a cognitive hierarchy (ch) model of games：一个认知层次（ch）模型的游戏

ACognitiveHierarchy(CH)

ModelofGamesTeckH.HoHaasSchoolofBusinessUniversityofCalifornia,BerkeleyJointworkwithColinCamerer,CaltechJuin-KuanChong,NUSTeckH.HoMotivationNashequilibriumanditsrefinements:Dominanttheoriesineconomicsandmarketingforpredictingbehaviorsincompetitivesituations.SubjectsdonotplayNashinmanyone-shotgames.BehaviorsdonotconvergetoNashwithrepeatedinteractionsinsomegames.Multiplicityproblem(e.g.,coordinationgames).Modelingheterogeneityreallymattersingames.TeckH.HoMainGoalsProvideabehavioraltheorytoexplainandpredictbehaviorsinanyone-shotgameNormal-formgames(e.g.,zero-sumgame,p-beautycontest)Extensive-formgames(e.g.,centipede)ProvideanempiricalalternativetoNashequilibrium(Camerer,Ho,andChong,QJE,2004)andbackwardinductionprinciple(Ho,Camerer,andChong,2005)TeckH.HoModelingPrinciplesPrinciple

Nash

CHStrategicThinking

BestResponse

MutualConsistency

TeckH.HoModelingPhilosophySimple (Economics)General (Economics)Precise (Economics)Empiricallydisciplined (Psychology)“theempiricalbackgroundofeconomicscienceisdefinitelyinadequate...itwouldhavebeenabsurdinphysicstoexpectKeplerandNewtonwithoutTycho

Brahe”(vonNeumann&Morgenstern‘44)“Withouthavingabroadsetoffactsonwhichtotheorize,thereisacertaindangerofspendingtoomuchtimeonmodelsthataremathematicallyelegant,yethavelittleconnectiontoactualbehavior.Atpresentourempiricalknowledgeisinadequate...”(EricVanDamme‘95)TeckH.HoExample1:“zero-sumgame”

Messick(1965),BehavioralScienceTeckH.HoNashPrediction:

“zero-sumgame”TeckH.HoCHPrediction:

“zero-sumgame”TeckH.HoEmpiricalFrequency:

“zero-sumgame”/simulations/CH/

TeckH.HoTheCognitiveHierarchy(CH)ModelPeoplearedifferentandhavedifferentdecisionrulesModelingheterogeneity(i.e.,distributionoftypesofplayers).Typesofplayersaredenotedbylevels0,1,2,3,…,ModelingdecisionruleofeachtypeTeckH.HoModelingDecisionRuleProportionofk-stepis

f(k)Step0chooserandomlyk-stepthinkersknowproportionsf(0),...f(k-1)Formbeliefsandbest-respondbasedonbeliefsIterativeandnoneedtosolveafixedpointTeckH.HoTeckH.HoTheoreticalImplicationsExhibits“increasinglyrationalexpectations”

NormalizedgK(h)approximatesf(h)morecloselyas k

∞

(i.e.,highestleveltypesare“sophisticated”(or"worldly")andearnthemostHighestleveltypeactionsconvergeask

∞

marginalbenefitofthinkingharder0TeckH.HoModelingHeterogeneity,f(k)A1:

sharpdrop-offduetoincreasingdifficultyinsimulatingothers’behaviorsA2:f(0)+f(1)=2f(2)TeckH.HoImplicationsA1Poissondistributionwithmeanandvariance=tA1,A2Poisson,t=1.618..(goldenratioΦ)

TeckH.HoPoissonDistributionf(k)withmeanstepofthinkingt:TeckH.HoTeckH.HoTheoreticalPropertiesofCHModelAdvantagesoverNashequilibriumCan“solve”multiplicityproblem(picksonestatisticaldistribution)Sensibleinterpretationofmixedstrategies(defactopurification)Theory:τ∞convergestoNashequilibriumin(weakly)dominancesolvablegamesTeckH.Ho

EstimatesofMeanThinkingStept

TeckH.HoNash:Theoryvs.DataTeckH.HoCHModel:Theoryvs.DataTeckH.HoEconomicValueEvaluatemodelsbasedontheirvalue-addedratherthanstatisticalfit(CamererandHo,2000)TreatmodelslikeconsultantsIfplayersweretohireMr.NashandMs.CHasconsultantsandlistentotheiradvice(i.e.,usethemodeltoforecastwhatotherswilldoandbest-respond),wouldtheyhavemadeahigherpayoff?TeckH.HoNashversusCHModel:EconomicValueTeckH.HoApplication:StrategicIQ54/siq13/default1.asp

Abatteryof30"well-known"gamesMeasureasubject'sstrategicIQbyhowmuchmoneyshemakes(matchedagainstadefinedpoolofsubjects)Factoranalysis+fMRItofigureoutwhethercertainbrainregionaccountsforsuperiorperformancein"similar"gamesSpecializedsubjectpoolsSolidersWritersChessplayersPatientswithbraindamagesTeckH.HoExample2:P-BeautyContestnplayersEveryplayersimultaneouslychoosesanumberfrom0to100ComputethegroupaverageDefineTargetNumbertobe0.7timesthegroupaverage

ThewinneristheplayerwhosenumberistheclosettotheTargetNumber

TheprizetothewinnerisUS$20Ho,Camerer,andWeigelt(AER,1998)TeckH.HoASampleofCEOsDavidBaltimore

President

CaliforniaInstituteofTechnologyDonaldL.Bren ChairmanoftheBoard

TheIrvineCompanyEliBroad

Chairman

SunAmericaInc.

LounetteM.Dyer

Chairman

SilkRouteTechnology

DavidD.Ho

Director

TheAaronDiamondAIDSResearchCenter

GordonE.Moore

ChairmanEmeritus

IntelCorporationStephenA.Ross

Co-Chairman,RollandRossAssetMgtCorpSallyK.Ride

PresidentImaginaryLines,Inc.,and

HibbenProfessorofPhysics

TeckH.HoResultsinvariousp-BCgames

TeckH.HoSummaryCHModel:DiscretethinkingstepsFrequencyPoissondistributedOne-shotgamesFitsbetterthanNashandaddsmoreeconomicvalueSensibleinterpretationofmixedstrategiesCan“solve”multiplicityproblemApplication:MeasurementofStrategicIQTeckH.HoResearchAgendaBoundedRationalityinMarketsRevisedUtilityFunctionsEmpiricalAlternativestoNashEquilibrium(Ho,Lim,andCamerer,JMR,forthcoming)ANewTaxonomyofGamesNeuralFoundationofGameTheoryTeckH.HoBoundedRationalityinMarkets:RevisedUtilityFunctionTeckH.HoBoundedRationalityinMarkets:AlternativeSolutionConceptsTeckH.HoNeuralFoundationsofGameTheoryNeuralfoundationofgametheoryTeckH.HoStrategicIQ:ANewTaxonomyofGamesTeckH.HoThankyouTeckH.HoNashversusCHModel:LLandMSD(in-sample)TeckH.HoEconomicValue:

DefinitionandMotivation“Anormativemodelmustproducestrategiesthatareatleastasgoodaswhatpeoplecandowithoutthem.”(Schelling,1960)Ameasureofdegreeofdisequilibrium,indollars.Ifplayersareinequilibrium,thenanequilibriumtheorywilladvisethemtomakethesamechoicestheywouldmakeanyway,andhencewillhavezeroeconomicvalueIfplayersarenotinequilibrium,thenplayersaremis-forecastingwhatotherswilldo.Atheorywithmoreaccuratebeliefswillhavepositiveeconomicvalue(andanequilibriumtheorycanhavenegativeeconomicvalueifitmisleadsplayers)TeckH.HoAlternativeSpecificationsOverconfidence:k-stepsthinkothersareallonesteplower(k-1)(Stahl,GEB,1995;Nagel,AER,1995;Ho,CamererandWeigelt,AER,1998)“Increasinglyirrationalexpectations”asK

∞

Hassomeoddproperties(e.g.,cyclesinentrygames)Self-conscious:k-stepsthinkthereareotherk-stepthinkersSimilartoQuantalResponseEquilibrium/NashFitsworseTeckH.HoTeckH.HoExample3:CentipedeGame1222110.400.100.200.801.600.400.803.206.401.603.2012.8025.606.40Figure1:Six-moveCentipedeGameTeckH.HoCHvs.BackwardInductionPrinciple(BIP)IsextensiveCH(xCH)asensibleempiricalalternativetoBIPinpredictingbehaviorinanextensive-formgameliketheCentipede?Isthereadifferencebetweenstepsofthinkingandlook-ahead(planning)?TeckH.HoBIPconsistsofthreepremisesRationality:Givenachoicebetweentwoalternatives,aplayerchoosesthemostpreferred.Truncationconsistency:Replacingasubgamewithitsequilibriumpayoffsdoesnotaffectplayelsewhereinthegame.Subgameconsistency:Playinasubgameisindependentofthesubgame’spositioninalargergame.Binmore,McCarthy,Ponti,andSamuelson(JET,2002)showviolationsofbothtruncationandsubgameconsistencies.TeckH.HoTruncationConsistencyVS.1222110.400.100.200.801.600.400.803.206.401.603.2012.8025.606.40Figure1:Six-moveCentipedegame12210.400.100.200.801.600.400.803.206.401.60Figure2:Four-moveCentipedegame(Low-Stake)TeckH.HoSubgameConsistency1222110.400.100.200.801.600.400.803.206.401.603.2012.8025.606.40VS.22111.600.400.803.206.401.603.2012.8025.606.40Figure1:Six-moveCentipedegameFigure3:Four-moveCentipedegame(High-Stake(x4))TeckH.HoImpliedTakeProbabilityImpliedtakeprobabilityateachstage,pjTruncationconsistency:Foragivenj,

pjisidenticalinboth4-move(low-stake)and6-movegames.Subgameconsistency:Foragivenj,

pn-j

(n=4or6)

isidenticalinboth4-move(high-stake)and6-movegames.TeckH.HoPredictiononImpliedTakeProbability