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Optimality and Robustness of the English Auction

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  • Giuseppe Lopomo

Abstract

This paper attempts to reconcile the observed popularity of the English auction with the hypothesis that the trading mechanism is chosen with the objective of maximizing the seller's expected revenue. Under the assumptions of Milgrom and Weber's [20] 'general symmetric model,' I show the following three results. First, the 'augumented' English auction, in which the auctioneer sets the reserve price after all but one bidder have dropped out, generates at least as much seller's expected revenue as any ex post incentive-compatible (EPIC) and individually rational (EPIR) direct mechanisms. EPIC and EPIR direct mechanisms correspond to "belief-free" selling procedures. Thus this restriction of the set of feasible selling mechanisms aims at capturing a notion of robustness with respect to pertubations of the buyers' beliefs about their opponents' private information. Second, in the larger set of mechanisms, characterized by the property that 'losers do not pay,' ther! e exist auctions that generate a higher seller's expected revenue than the (augmented) English auction. Third, with two buyers, for a large class of signals' distributions, the augmented English auction maximizes the seller's expected revenue among all selling procedures where the loser does not pay and each buyer's payment is nondecreaseing in his own signal. With private values, these two conditions are satisfied by many equilibria in a class of bidding mechanisms, which includes approximations of both the Dutch auction and the English auction with discrete price increments. With more than two buyers, the English auction is optmal among all ex post efficient mechanisms where the losers do not pay and each buyer's payment is monotone in his signal.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000391.

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Date of creation: 01 Sep 2004
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Handle: RePEc:cla:levrem:122247000000000391

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  1. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  2. Steven A. Matthews, 1981. "Selling to Risk Averse Buyers with Unobservable Tastes," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 480S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Lopomo, Giuseppe, 1998. "The English Auction Is Optimal Among Simple Sequential Auctions," Journal of Economic Theory, Elsevier, Elsevier, vol. 82(1), pages 144-166, September.
  4. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 97(5), pages 1060-90, October.
  6. John G. Riley, 1986. "Ex Post Information in Auctions," UCLA Economics Working Papers, UCLA Department of Economics 367, UCLA Department of Economics.
  7. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers, UCLA Department of Economics 152, UCLA Department of Economics.
  8. Bikhchandani, Sushil & Riley, John G., 1991. "Equilibria in open common value auctions," Journal of Economic Theory, Elsevier, Elsevier, vol. 53(1), pages 101-130, February.
  9. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1473-1518, November.
  10. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, Elsevier, vol. 72(2), pages 343-362, February.
  11. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, Econometric Society, vol. 56(6), pages 1247-57, November.
  12. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 69-94, January.
  13. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 779, Cowles Foundation for Research in Economics, Yale University.
  14. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 395-421, March.
  15. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Laurent Lamy, 2010. ""Upping the ante": How to design efficient auctions with entry?," PSE Working Papers halshs-00564888, HAL.
  2. Hannu Vartiainen, 2003. "Auction Design without Commitment," Working Papers, Fondazione Eni Enrico Mattei 2003.24, Fondazione Eni Enrico Mattei.
  3. Jeremy I. Bulow & Paul D. Klemperer, 2007. "When are Auctions Best?," NBER Working Papers 13268, National Bureau of Economic Research, Inc.
  4. Jeremy Bulow & Paul Klemperer, 2009. "Why Do Sellers (Usually) Prefer Auctions?," American Economic Review, American Economic Association, American Economic Association, vol. 99(4), pages 1544-75, September.
  5. Laurent Lamy, 2005. "The ‘Shill Bidding Effect’ Versus the ‘Linkage Principle’," Working Papers, Centre de Recherche en Economie et Statistique 2005-35, Centre de Recherche en Economie et Statistique.
  6. Ruqu Wang & Jun Zhang, 2010. "Common Value Auctions with Return Policies," Working Papers, Queen's University, Department of Economics 1235, Queen's University, Department of Economics.

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