Absorbing games with a clock and two bits of memory

• 成果类型: Article
• 署名作者: Hansen, Kristoffer Arnsfelt; Ibsen-Jensen, Rasmus; Neyman, Abraham
• 署名单位: Aarhus University; University of Liverpool; Hebrew University of Jerusalem
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.04.008
• 发表日期: 2021
• 页码: 213-230
• 关键词: Absorbing games; Finite memory; Markov strategies; stochastic games; Compact action sets

摘要

An absorbing game is a two-person zero-sum repeated game. Some of the entries are absorbing in the sense that, following the play of an absorbing entry, with positive probability all future payoffs are equal to that entry's payoff. The outcome of the game is the long-run average payoff. We prove that a two-person zero-sum absorbing game, with either finite or compact action sets, has, for each epsilon > 0, epsilon-optimal strategies with finite memory. In fact, we show that there is an epsilon-optimal strategy that depends on the clock and three states of memory. (C) 2021 Elsevier Inc. All rights reserved.