Dynamic stochastic games with asymmetric information

We consider a dynamic stochastic game with asymmetric information. Multiple controllers jointly control the evolution of a global state process and multiple local state processes. The global state affects every controller's cost while a controller's local state only affects its own cost. We assume that all controllers observe the global state, and in addition each controller observes its own local state. This information structure results in asymmetry of information among the controllers. In general, such asymmetry of information makes it difficult to find or characterize Nash equilibria. However, we show that a simple characterization of a class of Nash equilibria is possible under the assumption that the evolution of the local state processes depends only on the global state and control actions and not on the current or past values of local states. This class of equilibria and their characterization resemble the notion of Markov equilibrium and their characterization in games of symmetric information.