Markov Games with Frequent Actions and Incomplete Information - The Limit Case

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. Key-words: Markov games, incomplete information, zero-sum games, Hamilton-Jacobi equations, repeated games. A.M.S. classification : 91A05, 91A15, 60J10