Markov Equilibria in Discounted Stochastic Games
Abstract We show that Markov perfect equilibrium exists for stochastic games which have transition probabilities that are Markovian and product measurable in past period's realisation of the states of nature and actions, and norm continuous in past period's actions. The transition probabilities are assumed to be absolutely continuous with respect to some measure ν t every period. We then show that if the stochastic game is stationary and the measure ν is nonatomic, then there exists a semi-Markov equilibrium strategy. Throughout the analysis the state space S is assumed to be a complete separable metric space and the action spaces A i of the players are assumed to be compact metric spaces and invariant over time. The payoff is the usual sum of the discounted payoffs received every period. Journal of Economic Theory Literature Classification Numbers: C62, C72, C73, D81.