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Convergence in games with continua of equilibria

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  • Bervoets, Sebastian
  • Faure, Mathieu

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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  • Bervoets, Sebastian & Faure, Mathieu, 2020. "Convergence in games with continua of equilibria," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 25-30.
  • Handle: RePEc:eee:mateco:v:90:y:2020:i:c:p:25-30
    DOI: 10.1016/j.jmateco.2020.05.006
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