On the MaxMin Value of Stochastic Games with Imperfect Monitoring

We study zero-sum stochastic games in which players do not observe the actions of the opponent. Rather, they observe a stochastic signal that may depend on the state, and on the pair of actions chosen by the players. We assume each player observes the state and his own action. We propose a candidate for the max-min value, which does not depend on the information structure of player 2. We prove that player 2 can defend the proposed max-min value, and that in absorbing games player 1 can guarantee it. Analogous results hold for the min-max value. This paper thereby unites several results due to Coulomb