Information structures and values in zero-sum stochastic games

We consider a zero-sum stochastic game where two players have a common observation of a global state, and each player makes a private observation of its local state at every time step. This asymmetry of information among the players makes it difficult to the compute the equilibrium cost (called the value of the zero-sum game). To help us determine the value of such a game, we first consider a game with just the common observations and no local state. We argue that the value of this game with symmetric information can be computed using an information structure expansion followed by the methodology described in [1]. We then argue that the value of the asymmetric information game with global and local states is equal to the value of a virtual game with symmetric information. This allows us to use the results for the symmetric information game for computing the value of the game with global and local states.