Strict pure strategy Nash equilibrium in large finite-player games when the action set is a manifold

Konrad Podczeck, Guilherme Carmona

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Abstract

We present results on the relationship between non-atomic games (in distributional form) and approximating games with a large but finite number of players. Specifically, in a setting with differentiable payoff functions, we show that: (1) The set of all non-atomic games has an open dense subset such that any finite-player game that is sufficiently close (in terms of distributions of players’ characteristics) to a game in this subset and has sufficiently many players has a strict pure strategy Nash equilibrium (Theorem 1), and (2) any equilibrium distribution of any non-atomic game is the limit of equilibrium distributions defined from strict pure strategy Nash equilibria of finite-player games (Theorem 2). This supplements our paper Carmona and Podczeck (2020b), where analogous results are established for the case where the action set of players is a subset of some Euclidean space, with non-empty interior, and payoff functions are such that equilibrium actions are in the interior of the action set. The goal of the present paper is to remove these assumptions.

Original languageEnglish
Article number102580
Number of pages10
JournalJournal of Mathematical Economics
Volume98
Early online date2021
DOIs
Publication statusPublished - Jan 2022

Austrian Fields of Science 2012

  • 502047 Economic theory

Keywords

  • large games
  • pure strategy
  • Nash equilibrium
  • Generic property
  • Large games
  • MONOPOLISTIC COMPETITION
  • Pure strategy
  • Differentiable manifold

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