Strict pure strategy Nash equilibrium in large finite-player games when the action set is a manifold
- Author(s)
- Konrad Podczeck, Guilherme Carmona
- 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.
- Organisation(s)
- Department of Economics
- External organisation(s)
- University of Surrey
- Journal
- Journal of Mathematical Economics
- Volume
- 98
- No. of pages
- 10
- ISSN
- 0304-4068
- DOI
- https://doi.org/10.1016/j.jmateco.2021.102580
- Publication date
- 2021
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 502047 Economic theory
- Keywords
- ASJC Scopus subject areas
- Applied Mathematics, Economics and Econometrics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/strict-pure-strategy-nash-equilibrium-in-large-finiteplayer-games-when-the-action-set-is-a-manifold(a62edb54-ad29-4ffb-91c9-3418f965d899).html