Empirical approximation in markov games under unbounded payoff: Discounted and average criteria

This work deals with a class of discrete-time zero-sum Markov games whose state process fxtg evolves according to the equation xt+1 = F(xt; at; bt; ϵt); where at and bt represent the actions of player 1 and 2, respectively, and {ϵt} is a sequence of independent and identically distributed random variables with unknown distribution θ: Assuming possibly unbounded payo θ, and using the empirical distribution to estimate θ; we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria.