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A model of stochastic games where multiple controllers jointly control theevolution of the state of a dynamic system but have access to differentinformation about the state and action processes is considered. The asymmetryof information among the controllers makes it difficult to compute orcharacterize Nash equilibria. Using common information among the controllers,the game with asymmetric information is shown to be equivalent to another gamewith symmetric information. Further, under certain conditions, a Markov stateis identified for the equivalent symmetric information game and its Markovperfect equilibria are characterized. This characterization provides a backwardinduction algorithm to find Nash equilibria of the original game withasymmetric information in pure or behavioral strategies. Each step of thisalgorithm involves finding Bayesian Nash equilibria of a one-stage Bayesiangame. The class of Nash equilibria of the original game that can becharacterized in this backward manner are named common information based Markovperfect equilibria.

Nash Equilibria for Stochastic Games with Asymmetric Information-Part 1: Finite Games