The Value of Repeated Games with an Informed Controller

Jérôme Renault

52 citations0/0 files storedMathematics of Operations Research

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Game Theory and Applications Probability and Statistical Research Adaptive Dynamic Programming Control

Abstract

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform value, generalizing several results of the literature. A preliminary existence result is obtained for a particular class of stochastic games played with pure strategies.

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References

1953Stochastic Games 2011Repeated Games with Incomplete Information 1995Integration and Probability 2002A first course on zero-sum repeated games 1971The value of two-person zero-sum repeated games with lack of information on both sides 1981An orderfield property for stochastic games when one player controls transition probabilities 2006The Value of Markov Chain Games with Lack of Information on One Side 1981Ordered field property for stochastic games when the player who controls transitions changes from state to state

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2010Uniform value in dynamic programming 2013A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value 2016Zero-sum repeated games: Counterexamples to the existence of the asymptotic value and the conjecture $\operatorname{maxmin}=\operatorname{lim}v_{n}$

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