Markov equilibria in discounted stochastic games

We show that Markov perfect equilibrium exists for stochastic games which h ave transition probabilities that are Markovian and product measurable in p ast period's realisation of the states of nature and actions, and. norm con tinuous in past period's actions. The transition probabilities are assumed to be absolutely continuous with respect to some measure v(t) every period. We then show that if the stochastic game is stationary and the measure: v is nonatomic, then there exists a semi-Markov equilibrium strategy. Through out the analysis the state space S is assumed to be a complete separable me tric space and the action spaces Ai of the players are assumed to be compac t metric spaces and invariant over time. The payoff is the usual sum of the discounted payoffs received every period. Journal of Economic Theory Liter ature Classification Numbers: C62, C72, C73, D81. (C) 1999 Academic Press.