Invariant equilibria and classes of equivalent games

• 成果类型: Article
• 署名作者: Allison, Blake A.; Bagh, Adib; Lepore, Jason J.
• 署名单位: Emory University; University of Kentucky; University of Kentucky; California State University System; California Polytechnic State University San Luis Obispo
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2022.01.011
• 发表日期: 2022
• 页码: 448-462
• 关键词: Discontinuous games; Nash equilibrium; Invariance; sharing rules; Existence of equilibria

摘要

We consider classes of games for a fixed set of players with fixed strategy sets. For such classes, we analyze and develop the concept of invariance, which is satisfied when the set of Nash equilibria and corresponding equilibrium payoffs are identical for each payoff function within the class. We introduce the condition superior payoff matching, which requires that at any given strategy profile, each player can match her highest payoff near that strategy profile across all games within that class. If a specific game satisfies superior payoff matching, then its equilibria are invariant within a class of games with smaller sets of discontinuities. This condition can be used to prove existence of Nash equilibrium in games that are not quasiconcave or better reply secure. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).