The structure of non-zero-sum stochastic games

Strategies in a stochastic game are δ-perfect if the induced one-stage games have certain δ-equilibrium properties. In special cases the existence of δ-perfect strategies for all positive δ implies the existence of ϵ-equilibria for every positive ϵ. Using this approach we prove the existence of ϵ-equilibria for every positive ϵ for a special class of quitting games. The proof reveals that more general proofs for the existence of ϵ-equilibria in stochastic games must involve the topological structure of how the equilibria of one-stage games are related to changes in the payoffs.