Regular Article
Potential Games with Continuous Player Sets

https://doi.org/10.1006/jeth.2000.2696Get rights and content

Abstract

We study potential games with continuous player sets, a class of games characterized by an externality symmetry condition. Examples of these games include random matching games with common payoffs and congestion games. We offer a simple description of equilibria which are locally stable under a broad class of evolutionary dynamics, and prove that behavior converges to Nash equilibrium from all initial conditions. We consider a subclass of potential games in which evolution leads to efficient play. Finally, we show that the games studied here are the limits of convergent sequences of the finite player potential games studied by Monderer and Shapley [22]. Journal of Economic Literature Classification Numbers: C72, C73, D62, R41.

References (36)

  • M. Beckmann et al.

    Studies in the Economics of Transportation

    (1956)
  • U. Berger, and, J. Hofbauer, The Nash Dynamics, mimeo, Universität Wien,...
  • L.E. Blume

    Population games

  • L. E. Blume, How Noise Matters, mimeo, Cornell University,...
  • G.W. Brown et al.

    Solutions of games by differential equations

  • S. Cowan

    Dynamical Systems Arising from Game Theory

    (1992)
  • S. Dafermos et al.

    The traffic assignment problem for a general network

    J. Res. Nat. Bur. Standards B

    (1969)
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    This paper is based on Chapter 4 of my doctoral dissertation (Sandholm [29]). I thank Josef Hofbauer, an anonymous referee and Associate Editor, and seminar audiences at Caltech, Chicago, Columbia, Harvard (Kennedy), Michigan, Northwestern, Rochester, Washington University, and Wisconsin for their comments. I especially thank Eddie Dekel and Jeroen Swinkels for their advice and encouragement. Financial support from a State Farm Companies Foundation Dissertation Fellowship is gratefully acknowledged.

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