Mean Field Markov Decision Processes

Abstract We consider mean-field control problems in discrete time with discounted reward, infinite horizon and compact state action space. The existence of optimal policies is shown the limiting problem derived when number individuals tends to infinity. Moreover, we average reward show that policy this limit $$\varepsilon $$ ε -optimal for if large discount factor close one. This result very helpful, because it turns out special case does only depend on distribution individuals, obtain a interesting subclass where an can be obtained by first computing measure from static optimization then achieving Markov Chain Monte Carlo methods. give two applications: Avoiding congestion graph positioning market place which solve explicitly.