1979-Prospect-Theory--An-Analysis-of-Decision-unde

ProspectTheory:AnAnalysisofDecisionunderRiskAuthor(s):DanielKahnemanandAmosTverskySource:Econometrica,Vol.47,No.2(Mar.,1979),pp.263-292Publishedby:TheEconometricSocietyStableURL::20/10/201022:46YouruseoftheJSTORarchiveindicatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableat://=econosoc.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpageofsuchtransmission.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,[e-mail]ollaboratingwithJSTORtodigitize,preserveandextendaccesstoEconometrica.:ANANALYSISOFDECISIONUNDERRISKBYDANIELKAHNEMANANDAMOSTVERSKY'Thispaperpresentsacritiqueofexpectedutilitytheoryasadescriptivemodelofdecisionmakingunderrisk,anddevelopsanalternativemodel,calledprospecttheory.Choicesamongriskyprospectsexhibitseveralpervasiveeffectsthatareinconsistentwiththebasictenetsofutilitytheory.Inparticular,peopleunderweightoutcomesthataremerelyprobableincomparisonwithoutcomesthatareobtainedwithcertainty.Thistendency,calledthecertaintyeffect,contributestoriskaversioninchoicesinvolvingsuregainsandtoriskseekinginchoicesinvolvingsurelosses.Inaddition,peoplegenerallydiscardcomponentsthataresharedbyallprospectsunderconsideration.Thistendency,calledtheisolationeffect,leadstoinconsistentpreferenceswhenthesamechoiceispresentedindifferentforms.Analternativetheoryofchoiceisdeveloped,inwhichvalueisassignedtogainsandlossesratherthantofinalassetsandinwhichprobabilitiesarereplacedbydecisionweights.Thevaluefunctionisnormallyconcaveforgains,commonlyconvexforlosses,andisgenerallysteeperforlossesthanforgains.Decisionweightsaregenerallylowerthanthecorrespondingprobabilities,exceptintherangeoflowprob-abilities.Overweightingoflowprobabilitiesmaycontributetotheattractivenessofbothinsuranceandgambling.1.INTRODUCTIONEXPECTEDUTILITYTHEORYhasdominatedtheanalysisofdecisionmakingunderrisk.Ithasbeengenerallyacceptedasanormativemodelofrationalchoice[24],andwidelyappliedasadescriptivemodelofeconomicbehavior,e.g.[15,4].Thus,itisassumedthatallreasonablepeoplewouldwishtoobeytheaxiomsofthetheory[47,36],andthatmostpeopleactuallydo,mostofthetime.Thepresentpaperdescribesseveralclassesofchoiceproblemsinwhichpreferencessystematicallyviolatetheaxiomsofexpectedutilitytheory.Inthelightoftheseobservationswearguethatutilitytheory,asitiscommonlyinterpretedandapplied,isnotanadequatedescriptivemodelandweproposeanalternativeaccountofchoiceunderrisk.2.CRITIQUEDecisionmakingunderriskcanbeviewedasachoicebetweenprospectsorgambles.Aprospect(x1,Pi;...;xn,pn)isacontractthatyieldsoutcomexiwithprobabilityPi,wherePl+P2+...+pn=1.Tosimplifynotation,weomitnulloutcomesanduse(x,p)todenotetheprospect(x,p;0,1-p)thatyieldsxwithprobabilitypand0withprobability1-p.The(riskless)prospectthatyieldsxwithcertaintyisdenotedby(x).Thepresentdiscussionisrestrictedtoprospectswithso-calledobjectiveorstandardprobabilities.Theapplicationofexpectedutilitytheorytochoicesbetweenprospectsisbasedonthefollowingthreetenets.(i)Expectation:U(X1,Pi;...;Xn,Pn)=piu(x1)+...+PnU(Xn)1ThisworkwassupportedinpartbygrantsfromtheHarryF.GuggenheimFoundationandfromtheAdvancedResearchProjectsAgencyoftheDepartmentofDefenseandwasmonitoredbyOfficeofNavalResearchunderContractN00014-78-C-0100(ARPAOrderNo.3469)underSubcontract78-072-0722fromDecisionsandDesigns,Inc.toPerceptronics,Inc.WealsothanktheCenterforAdvancedStudyintheBehavioralSciencesatStanfordforitssupport.263264D.KAHNEMANANDA.TVERSKYThatis,theoverallutilityofaprospect,denotedbyU,istheexpectedutilityofitsoutcomes.(ii)AssetIntegration:(xi,Pi;...;Xn,P)isacceptableatassetpositionwiffU(w+x1,pl;...;w+Xn,Pn)u(w).Thatis,aprospectisacceptableiftheutilityresultingfromintegratingtheprospectwithone'sassetsexceedstheutilityofthoseassetsalone.Thus,thedomainoftheutilityfunctionisfinalstates(whichincludeone'sassetposition)ratherthangainsorlosses.Althoughthedomainoftheutilityfunctionisnotlimitedtoanyparticularclassofconsequences,mostapplicationsofthetheoryhavebeenconcernedwithmonetaryoutcomes.Furthermore,mosteconomicapplicationsintroducethefollowingadditionalassumption.(iii)RiskAversion:uisconcave(u0).Apersonisriskaverseifheprefersthecertainprospect(x)toanyriskyprospectwithexpectedvaluex.Inexpectedutilitytheory,riskavers