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Sequentially Optimal Auctions

  • McAfee, R. Preston
  • Vincent, Daniel

We examine equlibria in sequential auctions where a seller can post a reserve price but, if the auction fails to result in a sale, can commit keeping the object off the market only for an exogenously fixed period of time. We restrict attention to enviornments where bidders have independent private values and where the support of the bidder types lies strictly above the valuation of the seller. In the case where the seller sells by second price auction in each period, there is a unique perfect Bayesian equilbrium. A form of revenue equivalence is shown. There exists a perfect Bayesian equilibrium of repeated first price auctions with the feature that in every period, the seller's expected revenue from the continuation is the same in either auction mechanism. As the length of time the seller can commit to keeping the object off the market goes to zero, seller expected revenues converge to those of a static auction with no reserve price. As the number of bidders becomes large, the seller expected revenue approaches the revenue from an optimal static auction. We also characterize a parametrized auction game in which the simple equilibrium reserve price policy of the seller mirrors a policy commonly used by many auctioneers.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 18 (1997)
Issue (Month): 2 (February)
Pages: 246-276

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Handle: RePEc:eee:gamebe:v:18:y:1997:i:2:p:246-276
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. McAfee R. Preston & Vincent Daniel, 1993. "The Declining Price Anomaly," Journal of Economic Theory, Elsevier, vol. 60(1), pages 191-212, June.
  2. Larry M. Ausubel & Raymond J. Deneckere, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Levine's Working Paper Archive 201, David K. Levine.
  3. Xavier Freixas & Roger Guesnerie & Jean Tirole, 1985. "Planning under Incomplete Information and the Ratchet Effect," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 173-191.
  4. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
  5. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
  6. Ausubel, Lawrence M & Deneckere, Raymond J, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Econometrica, Econometric Society, vol. 57(3), pages 511-31, May.
  7. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
  8. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  10. Jeremy Bulow & Paul Klemperer, 1994. "Auctions vs. Negotiations," NBER Working Papers 4608, National Bureau of Economic Research, Inc.
  11. Peter Cramton, 1985. "Sequential Bargaining Mechanisms," Papers of Peter Cramton 85roth, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
  12. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
  13. Drew Fudenberg & David K. Levine & Jean Tirole, 1985. "Infinite-Horizon Models of Bargaining with One-Sided Incomplete Information," Levine's Working Paper Archive 1098, David K. Levine.
  14. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
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