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.
Citation
Sailes K. Sengupta. "Lower Semicontinuous Stochastic Games with Imperfect Information." Ann. Statist. 3 (2) 554 - 558, March, 1975. https://doi.org/10.1214/aos/1176343088
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