Existence of equilibrium stationary strategies in discounted noncooperative stochastic games with uncountable state space
This paper considers discounted noncooperative stochastic games with uncountable state space and compact metric action spaces. We assume that the transition law is absolutely continuous with respect to some probability measure defined on the state space. We prove, under certain additional continuity and integrability conditions, that such games have \(\epsilon\)-equilibrium stationary strategies for each \(\epsilon>0\). To prove this fact, we provide a method for approximating the original game by a sequence of finite or countable state games. The main result of this paper answers partially a question raised by \textit{T. Parthasarathy} [Sankhya, Ser. A 44, 114-127 (1982)].
approximation of discounted stochastic games
discounted noncooperative stochastic games
scientific article; zbMATH DE number 3865017
scientific article