Discounted stochastic games (Q2757578)

The author considers a discounted stochastic game with a finite number of players, measurable state and action states (possibly infinite), measurable, bounded and continuous payoff function, measurable and norm-continuous transition law. The main aim of the paper is to give an alternative proof of the result of \textit{J.-F. Mertens} and \textit{T. Parthasarathy} [Equilibria for Discounted Stochastic Games, CORE Discussion Paper No. 8750 (1987)] on the existence of stationary optimal strategies of the players and of the game value. The basic idea is to use a limit of \(\varepsilon\)-equilibrium payoffs in a one-shot game to define an equilibrium in the discounted game. The main tool that is used are selection theorems for measurable correspondences, and not fixed point theorems as in the case of finite state space.