Existence d'un équilibre de Nash dans un jeu discontinu
AbstractIn 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.
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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b05099.
Length: 7 pages
Date of creation: Dec 2005
Date of revision:
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Discontinuous games; better-reply secure; Nash equilibrium; payoff security.;
Other versions of this item:
- Jean-Marc Bonnisseau & Pascal Gourdel & Hakim Hammami, 2005. "Existence d'un équilibre de Nash dans un jeu discontinu," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00173781, HAL.
- 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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- 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).
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