Approachability with bounded memory

• 成果类型: Article
• 署名作者: Lehrer, Ehud; Solan, Eilon
• 署名单位: Tel Aviv University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2007.07.011
• 发表日期: 2009
• 页码: 995-1004
• 关键词: Approachability; repeated games; Vector payoffs; Bounded memory; Bounded recall; Automata; No-regret; adaptive learning

摘要

We study Blackwell's approachability in repeated games with vector payoffs when the approaching player is restricted to use strategies with bounded memory: either strategies with bounded recall, or strategies that can be implemented by finite automata. Our main finding is that the following three statements are equivalent for closed sets, (i) The set is approachable with bounded recall strategies. (ii) The set is approachable with strategies that can be implemented with finite automata. (iii) The set contains a convex approachable set. Using our results we show that (i) there are almost-regret-free strategies with bounded memory, (ii) there is a strategy with bounded memory to choose the best among several experts, and (iii) Hart and Mas-Colell's adaptive learning procedure can be achieved using strategies with bounded memory. (C) 2008 Elsevier Inc. All rights reserved.