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Sequentially Optimal Auctions

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  • McAfee, R. Preston
  • Vincent, Daniel

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
  2. 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.
  3. McAfee R. Preston & Vincent Daniel, 1993. "The Declining Price Anomaly," Journal of Economic Theory, Elsevier, vol. 60(1), pages 191-212, June.
  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. McAfee, R Preston, 1993. "Mechanism Design by Competing Sellers," Econometrica, Econometric Society, vol. 61(6), pages 1281-1312, November.
  6. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  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. Jeremy Bulow & Paul Klemperer, 1994. "Auctions vs. Negotiations," NBER Working Papers 4608, National Bureau of Economic Research, Inc.
  9. Freixas, Xavier & Guesnerie, Roger & Tirole, Jean, 1985. "Planning under Incomplete Information and the Ratchet Effect," Review of Economic Studies, Wiley Blackwell, vol. 52(2), pages 173-91, April.
  10. Ausubel, Lawrence M & Deneckere, Raymond J, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Econometrica, Econometric Society, vol. 57(3), pages 511-31, May.
  11. Larry M. Ausubel & Raymond J. Deneckere, 1989. "Reputation in Bargaining and Durable Goods Monopoly," Levine's Working Paper Archive 201, David K. Levine.
  12. Peter Cramton, 1985. "Sequential Bargaining Mechanisms," Papers of Peter Cramton 85roth, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
  13. Ashenfelter, Orley, 1989. "How Auctions Work for Wine and Art," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 23-36, Summer.
  14. 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.
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