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), xi(n)), n = 0, 1, . . . , where the disturbance process {xi(n)} is formed by independent and identically distributed R-k-valued random vectors, which are observable but their common density rho* is unknown for both players. Combining suitable methods of statistical estimation of rho* with optimization procedures, we construct a pair of average optimal strategies. (C) 2013 Elsevier Inc. AB rights reserved.