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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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Bibliographic Info

Paper provided by New York University, Leonard N. Stern School of Business, Department of Economics in its series Working Papers with number 95-03.

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Date of creation: Oct 1995
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Handle: RePEc:ste:nystbu:95-03

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Postal: New York University, Leonard N. Stern School of Business, Department of Economics, 44 West 4th Street, New York, NY 10012-1126
Phone: (212) 998-0860
Fax: (212) 995-4218
Web page: http://w4.stern.nyu.edu/economics/
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References

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  1. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-57, November.
  2. Giuseppe Lopomo, 2004. "The English Auction Is Optimal Among Simple Sequential Auctions," Levine's Bibliography 122247000000000369, UCLA Department of Economics.
  3. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  4. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
  5. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  6. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
  7. 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.
  8. Riley, John G, 1988. "Ex Post Information in Auctions," Review of Economic Studies, Wiley Blackwell, vol. 55(3), pages 409-29, July.
  9. Bikhchandani, Sushil & Riley, John G., 1991. "Equilibria in open common value auctions," Journal of Economic Theory, Elsevier, vol. 53(1), pages 101-130, February.
  10. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
  11. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-90, October.
  12. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  13. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, vol. 55(1), pages 69-94, January.
  15. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Lamy, Laurent, 2009. "The Shill Bidding Effect versus the Linkage Principle," Journal of Economic Theory, Elsevier, vol. 144(1), pages 390-413, January.
  2. Laurent Lamy, 2013. "“Upping the ante”: how to design efficient auctions with entry?," RAND Journal of Economics, RAND Corporation, vol. 44(2), pages 194-214, 06.
  3. Hannu Vartiainen, 2009. "Auction Design without Commitment," Discussion Papers 44, Aboa Centre for Economics.
  4. repec:hal:wpaper:halshs-00564888 is not listed on IDEAS
  5. Ruqu Wang & Jun Zhang, 2010. "Common Value Auctions with Return Policies," Working Papers 1235, Queen's University, Department of Economics.
  6. Paul Klemperer & Jeremy Bulow, 2007. "When are Auctions Best?," Economics Series Working Papers 2007-W03, University of Oxford, Department of Economics.
  7. Jeremy Bulow & Paul Klemperer, 2009. "Why Do Sellers (Usually) Prefer Auctions?," Economics Papers 2009-W05, Economics Group, Nuffield College, University of Oxford.

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