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1、ModelingforexplanationandpredictionStartingwithinterestinggames(carefullyselected)andprogressingtoboringones(randomlyselected)Modelsoflearning•We’regoingtostartbylookingagainatsomegameswe’vealreadylookedat(ultimatumandmarketgames),andonewehaven’tyettalkedabout(bests
2、hotgame),andseewhatwecanmodel/explainwithsimplelearningmodels.•Thenwe’llthinkabouthowtocomparetheirpredictiveabilitywithothermodels,including(especially)equilibrium.•Abigliteraturehasgrownupontheoriesoffairnesstoexplainsomeofthesamephenomena.Looselyspeaking,wemightt
3、hinkoftheoriesoffairnessastryingtoexplainwhathappensinthefirstperiodofthesegames,whiletheoriesoflearningaretryingtoexplainhowbehaviorchangeswithexperience.2“Bestshot”publicgoodsgame•Player1providessomequantityq1•Player2learnsq1,andprovidessomequantityq2.•Thisresults
4、inaquantityqofpublicgoodequalto•q=max{q1,q2}•Theplayersarepaidbasedona(common)payofftable,suchthatplayerj’spayoff(j=1,2)isoftheform•.pj=R(q)–cqi.•Thatis,playersarepaidsome(common)rewardbasedontheamountofpublicgood,buttheyareeachchargedfortheamountqitheyprovided.•(Th
5、ename“bestshot”reflectsthemaximumintheformulafortheamountofpublicgoodq.Whenitisaminimum,it’sthe“weaklink”game,closelyrelatedtotheminimumgamesweplayedinclass.)3“Best-Shot”publicgoodsgame:1q12q2Q=max{q1,q2}“bestshot”πi=R(Q)–cqii=1,24Payofftable.Cost:$0.82perunit5Harri
6、son,GlennW.andJackHirshleifer,“AnExperimentalEvaluationofWeakestLink/BestShotModelsofPublicGoods,”JournalofPoliticalEconomy,97,1989,201-225.•Theyreportedthattwo-playerbestshotgamesconvergedquicklytotheperfectequilibrium(whenplayers1and2movedsequentially).•Theyfurthe
7、rwrite:•“Nosubjectwasinformedofthepayoffsofanyothersubjectinourexperiments,andinparticularthefactthatallvaluationscheduleswerethesamewasnotrevealed.Ourtheoreticalanalysis,incontrast,presumesthatthepayoffsarecommonpublicknowledge.Thisinformationaldiscrepancymadeourex
8、perimentsquiteaseveretestoftheunderlyingtheory.”(emphasisadded)•Canyouthinkofotherhypothesestoaccountforwhythesegamesaresodifferentfromult
