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Common Value Allocation Mechanisms with Private Information: Lotteries or Auctions?

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  • Alexander Matros

    ()
    (Darla Moore School of Business, University of South Carolina)

  • Alex Possajennikov

    ()
    (Department of Economics, University of Nottingham)

Abstract

We consider mechanisms for allocating a common-value prize between two players in an incomplete information setting. In this setting, each player receives an independent private signal about the prize value. The signals are from a discrete distribution and the value is increasing in both signals. First, we characterize symmetric equilibria in four mechanisms: a lottery; and Â…rst-price, second-price, and all-pay auctions. Second, we establish revenue equivalence of these auction mechanisms in this setting. Third, we describe conditions under which the expected revenue is higher in the lottery than in any of the auctions. Finally, we identify an optimal mechanism and its implementation by means of reserve prices in lottery and auction mechanisms.

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Paper provided by The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham in its series Discussion Papers with number 2014-07.

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Handle: RePEc:not:notcdx:2014-07

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Keywords: common value; contests; auctions;

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  1. Lim, Wooyoung & Matros, Alexander, 2009. "Contests with a stochastic number of players," Games and Economic Behavior, Elsevier, vol. 67(2), pages 584-597, November.
  2. Klemperer, Paul, 1998. "Auctions with almost common values: The 'Wallet Game' and its applications," European Economic Review, Elsevier, vol. 42(3-5), pages 757-769, May.
  3. Kai A. Konrad, 2002. "Altruism and Envy in Contests: An Evolutionarily Stable Symbiosis," CESifo Working Paper Series 825, CESifo Group Munich.
  4. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Schwartz, 2012. "Lottery versus All-Pay Auction Contests – A Revenue Dominance Theorem," Ruhr Economic Papers 0315, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  5. Cédric Wasser, 2013. "Incomplete information in rent-seeking contests," Economic Theory, Springer, vol. 53(1), pages 239-268, May.
  6. Johannes Münster, 2009. "Repeated Contests with Asymmetric Information," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(1), pages 89-118, 02.
  7. Harstad, Ronald M, 1990. "Alternative Common-Value Auction Procedures: Revenue Comparisons with Free Entry," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 421-29, April.
  8. Maskin, Eric S & Riley, Joan G, 1985. "Auction Theory with Private Values," American Economic Review, American Economic Association, vol. 75(2), pages 150-55, May.
  9. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, September.
  10. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
  11. Wang, Ruqu, 1991. "Common-value auctions with discrete private information," Journal of Economic Theory, Elsevier, vol. 54(2), pages 429-447, August.
  12. Karl Wärneryd, 2012. "Multi-player contests with asymmetric information," Economic Theory, Springer, vol. 51(2), pages 277-287, October.
  13. Wärneryd, Karl, 2013. "Common-value contests with asymmetric information," Economics Letters, Elsevier, vol. 120(3), pages 525-527.
  14. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  15. Wilson, Robert, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Wiley Blackwell, vol. 44(3), pages 511-18, October.
  16. Malueg, David A. & Orzach, Ram, 2009. "Revenue comparison in common-value auctions: Two examples," Economics Letters, Elsevier, vol. 105(2), pages 177-180, November.
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