经济博弈论讲演

11••••——.B.,12•GameTheory•-Max-Max1.1,,,,!!————..13•——•(cooperativegame)(non-cooperativegame)•(bindingagreement)————•94•,:1994(Nash)(Selten)(Harsanyi)·141.2•——•————•——••(incentivecompatible)(self-selection)•——————•————•————15•••1(1,1)(1,1)(1,1)12216nnwrwrwr===L2211)(21Rrrrn=+++L1=wN,n11-+=nNNw12-+=nNnwnNnNL+-=nNrr=212“9”ABDDFDDFODFODF222111/wcrwcr=nNcc=12172.11•()i=1,2,3,…,nn•––),,,(21iikiiisssSL=),(2,1iikiiipppPL=11=∑=ikjijp•:•••••()••iiijikjSsdL,2,1=∈=),,(21niddduL=18(1)•(rational),(1738)·/1974.—E[U(x)]UxUxUxxu(x)=1-e-cxc(Pratt,1964)(intelligent)(2)192.2•–,–•––Kreps,Wilson(1982)Fudenberg,Tirole(1991)(1967-68)(1965)(1950-51)1101O•n=2,S1=S2=(A,B)•=(A,A),(A,B),(B,A),(B,B)•u1(A,A)=2,u1(A,B)=-1,u1(B,A)=-2,u1(B,B)=1,•u2(A,A)=-2,u2(A,B)=1,u2(B,A)=2,u2(B,B)=-11-1-22B-112-2ABA122.31-2B-12ABA21Mm21mM-2-11:*=BBu1*(B,B)=1u2*(B,B)=-1-12B1-2ABA21mM-2-1Mm212:,*=BBu1*(B,B)=1u2*(B,B)=-1111(2)(2)•Pareto()()•301121,2A,B•1(p1,p2)=(p,1-p)•2(q1,q2)=(q,1-q)1A2q-(1-q)≥0=3q-1≥0B-2q+(1-q)≥0=-3q+1≥02A2p-2(1-p)≤0=4p-2≤0B-p+(1-p)≤0=-2p+1≤01-2B-12ABA•1(p1p2)=(1/21/2)•2(q1q2)=(1/32/3)112•i=1,2,3,…,nsi•n:s=(s1,s2,…,sn)s1,s2,…,sn•is),,,(21iikiiisssSL=∑∑∑∑∑===++=--=⋅=+++---nnnniliiiliiiklnlijllinlnklklliiklliilkjijiissssusssssu1211111111111),,,,,()()()()()()(21111111111LLLLssssss∑∑===212112221111),()()()(lljljjssussusss()()01322312113223121=⎟⎠⎞⎜⎝⎛×+-×+⎟⎠⎞⎜⎝⎛-×+×=∑∑===212121121222),()()()(ljlljjssussusss()()01211213222122131=⎟⎠⎞⎜⎝⎛-×+×+⎟⎠⎞⎜⎝⎛×+-×=1-1-22B-112-2ABA1134O2,89,63,0D3,68,42,1M6,25,14,3URML12293D382M654URML12860D641M213URML122MR“”——2,83,0D3,62,1M6,24,3URL126,24,3URL12:(U,L)(4,3)32D23M46URL12114(1)–n•:Nash2.4-1-1-1500-15-8-821:(,),(-8,-8)•ABBA(2)115(3)Nash()dhcgDbfaeURL(U,L)NashDUdhcgDbfaeURLdhcgDbfaeURLdhcgDbfaeURLNash(4)Nash•s*i(i=1,2,…,n)s*Nash•s*Nash****),(),(iiiiiiiiuussssss≠∀≥--116IIIIII(5)Nash••3.1Nash()117(1)Nash/==WSgw(wg)v(vw)==I,Nh(hw)w-gv-ww-gv-w-hWw-w0-hSNINashx(1-x)y(1-y)Nashs2=y1-yxu1(s1,s2)xw(1–y)=w–gy=g/wx=h/w[][]))(1()1()1)(()()1()1(0),(211gwxyxwygwygwxywyxu--+-=--+--+-+⋅=ss118Nashh/w1-h/wg/w1-g/wNashu2(s1*,s2*)=v(1–x)–w(1–xy)–hy=v(1–h/w)–wvhwvhhvw=hv(3)entrydeterrance03000300-1004050Nash())3.2Nash0012W21-1-1TWTNashTWWT(1/2,1/2)(1/2,1/2)119Nash•1960“”•(-1/2,1/2)10010•x∈(-1/2,1/2)y=x•t∈(-1/2,1/2)(t,t)Nash•(x,y)(x≠y)(t,t)(t,t)•[0∝•003.3Cournot2iqi(i=1,2)Qi=[0∞]2P=P(Q);iqi·P(Q);Ci(qi)iqiui=qi·P(q1+q2)-C(qi)(1)2(2)iqiqjj=1,2,…,n,j≠i21qqQ+=12012Cournotr1:Q2→Q1r2:Q1→Q2Cournot)()(122211qrqqrq==0)(')()(),(0)(')()(),(2221221221211211211211=-∂+∂++=∂∂=-∂+∂++=∂∂qCqqqPqqqPqqquqCqqqPqqqPqqquNashq1*,q2*))(12,0max()(2121qqqqp+-=+⎩⎨⎧≤++-+=+12)(12120)(21212121qqqqqqqqpC(q1)=c·q1,C(q2)=c·q2c⎪⎩⎪⎨⎧--=--=212)(212)(112221cqqrcqqr121q1*=q2*=4–c/3Cournotc=0Nashq1*=q2*=4u1(4,4)=u2(4,4)=16ui(q1,q2)=qi(12-q1-q2),q1=q2=3u1(3,3)=u2(3,3)=3×6=183.4Bertrandp1p2i(i=1,2)qi(pi,pj)=a–pi+bpjb0ij=0c,cai))(2,1(]][[])[,(),(jiicpbppacpppqppuijiijiijii≠=-+-=-=122NashBertrand(1)2(2)CournotBertrand)(21jibpcap++=jiiibpcpapu++-=∂∂2()()⎪⎩⎪⎨⎧++=++=*1*2*2*12121bpcapbpcapbcapp-+==2*2*1⎥⎦⎤⎢⎣⎡-+-+,2,2bcabca•Cournot•Duopoly•3.5Cournot123PQc0)()(21qqbabQaQPP+-=-==2,1)]()[())((),(2121=+--=-==iqqbcaqcQPqqquuiiii⎪⎩⎪⎨⎧------**])[(max])[(max222122121121bqqbqqcabqqbqqcaqq0q1q20⎪⎩⎪⎨⎧=---=---****02)(02)(2112bqbqcabqbqcabcaqq321-==**⎪⎩⎪⎨⎧=---=---****02)(02)(2112bqbqcabqbqca⎪⎪⎩⎪⎪⎨⎧=--==--=****)(2)(2*1212*2121qrbbqcaqqrbbqcaq⎟⎠⎞⎜⎝⎛--bcabca3,3124••(credibility)•“”“”•————“”•••“”•4.1——•()i=1,2,3,…,nn•••••125Stackelberg••12•c0)()(21qqaQP+-=2,1))((),(21=-=icQpqqquii“”q12)(),(Max2122122cqqaqqquq---=12nS0Sn2)(112cqaqr--=12612r2(q1)q1))(())(,(max121112111cqrqaqqrqq---=p21caq-=*24)(122caqrq-==**2:1374.3BargainingModel•B300•S200•BS[0,100]BP1(300-P1,P1-200)P2(300-P2,P2-200)(0,0)BSarara:r:SP2(300-P2,P2-200)P1(300-P1,P1-200)(0,0)SBarar127Pie:••1001003%S99B297SS297B31.4548.35251.650.0051.65——10.0046.75——1.6053.25253.2521.4548.20251.800.0051.80——3……………………………………0.185.82294.180.0094.18——970.002.91——2.9197.09297.09980.093.00297.000.0097.00——990.000.00——3.00100.00300.00100BS128Rubinstein-Stahl(R-S)•2k(k=0,1,2,…)B(x,1-x)x•SS•S2k+1B•BS•Stahl1972•Rubinstein1982•dl1-l=d•ydyy•Nash“”•[Rubinstein]SBB0dB10dS1BSdS×(1-dB)/(1-dS×dB)(1-dS)/(1-dS×dB)S1294.4•GTG“T”G(T)GG(T)G(T)G(T)G•GTG(T)GG(T)GTG-1-1-1500-15-8-821-8-8-9-9-23-8-8-23-16-1621-16-161305.1BayesBayes1)Cournot1cq122112•)()(21qqaQP+-=⎩⎨⎧-=HLLHCCqCqCqCqq1)(2222•2•1•2CH•2CL•1)()(*2*2LHCqCq*1q)(*2HCq()[]22*12maxqCqqaHq⋅---)(*2LCq()[]22*12maxqCqqaLq⋅---*1q()[]()()[]{}1*211*211max1qcCqqaqcCqqaLHq⋅----+⋅---qq131()()()()()[]()()[]{}⎪⎩⎪⎨⎧---+--=--=--=2/12/2/*2*2*1*1*2*1*2cCqacCqaqCqaCqCqaCqLHLLHHqq()()()()()⎪⎪⎪⎩⎪⎪⎪⎨⎧-++-=-++-=--++-=3126326132*1*2*2LHLHLLLHHHCCcaqCCcCaCqCCcCaCqqqqq⎪⎩⎪⎨⎧-=-=33*1*2caqcaqCL=CH=c•Cournot•Cournot•()021)()(*2*2-=-LHHLCCCqCq()()032)()(321*1*2*2*1==+-+-==qqqcCaCqCqcCaqLLHH132•niAii=1,2,…,n•iti1,ti2Ti={ti1,ti2}•ti1pti21-p•iui(a1,a2,…,an,tij),(j=1,2)•:•G={A1,A2,…,An;T1,T2,…,Tn;p1,p2,…,pn;u1,u2,…,un}5.3••111222()1335.4•1•2•3•4p(g|s)p(b|s)p(g)p(b)p(s|g)p(s|b)⎪⎪⎩⎪⎪⎨⎧⋅+⋅⋅=⋅=⋅+⋅⋅=⋅=)|()()|()()|()()()|()()|()|()()|()()|()(