Zero-sum Stochastic Games with Asymmetric Information
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A general model for zero-sum stochastic games with asymmetric information is considered. For this model, a dynamic programming characterization of the value (if it exists) is presented. If the value of the zero-sum game does not exist, then the dynamic program provides bounds on the upper and lower values of the zero-sum game. 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 exists and can be characterized using the dynamic program. 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 and, this strategy can be computed using the dynamic program.
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