Note on unique Nash equilibrium in continuous games

• 成果类型: Article
• 署名作者: Rehbeck, John
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2018.04.005
• 发表日期: 2018
• 页码: 216-225
• 关键词: Continuous games; Separable games; Polynomial games; Nash equilibrium

摘要

This note studies whether any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium of a game. This note shows that if strategy spaces are metric spaces containing infinitely many points, then any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium to a separable game. If the strategy spaces are additionally subsets of Euclidean space with infinitely many cluster points, then any set of finitely supported mixed strategies can be represented as the unique Nash equilibrium to a polynomial game. (C) 2018 Elsevier Inc. All rights reserved.