Learning, hypothesis testing, and Nash equilibrium

• 成果类型: Article; Proceedings Paper
• 署名作者: Foster, DP; Young, HP
• 署名单位: Johns Hopkins University; University of Pennsylvania; The Santa Fe Institute
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/S0899-8256(03)00025-3
• 发表日期: 2003
• 页码: 73-96
• 关键词: Repeated game; Nash equilibrium; Subgame perfect equilibrium; Hypothesis Test

摘要

Consider a finite stage game G that is repeated infinitely often. At each time, the players have hypotheses about their opponents' repeated game strategies. They frequently test their hypotheses against the opponents' recent actions. When a hypothesis fails a test, a new one is adopted. Play is almost rational in the sense that, at each point in time, the players' strategies are epsilon-best replies to their beliefs. We show that, at least 1-epsilon of the time t these hypothesis testing strategies constitute an epsilon-equilibrium of the repeated game from t on; in fact the strategies are close to being subgame perfect for long stretches of time. This approach solves the problem of learning to play equilibrium with no prior knowledge (even probabilistic knowledge) of the opponents' strategies or their payoffs. (C) 2003 Elsevier Inc. All rights reserved.