北大微观经济学课件(英文版)Ch17 Auctions

2020/5/4中级微观经济学ChapterSeventeenAuctions2020/5/4中级微观经济学WhoUsesAuctions?Ownersofart,cars,stamps,machines,mineralrightsetc.Q:Whyauction?2020/5/4中级微观经济学WhoUsesAuctions?Ownersofart,cars,stamps,machines,mineralrightsetc.Q:Whyauction?A:Becausemanymarketsareimperfectanditishardtodiscoverpotentialbuyers’truevaluationsofyourasset.Auctionshelptodiscoverthisinformation.2020/5/4中级微观经济学TypesofAuctionsEnglishauction:–bidsarepublicannouncements–bidpricerisesuntiltherearenofurtherbids–highestbidwins–winnerpayshisbid.2020/5/4中级微观经济学TypesofAuctionsSealed-bidfirst-priceauction:–bidsareprivateinformation–bidsaremadesimultaneously–highestbidwins–winnerpayshisbid.2020/5/4中级微观经济学TypesofAuctionsSealed-bidsecond-priceauction:–bidsareprivateinformation–bidsaremadesimultaneously–highestbidderwins–winnerpayssecond-highestbid–alsoknownasaVickreyauction.2020/5/4中级微观经济学TypesofAuctionsDutchauction:–auctioneerannouncesahighbidandthengraduallylowersthebid–firstbuyertoacceptwinsandpaysthatprice.2020/5/4中级微观经济学ReservePriceAsellerspecifiedbidlevelbelowwhichnosaleismade.2020/5/4中级微观经济学Economists’ClassificationofAuctionsPrivate-valueauctions:–everypotentialbuyerknowsforsureherownvaluationoftheitemforsale–alltheseindividualvaluationsareindependentofeachother.2020/5/4中级微观经济学Economists’ClassificationofAuctionsCommon-valueauctions:–itemforsalehasthesamevaluetoeverypotentialbuyer–potentialbuyersdifferintheirownestimatesofthiscommonvalue.2020/5/4中级微观经济学AuctionDesignGoals:–Paretoefficiency–maximizationoftheseller’sprofit.2020/5/4中级微观经济学AuctionDesignParetoefficiency:–theitemmustselltothebuyerwiththehighestvaluationoftheitem.WhichauctionsareParetoefficient?2020/5/4中级微观经济学AuctionsandEfficiencyEnglishauctionwithnoreservepricemustbeefficientsince,ifabuyerwithalowvaluationwasabouttobuy,thehighestvaluationbuyerwouldbidhigher.2020/5/4中级微观经济学AuctionsandEfficiencyEnglishauctionwithareservepriceneednotbeefficientsinceifthereservepriceissetabovethe(unknowntotheseller)highestbuyervaluation,thentherewillbenosaleandsonogains-to-trade.2020/5/4中级微观经济学AuctionsandEfficiencyDutchauctionneednotbeefficient.Nobuyerknowsotherbuyers’valuations,sothehighestvaluationbuyermaydelaytoolongandlosetoanotherbidder.2020/5/4中级微观经济学AuctionsandEfficiencySealed-bidfirst-priceauctionneednotbeefficient.Nobuyerknowsotherbuyers’valuations,sothehighestvaluationbuyermaybidtoolowandlosetoanotherbidder.2020/5/4中级微观经济学AuctionsandEfficiencySealed-bidsecond-priceauctionisParetoefficienteventhoughnobuyerknowstheotherbuyers’valuations(moreonthislater).2020/5/4中级微观经济学WhyUseaReservePrice?Supposethereare2buyers.Thesellerbelieveseachbuyer’svaluationis$20withchance1/2and$50withchance1/2.I.e.withchance1/4each,thesellerbelievesshefacesbuyervaluations($20,$20),($20,$50),($50,$20)and($50,$50).2020/5/4中级微观经济学WhyUseaReservePrice?I.e.withchance1/4each,thesellerbelievesshefacesbuyervaluations($20,$20),($20,$50),($50,$20)and($50,$50).UseanEnglishauction.Bidsmustberaisedbyatleast$1.Withchance1/4each,winningbidswillbe$20,$21,$21and$50ifthereisnoreserveprice.2020/5/4中级微观经济学WhyUseaReservePrice?Withchance1/4each,winningbidswillbe$20,$21,$21and$50ifthereisnoreserveprice.Seller’sexpectedrevenueis($20+$21+$21+$50)/4=$28withnoreserveprice.2020/5/4中级微观经济学WhyUseaReservePrice?Withchance1/4each,thesellerbelievesshefacesbuyervaluations($20,$20),($20,$50),($50,$20)and($50,$50).Setareservepriceof$50.Withchance1/4therewillbenosale.Withchance3/4thewinningbidwillbe$50.2020/5/4中级微观经济学WhyUseaReservePrice?Setareservepriceof$50.Withchance1/4therewillbenosale.Withchance3/4thewinningbidwillbe$50.Seller’sexpectedrevenueis3450140375028$$$$.2020/5/4中级微观经济学ReservePriceandEfficiencyThereservepricecausesanefficiencylosssince,withchance1/4,thereisnotrade.2020/5/4中级微观经济学Second-Price,Sealed-BidAuction–bidsareprivateinformation–bidsaremadesimultaneously–highestbidderwins–winnerpayssecond-highestbid–alsoknownasaVickreyauction.2020/5/4中级微观经济学Second-Price,Sealed-BidAuctionNobidderknowsanyotherbidder’struevaluationoftheitemforsale.Yet,itisindividuallyrationalforeachbiddertostatetruthfullyhisownvaluation.Why?E.g.twobidderswithtruevaluationsv1andv2.2020/5/4中级微观经济学Second-Price,Sealed-BidAuctionE.g.twobidderswithtruevaluationsv1andv2.Bidsareb1andb2.Expectedgaintobidder1is()Pr()Pr()()Pr().vbvbbb1212120winlose2020/5/4中级微观经济学Second-Price,Sealed-BidAuctionExpectedgaintobidder1isHowisthismaximized?Ifv1b2,thenmaximizetheprob.ofwinning;i.e.setb1=v1.Ifv1b2,thenminimizetheprob.ofwinning;i.e.setb1=v1.Eitherway,tellingthetruthisbest!()Pr().vbbb12122020/5/4中级微观经济学Second-Price,Sealed-BidAuctionSincetruth-tellingisbestforeverybidder,thehighestvaluationbidderwillwin.Hencethesecond-price,sealed-bidauctionisPareto-efficient.2020/5/4中级微观经济学Common-ValueAuctionsTheitemforsalehasthesamevaluetoeverypotentialbuyer.Potentialbuyersdifferintheirownestimatesofthiscommonvalue.Bidderi’sestimateiswhereisthecommonvalueandisbidderi’sestimationerror.vviivi2020/5/4中级微观经济学Common-ValueAuctionsBidderi’sestimateiswhereisth