The structure of non-zero-sum stochastic games

Strategies in a stochastic game are delta-perfect if the induced one-stage games have certain delta-equilibrium properties. In special cases the existence of delta-perfect strategies for all positive delta implies the existence of epsilon-equilibria for every positive epsilon. Using this approach we prove the existence of epsilon-equilibria for every positive epsilon for a special class of quitting games. The proof reveals that more general proofs for the existence of epsilon-equilibria in stochastic games must involve the topological structure of how the equilibria of one-stage games are related to changes in the payoffs. (C) 2006 Elsevier Inc. All rights reserved.