Nash Equilibria as Limits of Equilibria of Nearby Finite Games

Francesc Dilmé ()

CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany

Abstract: We study finite-player normal-form games with compact metric ac on spaces and bounded measurable payoffs. Our main theorem shows that every Nash equilibrium of such a game can be recovered as the limit, in the product weak topology, of Nash equilibria of finite games obtained by discre zing the ac on spaces and perturbing payoffs by a uniformly vanishing amount. The proof samples from the target equilibrium, uses concentra on inequali es to control weak convergence and incen ve constraints on a growing finite set, and then applies a payoff perturba on to convert the resul ng approximate equilibrium into an exact one. We also provide an example of a con nuous game with a Nash equilibrium that cannot be approximated through Nash equilibria of finite games without perturbing payoffs.

Keywords: Infinite games; Nash equilibria; finite approxima ons (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Pages: 14
Date: 2026-05
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