Uniformly supported approximate equilibria in families of games

Levy, Y. J. (2022) Uniformly supported approximate equilibria in families of games. Journal of Mathematical Economics, 98, 102571. (doi: 10.1016/j.jmateco.2021.102571)

Abstract

This paper considers uniformly bounded classes of non-zero-sum strategic-form games with large finite or compact action spaces. The central class of games considered is assumed to be defined via a semi-algebraic condition. We show that for each ɛ > 0, the support size required for ɛ-equilibrium can be taken to be uniform over the entire class. As a corollary, the value of zero-sum games, as a function of a single-variable, is well-behaved in the limit. More generally, the result only requires that the collection of payoff functions considered, as functions of other players actions, have finite pseudo-dimension.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Levy, Dr John
• Authors: Levy, Y. J.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Journal of Mathematical Economics
• Publisher: Elsevier
• ISSN: 0304-4068
• ISSN (Online): 1873-1538
• Published Online: 29 September 2021
• Copyright Holders: Copyright © 2021 Crown Copyright
• First Published: First published in Journal of Mathematical Economics 98: 102571
• Publisher Policy: Reproduced in accordance with the publisher copyright policy