Lower Semicontinuous Stochastic Games with Imperfect Information

Abstract

Shapely's stochastic game is considered in a more general setting, with the accumulated payoff being regarded as a function on the space of infinite trajectories, and the set of states of the system taken as a compact metric space. It has been shown that any game with a lower semicontinuous payoff has value and one of the players has an optimal strategy. As a consequence, in Shapley's game both players have optimal strategies.