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Existence d'un équilibre de Nash dans un jeu discontinu

Author

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  • Jean-Marc Bonnisseau

    () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Pascal Gourdel

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Hakim Hammami

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we present a more simple and independent proof of Reny's theorem (1998), on the existence of a Nash equilibrium in discontinue game, with a better-reply secure game in a Hausdorff topological vector space stronger than Reny's one. We will get the equivalence if the payoff function is upper semi-contineous like in the second Reny's exemple. Our proof is based on a new version of the existence of maximal element of Fan-Browder given by Deguire and Lassonde (1995). Reny's proof used a lemma of approximation of payoff function by a continuous sequence and show the existence of Nash equilibrium by the existence of equilibrium in mixed strategy proved in continuous game by the classical result.

Suggested Citation

  • Jean-Marc Bonnisseau & Pascal Gourdel & Hakim Hammami, 2005. "Existence d'un équilibre de Nash dans un jeu discontinu," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00173781, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00173781
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00173781
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    Cited by:

    1. Philippe Bich, 2006. "A constructive and elementary proof of Reny's theorem," Cahiers de la Maison des Sciences Economiques b06001, Université Panthéon-Sorbonne (Paris 1).

    More about this item

    Keywords

    Discontinuous games; better-reply secure; Nash equilibrium; payoff security; Jeu discontinu; meilleur réponse sécurisée; équilibre de Nash; paiement sécurisé; théorème Fan Browder;

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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