Nash Equilibria as Limits of Equilibria of Nearby Finite Games

Francesc Dilmé ()
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Francesc Dilmé: University of Bonn

No 400, ECONtribute Discussion Papers Series from University of Bonn and University of Cologne, Germany

Abstract: We study finite-player normal-form games with compact metric action 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 discretizing the action spaces and perturbing payoffs by a uniformly vanishing amount. The proof samples from the target equilibrium, uses concentration inequalities to control weak convergence and incentive constraints on a growing finite set, and then applies a payoff perturbation to convert the resulting approximate equilibrium into an exact one. We also provide an example of a continuous game with a Nash equilibrium that cannot be approximated through Nash equilibria of finite games without perturbing payoffs.

Keywords: Nash equilibria; infinite games; finite approximations (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Pages: 14 pages
Date: 2026-04
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Persistent link: https://EconPapers.repec.org/RePEc:ajk:ajkdps:400

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