Finite state<i>N</i>-agent and mean field control problems

We examine mean field control problems on a finite state space, in continuous time and over horizon. characterize the value function of problem as unique viscosity solution Hamilton-Jacobi-Bellman equation simplex. In absence any convexity assumption, we exploit this characterization to prove convergence, N grows, functions centralized -agent optimal limit function, with convergence rate order [see formula PDF]. Then, assuming convexity, show that is smooth establish propagation chaos, i.e. trajectories limiting trajectory, an explicit rate.