The value of Repeated Games with an informed controller

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 certain class of stochastic games played with pure strategies

Using HMM in Strategic Games

In this paper we describe an approach to resolve strategic games in which players can assume different types along the game. Our goal is to infer which type the opponent is adopting at each moment so that we can increase the player's odds. To achieve that we use Markov games combined with hidden Markov model. We discuss a hypothetical example of a tennis game whose solution can be applied to any game with similar characteristics.Comment: In Proceedings DCM 2013, arXiv:1403.768

Markov games with frequent actions and incomplete information

We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation

A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games

We prove a Tauberian theorem for nonexpansive operators, and apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game v_{lambda} converges uniformly when lambda goes to 0 if and only if the value of the n-stage game v_n converges uniformly when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and Sorin (1992) to the two-player zero-sum case. We also provide the first example of a stochastic game with public signals on the state and perfect observation of actions, with finite state space, signal sets and action sets, in which for some initial state k_1 known by both players, (v_{lambda}(k_1)) and (v_n(k_1)) converge to distinct limits

Zero-sum stopping games with asymmetric information

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two continuous-time Markov chains (X, Y), where X is only observed by player 1 and Y only by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples

On A Markov Game with Incomplete Information

We consider an example of a Markov game with lack of information on one side, that was first introduced by Renault (2002). We compute both the value and optimal strategies for a range of parameter values.