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1、ModelingSocialPreferencesStephanieHurderG3,BusinessEconomicsFriday,April2,2010Motivation•Wehaveseenthatsubjectsdonotactinperfectlyselfish,payoff-maximizingwaysinthelaboratory–Averagegiftindictatorgameis~20%Forsytheetal.(1994)–Recipientsreciprocateintrustandgifte
2、xchangegames,evenwithinmarketse.g.FehrKirchstiegerRiedl(1993)Fehretal.(1998)Motivation•Evidencethatfairnessmatterstosubjects–Positiveultimatumgameoffersrejected,evenatverylargestakes(Andersonetal,WP)•Howeversurplusisnotalwayssplitbetweenbuyerandseller–Inmarketga
3、meofRothetal.(1991)withmanybuyersandoneseller,selleralwaysgetsentiresurplusLiteratureonsocialpreferences•Maybesubjectsaremaximizingtheirutilities,buttheirutilityfunctionstakemorecomplicatedformsthanwecurrentlyuse•SuggestthatutilityfunctionstakeformU(x,x)=x+A(x,x
4、,otherstuff)ijiijwherex=mypayoffix=otherplayer’spayoffjBigquestion:WhatisA(x,x,otherstuff)?ijOutcomes-BasedModels•FehrandSchmidt(1999)andBoltonandOckenfels(2000)bothintroducemodelsoftheformU(x,x)=x+f(x,x)ijiij•Calledoutcomes-basedmodelsbecausetheutilitydependson
5、lyonthepayoffeachplayerreceivesFehrandSchmidt(1999)•Utilityfunctionexhibitsself-centeredinequityaversionU(xi,xj)=xi-αimax{xj-xi,0}-βimax{xi-xj,0}•Assumesβi<αiand0<βi≤1:disadvantageousinequalityhurtsmore(Loewenstein,Thompson,andBazerman(1989))•Assumptionofheterog
6、eneityleadstodistributionofactionsinpopulationRecalltheUltimatumGame•Aproposerisgivenapieofsize1andofferssliceofsizestotheresponder•RespondercanacceptorrejectAccept→Proposergets1-s,RespondergetssReject→Bothget0UltimatumGame•Commonexperimentalresults:–Nooneoffers
7、morethan.5–Mostoffersbetween.4and.5–Fewoffersbelow.2Ultimatumgameoffersforapieofsize5(Forsytheetal.(1994))UltimatumGame•Proposition:Supposetheproposerdoesnotknowtheparameters(α,β)ofthe22responder’sutilitybutknowsthedensityfunctionofαon[α,α].Thentheproposer2LHwil
8、loffer.5ifβ1>.5ϵ[αH/(1+2αH),.5]ifβ1=.5ϵ(αL/(1+2αL),αH/(1+2αH)]ifβ1<.5•Aggregatedoverdistributionsofβandα,this12matchesthedistributionofobservedbehaviorabove•Thisispro