ON VALUES OF REPEATED GAMES WITH SIGNALS

• 成果类型: Article
• 署名作者: Gimbert, Hugo; Renault, Jerome; Sorin, Sylvain; Venel, Xavier; Zielonka, Wieslaw
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Sorbonne Universite; Universite Paris Cite; heSam Universite; Universite Pantheon-Sorbonne; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1095
• 发表日期: 2016
• 页码: 402-424
• 关键词: Stochastic games; incomplete information; Determinacy; controller

摘要

We study the existence of different notions of value in two-person zero sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in general. Then we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We also prove two other positive results without assumptions on the signaling structure: the existence of the sup value in any game and the existence of the uniform value in recursive games with nonnegative payoffs.