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1、ModelsoflearningWhatdowewanttoexplain?•Tofixideas,let’sinitiallyfocusonultimatumgames,bestshotgames,andmarkets.•Inultimatumgames,behavioris,robustly,farfromthe(extreme)perfectequilibrium.Respondersinparticularseemwillingtorejectsubstantialsums.•Inmarke
2、tgames,equilibriumisoftenagoodpredictor,eveningames(likethe9bidderauctions)inwhichequilibriumgivesthebiddersverylittle(e.g.muchlessthantheywouldbewillingtoacceptinanultimatumgame).•Inbestshotgames,whicharetwo-persongameswiththesamesequentialstructureas
3、ultimatumgames,behavioralsomovesquicklytothe(extreme)perfectequilibrium.2Roth,AlvinE.andIdoErev[1995]"LearninginExtensive-FormGames:ExperimentalDataandSimpleDynamicModelsintheIntermediateTerm,"GamesandEconomicBehavior,SpecialIssue:NobelSymposium,8,164-
4、212.•Inthispaperwesetouttoconsiderwhetherwecouldexplainthedatafromtheultimatumgame(andhowitwasdifferentindifferentcountries),thebestshotgame,andthenine-bidder,one-sellermarkets(fromthe4countrystudy),usingasimplelearningmodel.•i.e.wewanttofindamodelthat
5、helpsexplainwhysomegamesmovequicklytowardsanextremeperfectequilibrium,butnotinothers.•(Theoriesoffairness(FehrSchmidt,BoltonOckenfels)trytodothesamethingviastaticmodels.)3Twodesirablepropertiesbasedonthepsychologyliterature•CHOICESTHATHAVELEDTOGOODOUTC
6、OMESINTHEPASTAREMORELIKELYTOBEREPEATED.–Knownasthe"LawofEffect,"thishasbeenobservedinaverywidevarietyofenvironmentsatleastsinceThorndike,1898.)•LEARNINGCURVESTENDTOBESTEEPINITIALLY,ANDTHENFLATTER.–Thisobservationisknownasthe"PowerLawofPractice,"anddate
7、sbackatleasttoBlackburn,1936.4Somefurtherproperties:•Generalization(orExperimentation):Notonlyarechoiceswhichweresuccessfulinthepastmorelikelytobeemployedinthefuture,butsimilarchoiceswillbeemployedmoreoftenaswell.•Recency:Recentexperiencemayplayalarger
8、rolethanpastexperienceindeterminingbehavior.•outcomescanbeunderstoodaspositiveornegativereinforcementsonlyinrelationtosomereferencepoint5AONE-PARAMETER(boneheaded)REINFORCEMENTLEARNINGMODEL•Initialpropensities:Attimet=1(beforeanyexperie
