博弈论讲义auctions

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1、LectureXVI:AuctionsMarkusM.M¨obiusApril20,2006•Osborne,chapter9•Gibbons,chapter3•PaulKlemperer’swebsiteathttp://www.paulklemperer.org/hasfan-tasticonlinematerialonauctionsandrelatedtopics.Iparticularlyrec-ommendhisbeautifulonlinebook“Auctions:TheoryandPractice”forasupremelyreadableandnon-

2、technicaldiscussionofauctionsandthesurveychapter“ASurveyofAuctionTheory”foraconciseoverviewofthemaintheory.1IntroductionWealreadyintroducedaprivate-valueauctionwithtwobidderslasttimeasanexampleforagameofimperfectinformation.Inthislectureweexpandthisdefinitionalittlebit.Inallourauctionsther

3、earenparticipantsandeachparticipanthasavaluationviandsubmitsabidbi(hisaction).Therulesoftheauctiondeterminetheprobabilityqi(b1,..,bn)thatagentiwinstheauctionandtheexpectedpricepi(b1,..,bn)whichhepays.Hisutilityissimpleu=qv−p.aiiiiaTheagentisalwaysassumedtoberisk-neutralandjustmaximizehise

4、xpectedprofit-newissuesariseifthebiddersarerisk-averse.1Therearetwoimportantdimensionstoclassifyauctionswhicharebasedonthistemplate:1.Howarevaluesvidrawn?Intheprivatevalueenvironmenteachbidderhasaprivatevaluevifortheitemtobeauctionedoff.Intheimportantindependentprivatevaluecasethetypesaredr

5、awnindependentlyfromsomedistributionFiforeachplayeriwithsupport[v,v].Forourpurposeswenormallyassumethatallbidders’valuationsarenotjustprivatebutalsodrawnindependentlyandfromanidenticaldistributionF(wesayprivatevaluesarei.i.d.).1Inthecorrelatedprivatevalueenvironmenttheviarenotindependent-

6、forexampleifIhavealargevitheotherplayersarelikelytohavealargevalueaswell.Somewhatconfusinglythespecialcasewhereallbiddershavethesamevaluationv=viscalledthepurecommonvalueenvironment.2ij2.Whataretherules?Inthefirstpriceauctionthehighestbidwinsandthebidderpayshisbid.Inthecaseofatieafaircoini

7、sflippedtodeterminethewinner.3Inthesecondpriceauctionthehighestbidderwinsbutpaysthesecond-highestbid.Intheall-payauctionallbidderspayandthehighestbidderwins.Allthesethreeauctionsarestaticgames.ThemostfamousdynamicauctionistheEnglishauctionwherethepricestartsatzeroand