We will discuss dynamic stochastic games where multiple players jointly control the evolution of a dynamic system but have access to different information about it. The asymmetry of information among players makes it difficult to compute or characterize Nash equilibria. We will describe how common knowledge among players can be used to construct an equivalent game of symmetric information. When certain common knowledge based beliefs are strategy-independent, Markov perfect equilibria of this new symmetric information game can be computed by a backward induction algorithm. Each step of this algorithm involves finding Bayesian Nash equilibria of a one-stage Bayesian game. We will then specialize to zero-sum games and explore whether and to what extent the requirement that common knowledge based beliefs be strategy-independent can be dispensed with.
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