2013/01/09 by Fabien Gensbittel, Gensbittel, Fabien, Miquel Oliu‐Barton +4 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC
paper · pdf · doi:10.48550/arxiv.1301.1935
arxiv created 2013/01/09 · openalex publication_date 2013/01/09 · arxiv updated 2013/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.