The structure of non-zero-sum stochastic games

Strategies in a stochastic game are > 0 perfect if the induced one-stage games have certain equilibrium properties. Sufficient conditions are proven for the existence of perfect strategies for all > 0 implying the existence of equilibria for every > 0. Using this approach we prove the existence of equilibria for every > 0 for a special class of quitting games. The important technique of the proof belongs to algebraic topology and reveals that more general proofs for the existence of equilibria in stochastic games must involve the topological structure of how the equilibria of one-stage games are related to changes in the payoffs.