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Journal Articles Journal of Mathematical Economics Year : 2020

Convergence in games with continua of equilibria

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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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hal-02964989 , version 1 (10-02-2021)

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Attribution - NonCommercial - NoDerivatives - CC BY 4.0

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Sebastian Bervoets, Mathieu Faure. Convergence in games with continua of equilibria. Journal of Mathematical Economics, 2020, 90, pp.25-30. ⟨10.1016/j.jmateco.2020.05.006⟩. ⟨hal-02964989⟩
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