Borel stay-in-a-set games

Abstract.

Consider an n-person stochastic game with Borel state space S, compact metric action sets A ₁,A ₂,…,A _n , 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 (a ₁,a ₂,…,a _n ) 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 G _i , then there is an ε-equilibrium for every ε>0.