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Note on unique Nash equilibrium in continuous games

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  • Rehbeck, John

Abstract

This note studies whether any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium of a game. This note shows that if strategy spaces are metric spaces containing infinitely many points, then any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium to a separable game. If the strategy spaces are additionally subsets of Euclidean space with infinitely many cluster points, then any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium to a polynomial game.

Suggested Citation

  • Rehbeck, John, 2018. "Note on unique Nash equilibrium in continuous games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 216-225.
    • Handle: RePEc:eee:gamebe:v:110:y:2018:i:c:p:216-225
    DOI: 10.1016/j.geb.2018.04.005
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    References listed on IDEAS

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    1. Walter Bossert & Yves Sprumont, 2013. "Every Choice Function Is Backwards‐Induction Rationalizable," Econometrica, Econometric Society, vol. 81(6), pages 2521-2534, November.
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    4. Lee, SangMok, 2012. "The testable implications of zero-sum games," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 39-46.
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    6. Eleftherios Couzoudis & Philipp Renner, 2013. "Computing generalized Nash equilibria by polynomial programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 459-472, June.
    7. Sprumont, Yves, 2000. "On the Testable Implications of Collective Choice Theories," Journal of Economic Theory, Elsevier, vol. 93(2), pages 205-232, August.
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    More about this item

    Keywords

    Continuous games; Separable games; Polynomial games; Nash equilibrium;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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