Theoretical Economics 16 (2021), 1055–1093

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### Strict pure strategy Nash equilibria in large finite-player games

*Guilherme Carmona, Konrad Podczeck*

#### Abstract

In the context of anonymous games (i.e., games where the payoff of a player is, apart from his/her own action, determined by the distribution of the actions made by the other players) we present a model in which, generically (in a precise sense), finite-player games have strict pure strategy Nash equilibria if the number of agents is large. A key feature of our model is that payoff functions have differentiability properties. A consequence of our existence result is that, in our model, equilibrium distributions of non-atomic games are asymptotically implementable by pure strategy Nash equilibria of large finite-player games.

Keywords: Large games, pure strategy, Nash equilibrium, generic property

JEL classification: C72

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