Semi-infinite Stochastic Games

Abstract

We investigate two-person zero-sum stopping stochastic games with a finite number of states, for which the action sets of player I are finite and those for player II are countably infinite. Concerning the payoffs no restrictions are made. We show that for such games the value, possibly —∞ in some coordinates, exists; player I possesses optimal stationary strategies and player II possesses near-optimal stationary strategies with finite support. Furthermore we relate the existence of value and of (near-)optimal stationary strategies with a maximal solution to the Shapley-equation.