This work deals with a class of discrete-time zero-sum Markov games whose state process $\left\{x_t\right\}$ evolves according to the equation $x_{t+1}=F(x_t,a_t,b_t,{\xi }_t),$ where $a_t$ and $b_t$ represent the actions of player 1 and 2, respectively, and $\left\{{\xi }_t\right\}$ is a sequence of independent and identically distributed random variables with unknown distribution $\theta$. Assuming possibly unbounded payoff, and using the empirical distribution to estimate $\theta$, we introduce approximation schemes for the value of the game as well as for optimal strategies considering both,...

This paper deals with two-person stochastic games of resource extraction under both the discounted and the mean payoff criterion. Under some concavity and additivity assumptions concerning the payoff and the transition probability function a stationary Nash equilibrium is shown to exist. The proof is based on Schauder-Tychonoff's fixed point theorem, applied to a suitable payoff vector space.