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Convergence in games with continua of equilibria

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  • Sebastian Bervoets

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Mathieu Faure

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

In game theory, the question of convergence of dynamical systems to the set of Nash equilibria has often been tackled. When the game admits a continuum of Nash equilibria, however, a natural and challenging question is whether convergence to the set of Nash equilibria implies convergence to a Nash equilibrium. In this paper we introduce a technique developed in Bhat and Bernstein (2003) as a useful way to answer this question. We illustrate it with the best-response dynamics in the local public good game played on a network, where continua of Nash equilibria often appear.

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  • Sebastian Bervoets & Mathieu Faure, 2020. "Convergence in games with continua of equilibria," Post-Print hal-02964989, HAL.
    • Handle: RePEc:hal:journl:hal-02964989
    DOI: 10.1016/j.jmateco.2020.05.006
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02964989
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