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Auctions in which Losers Set the Price

  • Claudio Mezzetti

    ()

  • Ilia Tsetlin

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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File URL: http://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp06-8.pdf
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Paper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number 06/8.

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Date of creation: Jul 2006
Date of revision: Mar 2007
Handle: RePEc:lec:leecon:06/8
Contact details of provider: Postal: Department of Economics University of Leicester, University Road. Leicester. LE1 7RH. UK
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Fax: +44 (0)116 252 2908
Web page: http://www2.le.ac.uk/departments/economics
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  1. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Series Working Papers 2004-W09, University of Oxford, Department of Economics.
  2. 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.
  3. Kagel, John H & Levin, Dan, 1993. "Independent Private Value Auctions: Bidder Behaviour in First-, Second- and Third-Price Auctions with Varying Numbers of Bidders," Economic Journal, Royal Economic Society, vol. 103(419), pages 868-79, July.
  4. Vijay Krishna & John Morgan, 1994. "An Analysis of the War of Attrition and the All-Pay Auction," Game Theory and Information 9409002, EconWPA.
  5. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," NajEcon Working Paper Reviews 666156000000000593, www.najecon.org.
  6. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  7. Lopomo, Giuseppe, 2001. "Optimality and Robustness of the English Auction," Games and Economic Behavior, Elsevier, vol. 36(2), pages 219-240, August.
  8. 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.
  9. Milgrom, Paul R, 1981. "Rational Expectations, Information Acquisition, and Competitive Bidding," Econometrica, Econometric Society, vol. 49(4), pages 921-43, June.
  10. 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.
  11. Paul Klemperer, 2004. "Introduction to Auctions: Theory and Practice
    [Auctions: Theory and Practice]
    ," Introductory Chapters, Princeton University Press.
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