Subgame-Perfect Equilibria for Stochastic Games

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.