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Existence d'un équilibre de Nash dans un jeu discontinu




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-continuous like in the second Reny's example. 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," Cahiers de la Maison des Sciences Economiques b05099, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:b05099

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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


    Discontinuous games; better-reply secure; Nash equilibrium; payoff security.;

    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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