Subgame-Perfect Equilibria for Stochastic Games

Abstract

For an n-person stochastic game with Borel state space S and compact metric action sets A 1 , A 2 ,…, A n , 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 = (a 1 ,a 2 ,…,a n ) for the total variation norm and the payoff functions f 1 , f 2 ,…,f n are bounded, Borel measurable functions of the sequence of states (s 1 , s 2 ,…) ∈ S ℕ and, in addition, are continuous when S ℕ is given the product of discrete topologies on S.

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