1999 Nash Equilibrium and Welfare Optimality

《1999 Nash Equilibrium and Welfare Optimality》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ReviewofEconomicStudies(1999)66,23±380034-6527y99y00020023$02.00Ó1999TheReviewofEconomicStudiesLimitedNashEquilibriumandWelfareOptimality*ERICMASKINHarvardUniversityFirstversionreceivedJune1998;®nalversionacceptedOctober1998(Eds.)IfAisasetofsocialalternatives,asocialchoicerule(SCR)assigns

2、asubsetofAtoeachpotentialpro®leofindividuals'preferencesoverA,wherethesubsetisinterpretedasthesetof``welfareoptima''.Agameform(or``mechanism'')implementsthesocialchoiceruleif,foranypotentialpro®leofpreferences,(i)anywelfareoptimumcanariseasaNashequilibriumofthegameform(implying,inparticul

3、ar,thataNashequilibriumexists)and,(ii)allNashequilibriaarewelfareoptimal.ThemainresultofthispaperestablishesthatanySCRthatsatis®estwopropertiesÐmonotonicityandnovetopowerÐcanbeimplementedbyagameformiftherearethreeormoreindividuals.Theproofisconstructive.I.INTRODUCTIONAftersocietyhasdecide

4、donasocialchoiceruleÐarecipeforchoosingtheoptimalsocialalternative(oralternatives)onthebasisofindividuals'preferencesoverthesetofallsocialalternativesÐthesocialplannerstillfacestheproblemofhowtoimplementthatrule.Inparticular,theplannermaynotknowindividuals'preferences.Hemightattempttoelic

5、itthem,butthismaynotbeaneasytask,evenabstractingfromcommunicationcosts.Ifindividualsknowtherulebywhichtheplannerselectsalternativesonthebasisofreportedpreferences,theymayhaveanincentivetoreportfalsely.Onecanthinkoftheindividualsasplayingagameform.Theyareendowedwithstrategyspacescoinciding

6、withtheirsetsofpossibleannouncements.Thestrategiesthatplayerschoosedetermineanoutcome.Ideally,onemighthopetodevisegameformswhichensurethatindividualswillalwayswanttoannouncetheirtruepreferencesandthattherightoutcome(i.e.theoneprescribedbythesocialchoicerule)relativetothoseprefer-encesisse

7、lected.InthecasewherepreferencescanbeanythingÐthatis,whentheplannercanplacenoapriorirestrictionsonthenatureofindividuals'preferencesÐGibbard(1973)andSatterthwaite(1975)dashthishopebydemonstratingthatonlydictatorialgameformshavethepropertythatplayersalwayswishtoannou