可计算的不完全市场一般经济均衡

12GEIGEIGEI1Leon·Walras34A·Wald193519365WaldWald1936Wald620WaldVon·NeumannF.Nash1950WaldK·ArrowF·H·Hahn19711954ArrowDebreuA-DWalras7K·J·ArrowG·Debreu1954A-DArrow8Arrow9Debreu19531011972219773L·WalrasElementsdEconomiePolitiquePureLausanneL.Corbaz1987418775WaldNeisserStackelbergZeuthenSchlesinger6SamulesonWald7128K.J.Arrow19525CNRS9101111213Geanakoplos123(Generalequilibriumwithincompletefinancialmarkets(GE1)AD14GEIA-D:Geanakoplos1990MagilShafer199115GEIGEIGEIGEIGEIGEIGEIGEI20Radner1972GEI16Hart1975GEI17PolemarchakisKu1990Kreps1979Hart18GEI19Lutz-AlexanderBuschSrihariGovindan2004201112200313Meton/14ElA-D15Fisher16GEIGEI17GEIGEI18McManus,1984;Repullo,1986;MagillandShafer,1990DuffieandShafer(1985)19Geanakoplos1990202GEIhomotopy-path-followingGEIGEIGEI2GEIGEIT=0,10S=0,1SL1,2,...,,iII=∞∞1,2,...,,sSS=L∞{}1012(,,,...,),(1)MMSppppppMLS−++++=∈≡∈ℜ=+1M,−++M21i012(,,,...,)iiiiiTSxxxxx++=∈ℜisiisx+∈ℜLM012(,,,...,)iiiiiTSωωωωω++=∈ℜ22:iMu++ℜ→ℜN23j112(,,...,)NNqqqq=∈ℜ2412(,,...,),1,2,...,;1,2,...,jjjTSLjSAaaajNsS++=∈ℜ==jLsa∈ℜs;12(,,...,)SLNNAAAA×=∈ℜ2512000...0000...00000...SMsppQp×⎡⎤⎢⎥⎢⎥=∈⎢⎥⎢⎥⎣⎦ℜQLQ−1122(,,...,)jjjTLjSSQpapapa−S=∈ℜAj26js()SNLRpQA×−=∈ℜsp,(())sjRp1Nθ∈ℜ()Rpθ0qθ()iDuxpqI()1,2,...,1,2,...,(,)((),())iiiIiIuuωω===((,),))uAωΕ≡Ε(())RankRpS=(011)E212212324025nn263127(())RankRpS()E1Mp−++∈Nq∈ℜ(,)iUpq,000max()..()()()ixiiiiiuxstpxqQxRpθ,.iωθωθ−≤−−≤01(,)pq1,2,...,(,)iiiIxθ=(1)(,)iixθ(,),1,...,iUpqiI=(2)11IIiiiixω===∑∑(3)10Iiiθ==∑qCass1984(,)iUpq()E1,2,...,(,)iiixθ=I11110()arg[max()..()0]xxpuxstpxω=−=2110()arg[max()..()0,()()],2,...,iiixxpuxstpxQxRpiωωθ=−=−=I=311()IIiiiixpω===∑∑UC,Hart1975(())RankRpNix()E(())RankRpN=p(())RankRpNp3C,000max()..()0,()()ixiiuxstpxQxRpθω.ωθ−=−=(S=3,N=2)E12()((),()),()iRpRpRpRp3=∈ℜθ()(iQxRpω−≤)1274()Rp()Rp1x(iQx)ω−()Rp281-a()Rp29p1()Rp2()Rp30()Rp1()Rp2()Rpθ1-b1()Rp2()Rp311()Rp2()Rp11-c()Rpθ32p1()Rp2()Rp()iQxω−1()Rp2()Rp()iQxω−2()Rp2()Rp()iQxω−1-a1b”(())2RankRpN==1c”(())1RankRpN=3.1C1Mp−++∈[0,1]t∈(,)iPpt2,1max()(1)2..()0,()().ixiiuxtstpxQxRpθθωωθ−−−=−=21(1)2tθ−t1ti”t1(,)iPptp1()Rp2()Rp()iQxω−()Rp2829)Rp(303132Hart1975533xpθ()iQxω−()Rpx34[0,1]t∈t0t1t11t(,)iPpt3.2135n:nFℜ→ℜnn()0Fy=y∗()0,:nEyE=ℜ→ℜ0y0()0Ey=y[0,1]t∈:[0,1]nHnℜ×→ℜt(,0)(),(,1)()HyEyHyFy==t010y()Ey((0),0)y((1),1)y(,1)0Hy=(2)GEIZZ(p)0Brown1996bDemarzoEaves1996A-DGEI36Brown1996bDemarzoEaves1996373839U;()0(2)()0(3)uuuuDuxppxλω−=−=C3334Schmedders199635GarciaZangwill1981Judd1998AllgowerGeorg199036GEI37GEI38Judd(1998)396()0(4)(1)()()0(5)()0(6)()()0iiiiiTiiiiiiDuxpQtRppxQxRpλµθµωωθ−−=−−+=−=−−=(7)()()0(8)uuuuslslslslicxtxωω∈−+−=∑(1)0(9)slslp−=∑29t1GEI40uMω++∈ℜ2941uHω(,,(,,,),,)0uuuiiiiiCHxxptωλθλµ∈=GEI(,,(,,,),)(,1)0uuuuiiiiiCExxpHωωλθλµ∈≡=i1(1)(1)(1)MMNSHM+++++−+−D{:R()=N}MPprankp++=∈ℜ1()MMNSH−++++=ℜ×ℜ×ℜ×ℜ×ℜ×ℜuHω42(([0,1))([0,1]))MDP++×ℜ×∪×(,,(,,,)),(,)(([0,1))([0,1]))uuiiiiMiCxxDptPλθλµ∈++∈∈ℜ×∪×4344GEI11t→pp→()RankRpN=()iiCθ∈(,,(,,,),)uuiiiiuiCxxpλθλµ∈3;22,11maxt()(1)(1)22..()0,()().iixiiuxtxtstpxQxRpθωθωωθ−−−−−−=−=t14()(1)()0iiiiiitDuxtxpQωλµ−−−−−=8()()uuuuslslslslicxxωω∈−+−=∑0UupC40U41()Rpuω42uHωSchmedders(1996)4344Schmedders19967(,,,)iiiiiCxθλµ∈(10)(,,(,,,),,)(,,(,0,0,0),,0)uuiiiiuuiiCiCxxptxxλθλµλ∈∈=p104HOMPACK451DeMarzoEaves199646;GEII=3U,1,21S=3,N=2L=2C12(10,10;25,20;20,20;15,20)cTω=312120()(()())1113(1,,,),3334cssssuxBxxααππα−==−−==∑U(20,20;5,10;10,10;15,10)uTω=312120()(()())14ussssuxBxxββπβ−==−−=∑1010102-1102-1TA⎡⎤=⎢⎥⎣⎦GEI47C3132U,(0.10854,0.32561;0.079907,0.11986;0.045957,0.13787;0.033137,0.14912)up≈170.45uλ≈,,0,0,0uucccccxxωωθλµ=====(0.30239,0.22111;0.10096,0.07041;0.09662,0.06771;0.08005,0.06125)p≈48(5.9643,24.4789;6.2020,26.6775;6.7732,29.2549;8.7209,34.1946)uTx≈(17.0178,7.7605;24.3990,11.6612;21.6143,10.3725;18.1395,7.9027)cTx≈12(0.63405,4.43950)cTθ≈−−;0.100960.13151()0.096620.096620.080050.09885Rp⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦45HOMPACKDEC5000/200()Rp80(0.27763,0.32698)q≈C1200110U01s113s3U01s1C12UC12111,0ccθθ≤11221.62766qqθθ+=0U02.355321()(2)(1.29570,0.98041,0.97920)cRpθ−=T49s121U(20,20;8,24;10,30;6,18)uTω=(0.11394,0.34183;0.090705,0.090705;0.080037,0.080037;0.10137,0.10137)up≈0.0907050.090705()0.0800370.0800370.101370.10137Rp⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦,;()12rankRPN==(0.30197,0.23329;0.08974,0.05871;0.09640,0.05199;0.11044,0.05747)p≈(6.5885,25.5843;8.4517,38.7553;7.9068,43.9831;6.8188,39.3086)uTx≈(16.7057,7.2079;24.7741,12.6224;21.0466,13.00884;14.5906,9.3457)cTx≈(4.0107,6.7347)cTθ≈−6L·WalrasParetoK·ArrowF·H·HahnGEIGEIGEI1:iMu++ℜ→ℜ1iuiuC∞∈2MxR++∈()iMDuxR++∈4993MxR++∈:()()Miixuxux++∈ℜ≥MR40h()0iDuxh=2()0TihDuxh[1]BrownD·J.,DeMarzoP·M.,EavesB·C.Computingzeroesofsectionsofvectorbundlesusinghomotopiesandrelocalization[J].MathematicsofOperationsResearch,21,1996,26-43[2]CassD.Competitiveequilibriumwithincompletefinancialmarkets.CARESSWorkingPaper,UniversityofPennsylvania.1984.[3]DeMarzoP.M.,EavesB.C.ComputingequilibriaofGEIbyrelocalizationonaGrassmannmanifold[J].JournalofMathematicalEconomics,26,1996.479-497.[4]DuffeD,ShaferW.Equilibriuminincompletemarkets[J].JournalofMathematicalEconomics,14,19