Equilibrium Strategies in Stochastic Games with additive Cost and Transition Structure

Two-person stochastic games with additive transition and cost structure and the criterion of expected total costs are treated. State space and action spaces are standard Borel, and unbounded costs are allowed. For the zero-sum case, it is shown that there are stationary deterministic eη-optimal strategies for every e>0 and a certain weight function η if some semi-continuity and compactness conditions are fulfilled. Using these results, the existence of so-called quasi-stationary deterministic eη-equilibrium strategy pairs under corresponding conditions is proven.