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Symmetric Approximate Equilibrium Distributions with Finite Support

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  • Guilherme Carmona

Abstract

We show that a distribution of a game with a continuum of players is an equilibrium distribution if and only if there exists a sequence of symmetric approximate equilibrium distributions of games with finite support that converges to it. Thus, although not all games have symmetric equilibrium distributions, this result shows that all equilibrium distributions can be characterized by symmetric distributions of simpler games (i.e., games with a finite number of characteristics).

Suggested Citation

  • Guilherme Carmona, 2003. "Symmetric Approximate Equilibrium Distributions with Finite Support," Game Theory and Information 0311006, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0311006
    Note: Type of Document - pdf; prepared on win xp; to print on general; pages: 7; figures: 0. none
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    References listed on IDEAS

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    1. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
    2. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    3. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.
    4. Green, Edward J, 1984. "Continuum and Finite-Player Noncooperative Models of Competition," Econometrica, Econometric Society, vol. 52(4), pages 975-993, July.
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    Cited by:

    1. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.
    2. Guilherme Carmona, 2004. "Nash equilibria of games with a continuum of players," Nova SBE Working Paper Series wp466, Universidade Nova de Lisboa, Nova School of Business and Economics.

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    More about this item

    Keywords

    Equilibrium distributions; games with a continuum of players; symmetric distributions;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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