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Auctions in which Losers Set the Price

  • Mezzetti, Claudio

    (Department of Economics, University of Warwick)

  • Tsetlin, Ilia

    (INSEAD, Singaport)

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the k-th price auction generates higher revenue than the second-price auction, for all k > 2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t + 1)-st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the k-th price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.

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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 845.

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Length: 20 pages
Date of creation: 2008
Date of revision:
Handle: RePEc:wrk:warwec:845
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  1. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Levine's Bibliography 666156000000000035, UCLA Department of Economics.
  2. Giuseppe Lopomo, 2004. "Optimality and Robustness of the English Auction," Levine's Bibliography 122247000000000391, UCLA Department of Economics.
  3. Parlour, Christine A. & Prasnikar, Vesna & Rajan, Uday, 2007. "Compensating for the winner's curse: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 60(2), pages 339-356, August.
  4. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Papers 2004-W09, Economics Group, Nuffield College, University of Oxford.
  5. Wolfstetter, Elmar, 1995. "Third- and higher-price auctions," SFB 373 Discussion Papers 1996,3, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Kagel, J.H. & Levin, D., 1988. "Independent Private Value Auctions: Bidder Behavior In First, Second And Third-Price Auctions With Varying Numbers Of Bidders," Papers 13, Houston - Department of Economics.
  7. Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November.
  8. Vijay Krishna & John Morgan, 1994. "An Analysis of the War of Attrition and the All-Pay Auction," Game Theory and Information 9409002, EconWPA.
  9. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  10. Paul Klemperer, 2004. "Introduction to Auctions: Theory and Practice
    [Auctions: Theory and Practice]
    ," Introductory Chapters, Princeton University Press.
  11. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
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