Existence of Equilibrium in Single and Double Private Value Auctions

Authors

  • Matthew O. Jackson,

    1. 1 Humanities and Social Sciences 228-77, California Institute of Technology, Pasadena, CA 91125, U.S.A.; jacksonm@hss.caltech.edu
      and
      2Olin School of Business, Washington University in St. Louis, St. Louis, MO 63130, U.S.A.; swinkels@wustl.edu.
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  • and 1 Jeroen M. Swinkels 2

    1. 1 Humanities and Social Sciences 228-77, California Institute of Technology, Pasadena, CA 91125, U.S.A.; jacksonm@hss.caltech.edu
      and
      2Olin School of Business, Washington University in St. Louis, St. Louis, MO 63130, U.S.A.; swinkels@wustl.edu.
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    • We thank Leo Simon, Bill Zame, Mark Satterthwaite, and Phil Reny for helpful conversations. We also thank Kim Border, Martin Cripps, John Nachbar, Larry Samuelson, Tianxiang Ye, three anonymous referees, and the editor for helpful comments and suggestions. Financial support from the National Science Foundation under Grant SES-9986190 and from the Boeing Center for Technology and Information Management is gratefully acknowledged.


  • This paper supersedes the second part of Jackson and Swinkels (1999). That paper was split: The results on existence of equilibria in Bayesian games with type-dependent sharing were combined with Simon and Zame (1999) to become Jackson, Simon, Swinkels, and Zame (2002). The results on existence of equilibria in a class of private value auctions have evolved into this paper.

Abstract

We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of equilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard pricing rules, reserve prices, entry costs, and stochastic demand and supply. Valuations can be correlated and asymmetrically distributed. For double auctions, we show further that at least one equilibrium involves a positive volume of trade. The existence proof establishes new connections among existence techniques for discontinuous Bayesian games.

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