Consider an n-person stochastic game with Borel state space S, compact metric action sets A1, A2,…,An, and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a1, a2,…,an) of the players. If the payoff to each player i is 1 or 0 according to whether or not the stochastic process of states stays forever in a given Borel set Gi, then there is an ε-equilibrium for every ε > 0.
