetworkpositionscontributedintheall-humanexperiments.ACMSIGecomExchanges,Vol.10,No.2,June2011,Pages3{88S.SuriandD.WattsFowler,J.H.andChrist
akis,N.A.2010.Cooperativebehaviorcascade
akis,N.A.2010.Cooperativebehaviorcascadesinhumansocialnetworks.ProceedingsoftheNationalAcademyofSciences107,9,5334{5338.Glance,N.S.andHuberman,B.A.1993.Theoutbreakofcooperation.JournalofMathemat-icalSociology17,4,281{302.Hamilton,W.D.1964.Thegeneticalevolutionofsocialbehaviour.JournalofTheoreticalBiology7,1,17{52.Kearns,M.,Judd,S.,Tan,J.,andWortman,J.2009.Behavioralexperimentsonbiasedvotinginnetworks.ProceedingsoftheNationalAcademyofSciences106,5,1347.Kearns,M.,Suri,S.,andMontfort,N.2006.Anexperimentalstudyofthecoloringproblemonhumansubjectnetworks.Science313,5788,824{827.Newman,M.E.J.2003.Thestructureandfunctionofcomplexnetworks.SiamReview45,2,167{256.Nowak,M.A.,Tarnita,C.E.,andAntal,T.2010.Evolutionarydynamicsinstructuredpopulations.PhilosophicalTransactionsoftheRoyalSocietyB:BiologicalSciences365,1537,19.Strogatz,S.H.2001.Exploringcomplexnetworks.Nature410,6825,268{276.Watts,D.J.1999.SmallWorlds:TheDynamicsofNetworksBetweenOrderandRandomness.PrincetonUniversityPress,Princeton.Watts,D.J.,Dodds,P.S.,andNewman,M.E.J.2002.Identityandsearchinsocialnetworks.Science296,1302{1305.Watts,D.J.andStrogatz,S.H.1998.Collectivedynamicsof'small-world'networks.Na-ture393,6684,440{442.ACMSIGecomExchanges,Vol.10,No.2,June2011,Pag