Myerson 1981 - Optimal auction design

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1、MATHEMATICSOFOPERATIONSRESEARCHVol.6,No.1.February1981PrintedinU.S.A.OPTIMALAUCTIONDESIGN*?ROGERB.MYERSONNorthwesternUniversityThispaperconsiderstheproblemfacedbyasellerwhohasasingleobjecttoselltooneofseveralpossiblebuyers,whenthesellerhasimperfectinformationabouthowmuchthebuyersmightbewillingto

2、payfortheobject.Theseller'sproblemistodesignanauctiongamewhichhasaNashequilibriumgivinghimthehighestpossibleexpectedutility.Optimalauctionsarederivedinthispaperforawideclassofauctiondesignproblems.1.Introduction.Considertheproblemfacedbysomeonewhohasanobjecttosell,andwhodoesnotknowhowmuchhispros

3、pectivebuyersmightbewillingtopayfortheobject.Thissellerwouldliketofindsomeauctionprocedurewhichcangivehimthehighestexpectedrevenueorutilityamongallthedifferentkindsofauctionsknown(progressiveauctions,Dutchauctions,sealedbidauctions,discriminatoryauctions,etc.).Inthispaper,wewillconstructsuchopti

4、malauctionsforawideclassofsellers'auctiondesignproblems.Althoughtheseauctionsgenerallyselltheobjectatadiscountbelowwhatthehighestbidderiswillingtopay,andsometimestheydonotevenselltohighestbidder,weshallprovethatnootherauctionmechanismcangivehigherexpectedutilitytotheseller.Toanalyzethepotentialp

5、erformanceofdifferentkindsofauctions,wefollowVickrey[l11andstudytheauctionsasnoncooperativegameswithimperfectinforma-tion.(SeeHarsanyi[3]formoreonthissubject.)Noncooperativeequilibriaofspecificauctionshavebeenstudiedinseveralpapers,suchasGriesmer,Levitan,andShubik[I],Ortega-Reichert[7],Wilson[12

6、],[13].Wilson[14]andMilgrom[5]haveshownasymptoticoptimalitypropertiesforsealed-bidauctionsasthenumberofbiddersgoestoinfinity.HarrisandRaviv[2]havefoundoptimalauctionsforaclassofsymmetrictwo-bidderauctionproblems.IndependentworkonoptimalauctionshasalsobeendonebyRileyandSamuelson[8]andMaskinandRil

7、ey[4].AgeneralbibliographyoftheliteratureoncompetitivebiddinghasbeencollectedbyRothkopfandStark[lo].Thegeneralplanofthispaperisasfollows.$2presentsthebasicassumptionsandnotationneededtodescribetheclassofauctiondesignproblems