Repeated games with one-memory

• 成果类型: Article
• 署名作者: Barlo, Mehmet; Carmona, Guilherme; Sabourian, Hamid
• 署名单位: University of Cambridge; Sabanci University; Universidade Nova de Lisboa
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2008.04.003
• 发表日期: 2009
• 页码: 312-336
• 关键词: Repeated games; memory; bounded rationality; folk theorem

摘要

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an E-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for. (C) 2008 Elsevier Inc. All rights reserved.