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Auctions in which Losers Set the Price

Author

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  • Mezzetti, Claudio

    (Department of Economics, University of Warwick)

  • Tsetlin, Ilia

    (INSEAD, Singaport)

Abstract

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.

Suggested Citation

  • Mezzetti, Claudio & Tsetlin, Ilia, 2008. "Auctions in which Losers Set the Price," The Warwick Economics Research Paper Series (TWERPS) 845, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:845
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    References listed on IDEAS

    as
    1. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    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 868-879, July.
    4. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    5. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    6. Michael H. Rothkopf, 2007. "Thirteen Reasons Why the Vickrey-Clarke-Groves Process Is Not Practical," Operations Research, INFORMS, vol. 55(2), pages 191-197, April.
    7. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    8. Jeremy Bulow & Paul Klemperer, 2002. "Prices and the Winner's Curse," RAND Journal of Economics, The RAND Corporation, vol. 33(1), pages 1-21, Spring.
    9. 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.
    10. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
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    Cited by:

    1. Olga Gorelkina, 2014. "Bidder Collusion and the Auction with Target Bids," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2014_10, Max Planck Institute for Research on Collective Goods.
    2. Mares Vlad & Shor Mikhael, 2012. "On the Competitive Effects of Bidding Syndicates," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-33, September.

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    More about this item

    Keywords

    Auctions ; Second-Price Auction ; English Auction ; k-th Price Auction ; Affiliated Values ; Rationing ; Robust Mechanism Design;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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