效用函数与纳什均衡

(,,250100)(,,250100),,:(1),;(2),;(3),.,,1.,,.,.,,.,,(),.?..(),(Stableequilibria),,,,.(Harsanyi,Selten,1988),,Cooper,Dejong,Forsythe,Ross(1990).,,,,.,().,.,(Commonknowledge).,,(),,;,.(Nash,174200012MATHEMATICSINECONOMICSVo1117No.4Dec.2000:2000-05-231950),,.,.,()..,,.2.,,,,.211,,.,,:()N={1,2,,n},iN,.(),iSi={s1i,,skii},s=(sji1,,sjnn),ji=1,,ki,s={s1,,sn},S=ni=1Si.,iSi={s1i,,skii}kii=(p1i,,pki1),pjiiE0,kiji=1pjii=1,Mi={(p1i,,pkii)|kiji=1pjii=1},m(m=k1+k2++kn)=(1,n),M={(1,,n})|iMi,iN}=ni=1Mi.isi,(impropermixedstrategy),i=si.,(propermixedstrategy).i(carrier),C(i);C(i)=Si,,i(completelymixedstrategy).i(iN),,=s;(propermixed2strategyprofile).()(Payoff),i,:s=(sj11,,sjnn),ji=1,,ki,ai(s)=ai(sj11,,sj22,,sjnn),A=(ai(s))sS,iN,.=(1,2,,n),ai()=ai(1,2,,n){ai(s)|sS},Eai()=k1j1=1k2j2=1knjn=1ai(sj11,sj22,,sjnn)pj11pj22pjnn,,G=(N,(Si)iN,(ai)iN),2217.G,iN,=(i,,n)(i,-i).13=(31,,3n),iN,Eai(31,3-i)EEai(i,3-i),PiMi(1).3,,.,:()1950,,.1(Nash,1950).Debreu,GlicksbergFan,.(Debreu,1952;Glicksberg,1952;Fan,1952)nG,Si,ai(s)ssi,.Glicksberg.(Glicksberg,1952)nG,Si,ai(s)s,.,DasgutaMaskin.(Dasguta,Maskin;1986)n,Si,ai(s)si,s,,.(),,,,.(),,Wilson.(Silson,1971).,mni=1ki(),mni=1ki.(),.(Selten,1965)(Selten,1975),(Kreps,Wilson,1982).(Bernheim,1984)(Pearce,1984).,,324:ai(s)a3i(s-i)=maxsiSiai(si,s-i)s-i.(Harsanyi,Selten,1988),.212,.,iai(){ai(s)|sS)},ŽA={ai()|,iN},ŽAL,:11,M,ai()Lai().21,,M,ai()Lai()ai()Lai().31,,,M,ai()Lai()ai()Lai(),ai()Lai().41,€M,{M|ai(€)Lai(€)}{M|ai((€))Lai()}M.51,,,M,(0,1),ai()Lai(),ai(+(1-))Lai(+(1-)).L124,(RepresentationTheorem),ui,ui()ui(ai()),ai()Lai()Zui(ai())ui(ai())L5,ui,ui()==k1j1=1k2j2=1knjn=1ui(ai(sj11,sj22,,sjnn))pj11pj22pjnnui(iN),:E=(N,(Si)iN,(ai)iN,(ui)iN),.E:23=(31,,3n)E,iN,ui(ai(31,3-i))Eui(ai(i,3-i)),PiMi(2).3,,.3.311(VonNeumann,Morganstein,1944),,(Arrow2Pratt),..,,Allais.,,Machina,Quiggin...,Machina(1982),iui(ai())(1)(Frechet),(2)ai().(2),,M,ai()ai(),ui(ai())Eui(ai());a,aE0,aa,ui(a)ui(a).4217312.3u,RX()X,u(X)=u(EX-RX).,.ai(3i,3-i)ai(i,3-i)Ri(3i,3-i),Ri(i,3-i)ui(ai(3i,3-i))=i(Eai(i,3-i)-Ri(3i,3-i)),PiN.Ri(i,3-i)ui(ai(31,3-i))=i(Eai(i,3-i)-Ri(i,3-i),PiN,i(x)=ui(x)(PxR,PiN),:Eai(31,3-i)-RI(3i,3-i)EEai(i,3-i)-RI(i,3-i),PiN.(3)(3),,.1ui(PiN)(2),GE;.:3=(3i,3-i),,si,ai(3i,3-i)Eai(si,3-i)PiN(4)i,ai(i,3-i){ai(si,3-i)|siSi},,ai(3i,3-i)ai(i,3-i).(2),ui(ai(3i,3-i))Eui(ai(i,3-i)),PiMi(5)(3i,3-i).,(3i,3-i),(3),isi,Ri(si,3-i)=0,Ri(3i,3-i)=0,(3):ai(3i,3-i)Eai(si,3-i)PiN(6)i,i=(p1i,p2i,,pkii),kij=1pji=1,Eai(i,3-i)=kij=1pjiai(si,3-i)Fai(3i,3-i)3=(3i,3-i).,;,(2),.,.,..2,1(a).u1(x)=u2(x)=x(,u1(x)=0),:((1,0,0),(1,0,0));((0,1,0),(0,1,0));524:((0,0,1),(0,0,1))((0,01625,01375),(0,01444,01555));((01774,0,01225),(01757,0,01242));((01604,01277,01118),(01660,01106,01232));((01689,01310,0),(01800,01200,0)).:2112311100,21001100,01201150,06020150,11003100,51002100,210030120,11200150,11004100,61001(a):21123119100,3610019100,319627175,1116029175,1910051100,7510036100,3610033196,221569175,1910064100,841001(b)u1(x)=u2(x)=20x-x2(u1(x)0,),1(b),,:((0,01625,01375),(0,01404,01595));((01716,0,01283),(01706,0,01293));((01549,01322,01128)(01613,01104,01281))((01636,01363,0),(01775,01224,0)),,.,,,..,,.,,.,..Machina,,Camerer(1989),ChewWaller(1986),Conlisk(1987),,.,KrepsPorteus(1979).ui(i,-i)i().ui(i,-i)i:i,iMi,ii-ijiMi:ui(i+(1-)i,-i)min(ui(i,-i),ui(i,-i))6217,(0,1).-uii,ui.2E,i,ui(i,-i)i,E.:3,:i,3=(3i,3-i)PiMi,i3i,ui(i,3-i)ui(3i,3-i)..rrMr,r3rur(r,3-r)=ur(3r,3-r).(0,1),r=r+(1-)3rMr,ur,,ur(r,3-r)min{ur(r,3-r),ur(3r,3-r)}=ur(3r,3-r).3=(3r,3-r).3E,(1)iui,E3=(3i,3-i),3i;(2)iui(i,-i)i,E.:(1),,E(3i,3-i)3i,r(rE2){pi1i,pi2i,,piri}3i=rt=1sitipiti,rt=1piti=1,ui(i,3-i)i,ui(3i,3-i)max(ui(si1i,3-i),ui(si2i,3-i),ui(siri,3-i)).(3i,3-i),.(1),(2).3,,iui(i,-i)i,E,.4.,,,.,,,,.,,.,(),,,..,,.,..724:[1]Camerer,C.,Anexperimentaltestofseveralgeneralizedutilitytheories,JournalofRiskandUncertainty,2(1989),61-104[2]Chew,S.H.andWaller,W.S.,Empiricaltestsofweighteduntility,JournalofMathematicalPsychololgy,30(1986),55-72.[3]Conlisk,J.,Verifyingthebetweennesaxiomwithquestionnaireedidence,ornot:takeyourpick,EconomicLetter,25(1987),319-322.[4]Cooper,R.,DeJong,D.,Forsythe,R.AndRoss,T.,Selectioncriteriaincoordinationgames:someexperimen2talresults,AmericaEconomicReview,80(1987),218-233.[5]Dasgupta,P.AndE.Maskin,Theexistenceofequilibriumindiscontinuouseconomicgames.1:Theory,Pre2viewofEconomicStudies,53(1986),1-26.[6]Debreu,D.,Asocialequilibriumexistencetheorem,ProceedingoftheNationalAcademyofSeience,38(1952),886-893.[7]Fan,K.,Fixedpointandminmaxtheoremsinlocallyconvextopologicallinearspaces,ProceedingoftheNa2tionalAcademyofScience,38(1952),121-126.[8]Gilicksberg,I.L.,Afurthergeneralizationofthekakutanifixedpointtheoremwithapplicationtonashequi2libriumpoints,ProceedingsoftheNationalAcademyofScience,38(1952),170-174.[9]Harsanyi,J.andSelten,R.,AGeneralTheoryofEquilibriumSelectioninGames,TheMITPress.1988.[10]Kreps.D.andPorteus,E.,TemporalVonNeumaun2MorgenstenandinducedPreferences,JournalofEco2nomicTheory,20(1970),81-109.[11]Machina,M.J.,Expectedutilityanalysiswithouttheindependentaxiom,Econometri