For an n–person stochastic game with Borel state space S and compact metric action sets A1, A2,…, An, sufficient conditions are given for the existence of subgame–perfect equilibria. One result is that such equilibria exist if the law of motion q(⋯∣ s, a) is, for fixed s, continuous in a= a1, a2,…, an for the total variation norm and the payoff functions f1, f2,…, fn are bounded, Borel measurable functions of the sequence of states (s1, s2,…) ∈ Sℕ and, in addition, are continuous when Sℕ is given the product of discrete topologies on S.
