Local control of Markovian processes of interaction on a graph with a compact set of states (Q1407136)

Discrete-time Markov processes with a multidimensional state space are considered. The coordinate processes are locally interacting and assumed to change their states synchronously. Conditions are given that in the class of local randomized strategies there exist deterministic stationary Markovian strategies which maximize asymptotic average expected rewards. The considered processes generalize the concept of usual processes controlled in time. The compactness and continuity conditions imposed on the state space and the space of control actions are borrowed from studies on stochastic dynamic optimization and dynamic programming.