Zero-sum Stochastic Games with Asymmetric Information

Abstract

A general model for zero-sum stochastic games with asymmetric information is considered. For this model, a dynamic programming characterization of the value is presented under some assumptions on its existence. This dynamic program is then used for a class of zero-sum stochastic games with complete information on one side and partial information on the other, that is, games where one player has complete information about state, actions and observation history while the other player may only have partial information about the state and action history. For such games, the value is characterized using dynamic programming without making any existence assumptions. It is further shown that for this class of games, there exists a Nash equilibrium where the more informed player plays a common information belief based strategy. A dynamic programming approach is presented for computing this strategy.