Existence of the uniform value in zero-sum repeated games with a more informed controller
Gensbittel, Fabien; Oliu-Barton, Miquel; Venel, Xavier (2014), Existence of the uniform value in zero-sum repeated games with a more informed controller, Journal of Dynamics and Games, 1, 3, p. 411-445. 10.3934/jdg.2014.1.411
TypeArticle accepté pour publication ou publié
Journal nameJournal of Dynamics and Games
MetadataShow full item record
Groupe de recherche en économie mathématique et quantitative [GREMAQ]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Statistics and Operations Research [Tel Aviv]
Abstract (EN)We prove that in a general zero-sum repeated game where the first player is more informed than the second player and controls the evolution of information on the state, the uniform value exists. This result extends previous results on Markov decision processes with partial observation (Rosenberg, Solan, Vieille 2002), and repeated games with an informed controller (Renault 2012). Our formal definition of a more informed player is more general than the inclusion of signals, allowing therefore for imperfect monitoring of actions. We construct an auxiliary stochastic game whose state space is the set of second order beliefs of player 2 (beliefs about beliefs of player 1 on the true state variable of the initial game) with perfect monitoring and we prove it has a value by using a result of Renault 2012. A key element in this work is to prove that player 1 can use strategies of the auxiliary game in the initial game in our general framework, which allows to deduce that the value of the auxiliary game is also the value of our initial repeated game by using classical arguments.
Subjects / Keywordsrepeated games; Zero-sum games; uniform value; incomplete information; stochastic games
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