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