Local Control of Interacting Markov Processes on Graphs with Compact State Space Local Control of Interacting Markov Processes on Graphs with Compact State Space

Discrete time Markov processes with multidimensional compact state space are considered where the coordinate processes are locally interacting and change their states synchronously. The interaction structure of the process is determined by some general graph. Decision makers control synchronuosly the system's behaviour on the coordinate level using only local information. Conditions are given which guarantee that in the class of local randomized strategies there exist deterministic stationary Markov strategies which achieve maximal asymptotic average expected rewards. If the reward structure is separabel these strategies are even globally optimal.