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On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games

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  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Rida Laraki

    (X - École polytechnique, IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

New relaxations of the Nash equilibrium concept are shown to exist in any strategic game with discontinuous payoff functions. The new concepts are used (1) to show the equivalence between Reny's better-reply security condition [28] and Simon-Zame's endogenous tie-breaking rule equilibrium concept [32], (2) to obtain conditions for the existence of approximated equilibria in a class of discontinuous games that naturally extends Reny's better-reply secure games, and (3) to show the existence of approximated equilibria in a large family of two-player games that contains all standard models of auctions.

Suggested Citation

  • Philippe Bich & Rida Laraki, 2013. "On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00846143, HAL.
    • Handle: RePEc:hal:cesptp:hal-00846143
    Note: View the original document on HAL open archive server: https://hal.science/hal-00846143
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    References listed on IDEAS

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    Cited by:

    1. Shino Takayama & Yuki Tamura, 2015. "A Nash Equilibrium in Electoral Competition Models," Discussion Papers Series 546, School of Economics, University of Queensland, Australia.
    2. Philippe Bich & Rida Laraki, 2015. "Abstract Economies with Endogenous Sharing Rules," Documents de travail du Centre d'Economie de la Sorbonne 15058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Philippe Bich & Rida Laraki, 2015. "Abstract Economies with Endogenous Sharing Rules," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01179102, HAL.
    4. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    5. Philippe Bich & Rida Laraki, 2015. "Abstract Economies with Endogenous Sharing Rules," Post-Print halshs-01179102, HAL.

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    Keywords

    diagonal games; Discontinuous games; better-reply security; sharing-rule equilibrium; approximated equilibrium; strategic approximation; auctions; diagonal games.;
    All these keywords.

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