搜索
200211:100026788(2002)01200832061,2(1.,100080;2.,100083):,,,L:;;:F724.59;O22:AaOnBiddingDecision2makingofN2PersonJ2ObjectAuctionMAJun1,QIUWan2hua2(1.AcademyofMathematicsandSystemSciences,ChineseAcademyofSciences,Beijing100080,China;2.SchoolofEconomics&Management,BeijingUniversityofAeronauticsandAstronautics,Beijing100083,China)Abstract:Inthispaper,thebiddingdecision2makingmodelforN2persontwo2objectEnglishauctionsisimproved.Andthebiddingdecision2makingproblemforthree2objectEnglishauctionsisstudied.Thefirstmodelshowsthatthebidders’profitandthebid2taker’srevenuevarywiththechangeinthesequenceoftheobjectsforauction.Inaddition,auctioningobjectswithhighvaluefirstisbeneficialtothebid2taker.Keywords:auction;biddingdecision2making;sequentialauction1LR.P.McAfee1987:,L,,LL2080,L,,,,LL:,,,,LL,:L,LPaulR.MilgromL,a:2000204210:(79930900)©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:(SimultaneousDependentAuctionSDA),,,;SDA,,(SimultaneousIndependentAuctionSIA),,;(SequentialAuctionSA),,L,,LL21,,L,,,L,nLL,,,,,L,,n,L:Bi=i;Ci=Bi;Vj=j;i=Bi;bij=Bij,i=1,2,,n;j=1,2Z:A1:;A2:V1V2;A3:C1C2Cn,2Ci+2Ci;A4:k,kZ,ii=6Jj=1Dij(b1j,,bnj)õ(Vj-bij)Dij=1bijbkj,Pki,0bijbkj,vki,i=1,2,,n;j=1,2,,JJ,J=2ZA4,kbij,Dij=1ök.[1],,B1B2,1Z1VkC1(k=1,2),A1-A4,bB1:C3bmin{C1,(V1-V2+C3)}(1)B2:C3bmin{C2,(V1-V2+C3)}(2)2,Z1,,:B1:C3bmin{C1,(V2-V1+C3)}(3)B2:C3bmin{C2,(V2-V1+C3)}(4)V1V2,V1-V2+C3C3,(1)C3bV1-V2+C3,U,B1,B2C3,B1C3,2C3Z,V2-V1+C3C3,(3)(4),b+C32C3Z,Z2.[1],,4820021©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.ZZ2,V1V2,V1V2ZA2,C1C2Cn,2C3C1,[1],Z1)VkC1(k=1,2),1;2)V1C11in,Ci+1V2CiZi2,,B2C2,B1C2+E(E),B1,V1-C2-E;B2C2B1,B2,B1,B3,,B1C3+E,V2-C3-EZB1,ZV1-C2V2-C3,B1C2+E,B2C3+E;V1-C2V2-C3,B1,C3+E,V2-C3-E,B2(C2)Zi2,B1C2+E,B2,,BiV21ö(i-1)Z3)1i,jn,Cj+1V2CjCi+1V1CiZi=1,j=2,2)Zi=1,j2,B1C2+E,B2,,BjV21ö(j-1)Zi1,j2,B1,,BiV11ö(i-1),,B1,,BjV21ö(j-1)Z,Z11,V1V2,:1)VkC1(k=1,2),1;2)V1C1iCi+1V2CiZi2,V1-C2V2-C3,B1C2+E,B2C3+E;i2,V1-C2V2-C3,B1C3+E,B2C2Zi2,B1C2+E,B2,,BiV21ö(i-1)Z3)1i,jn,Cj+1V2CjCi+1V1CiZi=1,j=2,2)i2;i=1,j2,B1C2+E,B2,,BjV21ö(j-1)Zi1,B1,,BiV11ö(i-1),,B1,,BjV21ö(j-1).4)i,Ci+1V1,V2CiZi=1,(2)i2;i1,B1,,BiV11öi,,B1,,BiV21ö(i-1).5)i,Ci+1V1Ci,V2CnZi=1,B1C2+E,B2,,Bn-1V21ö(n-1);i1,B1,,BiV11öi,,B1,,BnV21ö(n-1).6)VkCn(k=1,2),Vk,1ön()Z,n3,B3,,ZZ581©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.32,jVj(j=1,2,3,),V1V2V3C1ZA22Ci+2Ci2Ci+3Ci,1,Z,,,ZZBi-1,Bi,Bi+1,Bi+2ZCi+2Ci+1CiCi-1,Bi+2b,Bi-1,Bi,Bi+1,Bi+2,,,Bi-1,BiBi+1,,Bi+1,bCi+2,Bi+2,Z,,B1,B2,B3,B4ZB1,B2,B3,B4(,C12C4,),B4C4,,B3b,bC4,B4,B1Z1)B1,b+E,B2,B3,B1b+E,V1-(b+E),C1-(b+E),EZC1-(b+E)C3,B1,B3,C1-C3,Z2)B2bC3,B3,B1b+E,B1,V1-(b+E);B1,B2,V1-b,C2-b;,bC3]bC4,3)Z3)B1,B3,B2,b+E,B2,V1-b,C2-b,C2-bC4(bC4,22C4);Z{C1,C2-b,C3,C4},1:B1:C4b2min{C1,(V2-V3+C4)}B3:C4b2min{C3,(V2-V3+C4)},B1,B2,B3,,B4,C4,V1-(b+E)V2-min{C1,(V2-V3+C4)},V1-(b+E)V3-C4(),B1ZB1max{C1-C3,C4}b1min{C1,V1-V2+min{C1,(V2-V3+C4)},V1-V3+C4}A2,2Ci+3Ci,2C4C1,C1-C3C1-C4C4,C4b1min{C1,V1-V2+min{C1,(V2-V3+C4)},V1-V3+C4}4)B1,B2,B3,V1-b,C3-bZ{C1,C2,C3-b,C4}C1C2C4C3-b,3)ZB2B3,:2,1Z,C4Z1B1C4b1min{C1,V1-V2+min{C1,(V2-V3+C4)},V1-V3+C4}C4b2min{C1,(V2-V3+C4)}B2C4b1min{C2,V1-V2+min{C2,(V2-V3+C4)},V1-V3+C4}C4b2min{C2,(V2-V3+C4)}B3C4b1min{C3,V1-V2+min{C3,(V2-V3+C4)},V1-V3+C4}C4b2min{C3,(V2-V3+C4)}6820021©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.4V1=150,V2=120,V3=80,B1,B2,B3,B4,B5,C1=100,C2=80,C3=60,C4=50,C5=40Z,2,Z,B1:C4b1min{C1,V1-V2+min{C1,(V2-V3+C4)},V1-V3+C4}50b1min{100,150-120+min{100,120-80+50},150-80+50}50b1100B2:C4b1min{C2,V1-V2+min{C2,(V2-V3+C4)},V1-V3+C4}50b1min{80,150-120+min{100,120-80+50},150-80+50}50b180B3:C4b1min{C3,V1-V2+min{C3,V2-V3+C4},V1-V3+C4}50b1min{60,150-120+min{100,120-80+50},150-80+50}50b160,B1100,B280,B360,B450,B1,B2,B350,B180Z,{C1-80,C2,C3,C4}ZB1ZB2:C4b2min{C2,(V2-V3+C4)}50b2min{80,(120-80+50)}=80B3:C4b2min{C3,(V2-V3+C4)}50b2min{60,(120-80+50)}=60,B1,B280,B360,B450,B2,B350,B260ZB350Z:B1b1=80,1=150-80=70,=100-80=20;B2b2=60,2=120-60=60,=80-60=20;B3b3=50,3=80-50=30,=60-50=10;:80+60+50=190Z5,Z,,Z781©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:[1].[J].,1996,24(11):82-84.[2]ThomsRPalfrey.Multiple2object,discriminatoryauctionswithbiddingconstraints:agame2theoreticanalysis[J].ManagementScience,1980,26(9):935-945.[3]DonaldBHausch.Multi2objectauctions:sequentialvs.simultaneousseals[J].ManagementScience,1986,32(12):1599-1610.[4]MichaelHRothkopf.Biddinginsimultaneousauctionswithaconstraintonexposure[J].OperationsResearch,1977,25(7-8):620-629.[5]ShmuelSOren,MichaelHRothkopf.Optimalbiddinginsequentialauctions[J].OperationsResearch,1975,23(11-12):1080-1090.(70),,,LBP,,,LBP,,L:[1]AlexanderGParlos.Anacceleratedlearningalgorithmformultilayerperceptronnetworks[J].IEEETransonNeuralNetworks,1994,5(3):493-497.[2]VoglTP,MangisJK,etal.Acceleratedtheconvergenceofthebackpropagationmethod[J].BioCybern,1988,59(9):256-264.[3],,.[M].:,1995.[4]JacqnesSavoy.Statisticalinferenceinretrievaleffectivenessevaluation[J].InformationProcessingandManagement,1997,33(4):495-512.[5]GeorgeChryssolouris,MoshinLee.Confidencei