Controlled Markov Fields with Finite State Space on Graphs

Discrete time Markov chains with multidimensional state space are considered where the coordinates are locally interacting and develop synchronously. The interaction structure of the process is given by some general graph. Decision makers control the system's behaviour on the coordinate level using only local information. In the class of local strategies there exist deterministic stationary strategies which achieve minimal asymptotic average expected costs. If the cost structure is separable these strategies are even globally optimal.