Semi-infinite stochastic games

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.keywordsstationary strategystochastic gamematrix gamemixed actionfinite supportthese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.