通过竞争提升战略(英文版(1)

EvolvingStrategicBehaviorsthroughCompetitiveInteractionintheLargeKimitakaUno&AkiraNamatameDept.ofComputerScienceNationalDefenseAcademyYokosuka,239-8686,JAPANE-mail:{kimi,nama}@cc.nda.ac.jpTel:[phone](ext.3776)Fax:[phone]AbstractThepurposeofthispaperistoprovideanewapproachforinvestigatingthecompetitiveinteractionsinthelarge.Anotherpurposeofthispaperistostudyemergentstrategicbehaviorsandtoanalyzetheeffectsofboundedrationalityandthemimicrystrategyinthecompetitivesituations.Weshowhowthesocietygropesforitswaytowardsequilibriuminanimperfectworldwhereagentsaresensiblebutnotperfectlyrational.Theyhavelimitedinformation,andthereisnocommonknowledgeamongthem.Thispaperisalsoaboutsociallearningandshowshowthesocietyasawholelearnsevenwhentheindividualscomposingitdonot.Specifically,itisabouttheevolutionofsocialnorms.Weespeciallyexaminehowconventionsevolveinasocietythatbeginsinanamorphousstatewherethereisnoestablishedcustom,andindividualsrelyonhearsaytodeterminewhattodo.Withsimulations,weprovidespecificconditionsastowhichconventionsaremostlikelytoemerge.Keyword:boundedrationality,localinteraction,strategicinteraction,mimicry,socialconvention1.IntroductionAconventionisapatternofbehaviorthatiscustomary,expected,andself-enforcing.Everyoneconforms,everyoneexpectsotherstoconform,andeveryonewantstoconformgiventhateveryoneelseconforms.Familiarexamplesincludedrivingontherightwhenothersdriveontheright,goingtolunchatnoonifothersgoatnoon,andsoforth.Foreachroleinsuchasymmetricinteractionsthereisacustomaryandexpectedbehavior,andeveryonepreferstofollowthebehaviorexpectedofhimprovidedthatothersfollowthebehaviorexpectedofthem.Underthesecircumstanceswesaythatpeoplefollowaconvention.Aconventionisanequilibriumthateveryoneexpects,buthowdomutualexpectationsbecomeestablishedwhenthereismorethanoneequilibrium?Oneexplanationisthatsomeequilibriaareapriorimorereasonablethanothers.AdeductivetheoryofthistypehasbeenproposedbyHarsanyiandSelten[3].Asecondexplanation,proposedbySchelling[7],isthatagentsfocustheirattentionononeequilibriumbecauseitismoreprominentorconspicuousthantheothers.Athirdexplanationisalsopossiblesuchthat,overtime,expectationsconvergeononeequilibriumthroughpositivefeedbackeffects.Eventually,oneequilibriumbecomesentrenchedastheconventionalone,notbecauseitisinherentlyprominentorfocal,butbecausethedynamicsoftheprocesshappentoselectit.Consider,forinstance,anN-persongamethatisplayedrepeatedly,butbydifferentagents.Ineachperiod,Nplayersaredrawnatrandomfromalargefinitepopulation.Eachplayerchoosesanoptimalstrategybasedonasampleofinformationaboutwhatothersplayershavedoneinthepast.Thesamplingdefinesastochasticprocessthat,foralargeclassofgamesthatincludescoordinationgamesandcommoninterestgames,convergesalmostsurelytoapurestrategyNashequilibrium.Suchanequilibriumcanbeinterpretedastheconventionalwayofplayingthegame.If,inaddition,theplayerssometimesexperimentormakemistakes,thensocietyoccasionallyswitchesfromoneconventiontoanother.Asthelikelihoodofmistakesgoestozero,onlysomeconventions(equilibria)havepositiveprobabilityinthelimit.Theseareknownasstochasticallystableequilibria.Theyareessentiallythesameastheriskdominantequilibria[3].ThisconceptwasfirstdefinedforgeneralevolutionaryprocessesbyFosterandSmith[9].SubsequentlyitwasappliedtoadiscretemodelofequilibriumselectioninapioneeringpaperbyKandoriandhiscollogues[4].Theyconsideranevolutionarylearningprocessdefinedonsymmetric2x2games.Ineachperiodeveryplayerplayseveryother.Successfulstrategiesareadoptedwithhigherprobabilitythanunsuccessfulones.Thisevolutionaryexplanationfortheoriginofconventionshasbeensuggestedinavarietyofpapers[2][9][10],buttheprecisedynamicsoftheprocessbywhichexpectationsandbehaviorsevolvehasnotbeenclearlyspelledout.Thepurposeofthispaperistoexplaintheproblemofboundedrationalityandevolution.Weformalizetheseideasinamodelwithafinitepopulationofagentsinwhichagentsarerepeatedlymatchedwithinaperiodtoplayastagegame.Weonlyimposeaweakmonotonicityconditionreflectingtheinertiaandmyopiahypothesesonthedynamics,whichdescribetheintertemporalchangesinthenumberofagentsplayingeachstrategy.Thehypothesesweemployherereflectlimitedability(ontheagent'spart)toreceive,decide,andactuponinformationtheygetinthecourseofinteractions.Ourspecificationofdynamicsdrawsheavilyonthebiologicalliterature.Inthatliterature,agentsareviewedasbeinggeneticallycodedwithastrategyandselectionpressurefavorsanimals,whicharefitter(i.e.,whosestrategyyieldsahigherreproductivefitnessorpayoffagainstthepopulation).Therearealsogrowingliteraturesontheboundedrationalityandtheevolutionalapproach,thehypothesesemployedintheseresearchesreflectlimitedabilityofeachplayeroragenttoreceive,decide,andactuponinformationtheygetinthecourseofinteractions.Specificationofdynamicsdrawsheavilyonthebiologicalliterature,andagentsareviewedasbeinggeneticallycodedwithastrategyandselectionpressurefavorsanimals,whicharefitter(i.e.,whosestrategyyieldsahigherreproductivefitnessorpayoffagainstthepopulation).Ourmodelcanbeinterpretedinlikemanner,however,weintendt