Semicontinuous nonstationary stochastic games. II
This paper is a continuation of an earlier work of the author [ibid. 117, 84-99 (1986; Zbl 0594.90105)], which was devoted to general stochastic dynamic games with zero-sum, metric state spaces, weakly continuous transition probabilities, and lower semi-continuous payoff function. In this paper transition probabilities are assumed to be norm continuous, but with respect to actions of one player only (the minimizer). The payoff function depends lower semicontinuously on the minimizer's actions and is measurable with respect to random states of the game. Some general conditions that guarantee the existence of a value and optimal strategies for the players are given. It is also shown that the minimizer (whose action spaces are assumed to be compact) has a subgame-perfect optimal strategy. We point out that zero-sum Markov games belong to the large class of stochastic games studied in this paper.
norm continuous transition probabilities
scientific article; zbMATH DE number 4172792
scientific article