Optimal strategies for adaptive zero-sum average Markov games

We consider a class of discrete-time two person zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs. The game evolves according to the recursive equation x_n+1=F(x_n, a_n, b_n, ξ_n), n=0, 1, . . ., where the disturbance process {ξ_n} is formed by independent and identically distributed Rk-valued random vectors, which are observable but their common density ρ^* is unknown for both players. Combining suitable methods of statistical estimation of ρ^* with optimization procedures, we construct a pair of average optimal strategies.