密封价格拍卖或招标中的有限腐败

3:,,,,,,(aggressive),,,,,:3,,:200433;,,,:430063,:[e-mail],,,,,,,,,,,,,,,,,,,,?(),(,),,,,,611:,,,(),,,,,,,JonesMenezes(1995),LengwilerWolfstetter(2004),MenezesMonteiro(2003),()ArozamenaWeinschelbaum(2005),,BurguetPerry(2004),,Compteetal.(2007),,,:,,,(),,,,,,,(),,,,:(1);(2);(3);(4):,,,,,,,,,,,,,,,,,,71120085,,,,,,,,,,,(),CelentaniGanuza(2002),BurguetChe(2004)(favoritism),,,,LaffontTirole(1991),Vagstad(1995)(,),McAfeeMcMillan(1998),Branco(1994),NaegelenMougeot(1998)(),,,,,,:(1)N:;(2)vi(i=1,2,,N):;(3)(),():;(4)F(v),f(v):;(5)[0,v]:,,,,,,:,,(,),,,811:1.,,,,,,LengwilerandWolfstetter(2004)2.,,,:blbh,:(1)Vjj,j=1,2,,N;(2)Y1=Y(N-1)1N-1;(3)G()g()Y1;(4)(),()b(biddingfunction)(reversebiddingfunction);(5)l(),l(),bl,h(),h()bh(6)EU0,Em0;EU,Em;EUc,Emc;E0,E,;,;,;,,,:max:(v-b)G((b)).:(v-b)=F((b))(N-1)f((b))(b)(1):v=(b),:(v)=v-v0G(x)G(v)dx,(2)G(x)=(F(x))N-1.,h(v)(v),v[0,v],v3(0,v)h(v)(v),Pv[0,v3);h(v)=(v),Pv[v3,v]:v[0,v3]:max:(v1-bl)G((bl))+(v1-bh)[G((bh))-G((bl))]v(v3,v):max:(v1-bl)G((bl))+(v1-bh)[1-G((bl))]91120085,,()();blbh.:bl(bh-bl)=F((bl))(N-1)f((bl))(bl)(3)bh(v-b)(N-1)f((bh))(bh)F((bh))+F((bl))F((bh))N-1=1v[0,v3]0,v(v3,v](4)v3(bh(v))=v,v1=h(bh)v[0,v3].(1)(4),:h(b)(b),:(v)h(v)1,(6)(7),(2);:l(v)(v)h(v)(5)l(v)=bh-bh0G(x)G(bh)dx(6)h(v)=v-1-F(bh)N-1F((bh))N-1(bh)0G(x)G((bh))dxv[0,v3]h(v3)v(v3,v](7).(1),(2),(3),(4)l()h()[0,v3](6)(7),h()(v3,v)(4)l(v)(v),l(v)(v),:v=((v))(l(v))=h(v)h(v)v,,l(v)01(),,,,,(aggressive),:,,()021:,,p=F((b))N-2F(h(b)),:EU=v0(v-b)F((b))N-2F(h(b))f(v)dv.(8):Em=v0b(v)F((b))N-2F(h(b))f(v)dv.(9),EU0Em0EU0=v0(v-b)F((b))N-1f(v)dv=v0v0G(s)dsf(v)dv(10)Em0=v0bF((b))N-1f(v)dv=v0vG(v)-v0G(s)dsf(v)dv.(11):2,,:,:p3=F((b))N-1,(b)h(b),p3p(8)(10)(9)(11),EUEU0EmEm0,,?,,,:EUc=v0{(v1-bh)F(min{(bh),v})N-1+(bh-b1)F((bl))N-1}f(v1)dv1v301-F(bh)N-1F((bh))N-1(bh)0G(s)ds+bh0G(s)dsf(v1)dv1+vv3{(v1-bh(v3))+(bh(v3)-bl(v3))F(bh(v3))F(bh(v3))N-1}f(v1)dv1(12):Emc=v30vF((bh))N-1f(v)dv+vv3vf(v)dv-EU1(13):r,:r(v)=E[max{Y(1),r}|Y(1)v]=v-vrG(x)G(v)dx.(14)121200853,,,:F(min{(bh),v})N-1(bh(v))v,F((bh))N-1F((b))N-1=F(v)N-1,3h(v)bh(14):3h(v)=v-vbhG(x)G(v)dx(15)3h(v)h(v):vbhG(x)dx=(v-3h(v))G(v)(16)v[0,v3]:Uc-U0={(v-bh)F((bh))N-1+(bh-bl)F((bl))N-1}-(v-b)F((b))N-1=(v-bh)F((bh))N-1+bh0G(s)ds-v0G(s)ds=(v-bh)F((bh))N-1-vbhG(s)ds=(v-bh)F((bh))N-1-(v-b3h)F(v)N-10(17)v(v3,v]:Uc-U0={(v-bh)+(bh-bl)F((bl))N-1}-(v-b)F((b))N-1=(v-bh)+bh0G(s)ds-v0G(s)ds=vbh(1-G(s))ds0(18)Uc-U00,v[0,v3]:mc-m0={bhF((bh))N-1-(bh-bl)F((bl))N-1}-bF((b))N-1=bhG((bh))-bh0G(s)ds+v0G(s)ds-vG(v)=bhG((bh))+vbhG(s)ds-vG(v)=bhG((bh))+(v-b3h)G(v)-vG(v)=bhG((bh))-b3hG(v)(19)v(v3,v]:mc-m0={bh-(bh-bl)F((bl))N-1}-bF((b))N-1=bh(v3)-bh(v3)0G(s)ds+v0G(s)ds-vG(v)=bh(v3)+vbh(v3)G(s)ds-vG(v)221:=bh(v3)+(v-b3h(v))G(v)-vG(v)=bh(v3)-b3h(v)G(v).(20),bh(v)G((bh(v)))b3h(v)G(v),Emc-Em00,:v(v3,v]vbh(v3)b3h(v)G(v),v[0,v3)bh(v)G((bh(v)))b3h(v)G(v)Emc-Em0?,,:E0=NEm0=Nv0bF((b))N-1f(v)dv=Nv0vG(v)-v0G(s)dsf(v)dv(21),:E=(N-1)Em+Emc=(N-1)v0bF((b))N-2F(h(b))f(v)dv+v30[bhF((bh))N-1-(bh-bl)F((bl))N-1]f(v)dv+v0[bh(v3)-(bh(v3)-bl)F(bl)N-1]f(v)dv=v0{(N-1)bF((b))N-2F(h(b))+[bhF((bh))N-1-(bh-bl)F((bl))N-1]}f(v)dvvv3{(N-1)bF((b))N-2F(h(b))+[bh(v3)-(bh(v3)-bl(v3))F(bl)N-1]}f(v)dv(22)4,,bh(v)G((bh(v)))b3h(v)G(v),bh(v)G((bh(v)))-b3h(v)G(v)0(v[0,v3]),3(21),(22),,,,k(2),k:(1)(2)(k);:b(1)b(2)b(k),:max:(v1-b(1))G((b(1)))+(v1-b(2))[G((b(2)))-G((b(1)))]++(v1-b(k)[G(min{(b(k)),v})-G((b(k-1)))]:b(1)(b(2)-b(1))=F((b(1)))(N-1)f((b(1)))(b(1))(23)b(2)32120085(b(3)-b(2))=F((b(2)))(N-1)f((b(2)))(b(2))(24)b(k-1)(b(k)-b(k-1))=F((b(k-1)))(N-1)f((b(k-1)))(b(k-1))(25)b(k)(v1-b(k))(N-1)f((b(k)))(b(k))F((b(k)))+F((b(k-1)))F((b(k)))N-1=1v[0,v3]min{(b(k)(v)),v}vv[v3,v][v3,v](26)v3(b(k)(v))=v,v1=(k)(b(k))v[0,v3](1)(26),(k)(b)(b),:(v)(k)(v).(1),(2),(23)(26):(1)(v)=b(2)-b(2)0G(x)G(b(2))dx(27a)(2)(v)=b(3)-b(3)0G(x)G(b(3))dx(27b)(k-1)(v)=b(k)-b(k)0G(x)G(b(k))dx(27c)(k)(v)=v-1-F(b(k))N-1F((b(k)))N-1(b(k))0G(x)G((b(k)))dxv[0,v3](27d)5,(27a)(27c)(28),(2);:(1)(v)(2)(v)(k-1)(v)(v)(k)(v)(k)(v)=v-1-F(b(k))N-1F((b(k)))N-1(b(k))0G(x)G((b(k)))dxv[0,v3]b(v)v(v3,v)(28):(28),v[0,v3](27d),(28)v(v3,v],1(28)(k-1)(v)(v),(k-1)(v)(v),:v=((v))((k-1)(v))=(k)(v)(k)(v)v,,(1)(v)0(6)(28),,,h(v)=(k)(v),[0,v],k-1[0,b(v)],,421::6,;,;:k(2),,,p=F((b))N-2F((k)(b)):EUk=v0(v-b)F((b))N-2F((k)(b))f(v)dv(29):Emk=v0b(v)F((b))N-2F((k)(b))f(v)dv(30)h(v)=(k)(v),:h(b(v))=(k)(b(v)),EUk=EU;Emk=Em,,:EUkc=v30{(v1-b(k))F((b(k)))N-1+(b(k)-b(k-1))F((b(k-1)))N-1+(b(k-1)-b(k-2))F((b(k-2)))N-1+(b(k-2)-b(k-3))F((b(k-3)))N-1++(b(3)-b(2))F((b(2)))N-1+(b(2)-b(1))F((b(1)))N-1}f(v1)dv1+vv3{(v1-b(k)(v3))+(b(k)(v3)-b(k-1))F((b(k-1)))N-1+(b(k-1)-b(k-1))F((b(k-2)))N-1+(b(k-2)-b(k-3))F((b(k-3)))N-1++(b(3)-b(2))F((b(2)))N-1+(b(2)-b(1))F((b(1)))N-1}f(v1)dv1=v301-F(b(k))N-1F((b(k)))N-1(b(k))0G(s)ds+b(k)0G(s)ds+b(k-1)0G(s)ds+b(k-2)0G(s)ds++b(2)0G(s)dsf(v1)dv1+vv3(v1-b(n)(v3))+b(k)(v3)0G(s)ds+b(k-1)0G(s)ds+b(k-2)0G(s)ds++b(2)0G(s)dsf(v1)dv1(31):Emkc=v30{