The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an $ϵ$-equilibrium. To reach this goal, the results of Markov decision processes are used to find $ϵ$-optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the $ϵ$-equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented....

We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations $x_{t+1}=F(x_t,a_t,{\xi }_t)$, t=1,2,..., with i.i.d. ${ℝ}^k$-valued random vectors ${\xi }_t$, which are observable but whose density ϱ is unknown.

We study the stability of average optimal control of general discrete-time Markov processes. Under certain ergodicity and Lipschitz conditions the stability index is bounded by a constant times the Prokhorov distance between distributions of random vectors determinating the “original and the perturbated” control processes.