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1、RAND Journal of Economics Vol. 42, No. 2, Summer 2011 pp. 313336Auctions with heterogeneous entry costsDiego MorenoandJohn WoodersIf bidders have independent private values and homogeneous entry costs, a first- or second- price auction with a reserve price equal to the sellers value maximizes social
2、 surplus and seller revenue. We show that if entry costs are heterogeneous and private information, then the revenue- maximizing reserve price is above the sellers value, a positive admission fee (and a reserve price equal to the sellers value) generates more revenue, and an entry cap combined with
3、an admissionfeegeneratesevenmorerevenue.Socialsurplusandsellerrevenuemayeitherincrease or decrease in the number of bidders, but they coincide asymptotically.1.Introduction?A classic result of the auction literature is that in a standard auction with an exogenouslyfixednumber ofbidderswhohave indepe
4、ndent privatevalues,maximizingsellerrevenue requires screening bidders; that is, the rules of the revenue-maximizing auction are such that a bidderwhose value is below the screening value will find it unprofitable to bid. Moreover, the revenue- maximizingscreeningvalueisabovethesellersvalueandisinde
5、pendentofthenumberofbidders(see Myerson, 1981; Riley and Samuelson, 1981). In first- and second-price sealed-bid auctions, for example, the screening value is just the reserve price. Hence, the revenue-maximizing reserve price is above the sellers value and is independent of the number of bidders. I
6、n many instances, however, the number of bidders is endogenously determined as the result of costly entry decisions. As noted by Milgrom (2004), “auctions for valuable yet highlyspecialized assets often fail because of insufficient interest by bidders.because buyers are naturallyreluctanttobeginanex
7、pensive,time-consumingevaluationofanassetwhentheybelieveUniversidad Carlos III de Madrid; diego.morenouc3m.es.University of Arizona; jwooderseller.arizona.edu.This article is based on Moreno and Wooders (2006). We are grateful to Philip Haile and two anonymous referees for useful suggestions. We tha
8、nk Angel Hernando-Veciana, Vladimir Karamychev, Sander Onderstal, Mark Stegeman, Juuso Valimaki, and Hal Varian, and seminar audiences at the Helsinki School of Economics, Arizona State University, USC, Universidad Carlos III, University of Arizona, Erasmus University Rotterdam, the 2006 European Ec
9、onometric Society Meeting (Vienna), the Southwest Economic Theory Conference (Santa Barbara, CA), and the Exchange Mechanisms andAuctions Conference in Honor of Vernon Smith for helpful comments. We gratefully acknowledge financial support from the Fundaci on BBVA, from the Spanish Ministry of Educa
10、tion (grants SEJ2007-67436 and Consolider-Ingenio 2010), and from the Comunidad de Madrid (grant Excelecon. Part of this work was completed while Moreno was visiting IDEI, Universit e Toulouse I. He is grateful for their hospitality.CopyrightC?2011, RAND.313314/THE RAND JOURNAL OF ECONOMICSthat they
11、 are unlikely to win at a favorable price.” Indeed, McAfee and McMillan (1987) andLevin and Smith (1994) have shown that endogenous entry has important implications in first-andsecond-price sealed-bidauctions.Specifically, when allbuyers have thesame(homogeneous) entry cost, a reserve price equal to
12、 the sellers value is optimal both for the seller and for society. Henceforth, we use the term buyer to refer to an agent potentially interested in buying the object, and the term bidder to refer to a buyer who has entered the auction. We study standard auctions with endogenous entry, but where buye
13、rs have heterogeneousprivatelyknownentrycosts.Inthesaleofafirm,forexample,buyersmayfacedifferentregulatory restrictions: some buyers may have to seek approval by regulatory authorities whereas others may not. Hence, different buyers may have substantially different costs of discovering their value f
14、orthe firm. Another example is Internet auctions, where a buyers cost of discovering her value is the opportunity cost of her time, and it varies across buyers. In our setting, like in McAfee and McMillan (1987) and Levin and Smith (1994), buyers simultaneously choose whether to enter the auction. E
15、ach buyer who enters the auction observes her value for the object and then bids. Our setting differs in that each buyers entry cost is an independent draw from a common distribution, and is privately observed prior to entry. Our theoreticalanalysisprovidesaricherframeworkforempiricalstudiesofauctio
16、nsusingdataeitherfrom the field or from experiments (see, e.g., Li and Zheng, 2009; Reiley, 2006). Heterogeneity of entry costs leads to results substantially different from those obtained when entry costs are homogeneous. We show that although a screening value equal to the sellers value remains socially optimal, the revenue-maximizing screening value is above the sellersvalue. (Thus, in first- and second-price sealed-bid auctions, for example, the revenue-maximizing re
