Vickery-Clark-Groves Mechanism

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1、Vickrey-Clarke-GrovesMechanismsJonathanLevin1Economics285MarketDesignWinter20091TheseslidesarebasedonPaulMilgrom’s.JonathanLevinVCGMechanismsWinter20091/23MotivationWeconsidertheproblemofhowtoimplemente¢cientallocationsinanenvironmentwhereeachparticipanthasprivateinformationabouttheirp

2、references.Participantsmaymisrepresenttheirpreferences.Abankmayoverstateitsneedforafederalbailout,hopingtogettaxpayerstoabsorbitslosses.Abuyermightunderstateitsvalue,hopingtogetalowerprice.VCGmechanismsachieve“strategy-proof”implementationofe¢cientallocationsinquasi-linearenvironments,

3、butcanhavetroublewithbudgetbalance.JonathanLevinVCGMechanismsWinter20092/23ThemodelAsetofparticipantsN(SN),andthedesigner0.Typest=(t1,...,tN)describeparticipantinformation.Outcomeis(x,p),wherex2Xisadecisionandp=(p1,...,pN)areparticipantpayments.Payo¤s:ui(x,p,t)=vi(x,ti)pi.De…ne:V(S,t

4、)=max∑vi(x,ti)x2Xi2Sxˆ(S,t)2argmax∑vi(x,ti)x2Xi2SJonathanLevinVCGMechanismsWinter20093/23GeneralityofthemodelThemodelcoversabroadrangeofpossiblesituations.ThedecisionxcanbeanythingTheallocationofgoodsinanauctionThedecisiontobuildapublicprojectAdecisionaboutgovernmentor…rmpolicyTheresol

5、utionofadisputebetweentwoormoreparties.Therearenoapriorirestrictionsonwhopayswhatasafunctionofthedecision.JonathanLevinVCGMechanismsWinter20094/23ImportantrestrictionsofthemodelEachparticipantknowshisorherownvalues.Preferencesareover…naloutcome,notprocess.Preferencesmustbequasi-lineari

6、nmoney.Therearenolimitstomakingtransferpayments.JonathanLevinVCGMechanismsWinter20095/23TheVCGMechanismLookforamechanismwiththreecharacteristicsDirectrevelationmechanismE¢cient(surplus-maximizing)decisionPlayeri’sreportdoesnota¤ectthetotalpayo¤toallothers(w/designerincluded).JonathanLe

7、vinVCGMechanismsWinter20096/23DerivingtheVCGMechanismBasecase:ireportsthatallvaluesarezero.Optimaldecisionsatis…es(nb:canignorei):xˆ(Ni,ti)2argmax∑vj(x,tj)x2Xj2NiTotalpayo¤toplayersiis:V(Ni,ti)+pi(0,ti)=V(Ni,ti)+hi(ti).wherehi(ti),pi(0,ti).JonathanLevinVCGMechanismsWinter