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1、AxiomaticSystemsoftheExpectedUtilityTheoryTheExpectedutilitytheorywasproposedbyBernoulli(1738),Ramsey(1931),vonNeumann-Morgenstern(1947)andfullydevelopedbySavage(1954).inwhichchoiceoversubjectivelyuncertainprospectsischaracterizedbyexpectedutilityriskpreferencesandstandardprobabili
2、sticbeliefs.ThedifferenceoftheseearlierstudiesandRamseyisthemannerwhichrepresentsuncertainty.Intheearlierstudies,theobjectiveframework,uncertaintycomesprepackagedintermsofnumericalprobabilities.Ontheotherhand,RamseytreatsthechoiceofprobabilitydistributionsoveroutcomesorlotteriesAsi
3、milarandrelativelysimpleformulation,thatprovidesinsightsintothemostimportantassumptionsofexpectedutilityforstatisticalpurposes,wasproposedbyAnscombeandAumann(1963).TheExpectedUtilityMaximizationTheorem(Savage,1954)Sure-ThingPrincipleisalsocalledthe‘strongindependenceassumption’.Its
4、tatesthatifoutcomexandoutcomex′areindifferentinthemselves,thenforanyoutcomey,aprobabilitymixofxandymustbeindifferenttoaprobabilitymixofx′andy.DenyingtheprincipleisapossibleresponsetotheAllaisparadox.Sure-ThingPrincipleworLotteryLotterywzxoryTAILSHEADSPossibleDecisions:Takew.([w])Re
5、fusew,andtakexiftails.(.5[x]+.5[z])Refusew,andtakeyiftails.(.5[y]+.5[z])supposeanindividualwouldpreferxovery,buthewouldalsoprefer.5[y]+.5[z]over.5[x]+.5[z],inviolationofsubstitution.Supposethatwissomeotherprizethathewouldconsiderbetterthan.5[x]+.5[z]andworsethan.5[y]+.5[z].Thatis,x
6、>ybut.5[y]+.5[z]>[w]>.5[x]+.5[z].Therefore,thethirdstrategywouldbebest.However,ifshe/hetakesthethirdstrategy,andthecoincomesupTails,thenshe/hewouldchoosex!Thatisactuallyendupwiththesecondstrategy,whichisworst.RogerB.Myerson,GameTheory:AnalysisofConflict,1997.WhyweneedSure-ThingPrin
7、ciple?ABriefProofoftheTheoremSupposespeciallotteries;a:alwaysgivesthebestprizeforeverystate.z:alwaysgivestheworstprizeforeverystate.bt:givesaifstate=t,andgiveszotherwise.Defineβas[x]≈{t}βa+(1−β)zDefineγasbt≈Sγa+(1−γ)zWecanshowthatβisu(x
8、t),andγisp(t
9、S),satisfyingtheaxiom.NOTE≈{t}me
10、ans“indifferentifadecision
