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Existence of perfect equilibria: a direct proof

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  • Iryna Topolyan

Abstract

We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game. Copyright Springer-Verlag 2013

Suggested Citation

  • Iryna Topolyan, 2013. "Existence of perfect equilibria: a direct proof," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 697-705, August.
    • Handle: RePEc:spr:joecth:v:53:y:2013:i:3:p:697-705
    DOI: 10.1007/s00199-012-0701-7
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    References listed on IDEAS

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    More about this item

    Keywords

    Perfect equilibrium; Best response correspondence; Unit simplex; Straight-line homotopy; Fixed point; C70; C72;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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