A complete characterization of infinitely repeated two-player games having computable strategies with no computable best response under limit-of-means payoff

• 成果类型: Article
• 署名作者: Dargaj, Jakub; Simonsen, Jakob Grue
• 署名单位: University of Copenhagen
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2023.105713
• 发表日期: 2023
• 关键词: Repeated games; Limit-of-means payoff; Computability; Best response strategies; Subgame-perfect; equilibria

摘要

It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or for classes of games satisfying certain conditions not known to be both necessary and sufficient.We derive a complete characterization in the form of simple necessary and sufficient conditions for the existence of a computable strategy without a computable best response under limit-of-means payoff. We further refine the characterization by requiring the strategy profiles to be Nash equilibria or subgame-perfect equilibria, and we show how the characterizations entail that it is efficiently decidable whether an infinitely repeated game has a computable strategy without a computable best response.& COPY; 2023 Elsevier Inc. All rights reserved.