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Optimality and Robustness of the English Auction

  • Lopomo, Giuseppe

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

Volume (Year): 36 (2001)
Issue (Month): 2 (August)
Pages: 219-240

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Handle: RePEc:eee:gamebe:v:36:y:2001:i:2:p:219-240
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  1. 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.
  2. 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.
  3. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  4. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  5. John G. Riley, 1986. "Ex Post Information in Auctions," UCLA Economics Working Papers 367, UCLA Department of Economics.
  6. McAfee, R Preston & Reny, Philip J, 1992. "Correlated Information and Mechanism Design," Econometrica, Econometric Society, vol. 60(2), pages 395-421, March.
  7. Bikhchandani, Sushil & Riley, John G., 1991. "Equilibria in open common value auctions," Journal of Economic Theory, Elsevier, vol. 53(1), pages 101-130, February.
  8. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  9. Roger B. Myerson, 1978. "Optimal Auction Design," Discussion Papers 362, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
  11. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
  12. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
  13. Giuseppe Lopomo, 2004. "The English Auction Is Optimal Among Simple Sequential Auctions," Levine's Bibliography 122247000000000369, UCLA Department of Economics.
  14. 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.
  15. 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.
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