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

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

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