Quantitative propagation of chaos for mean field Markov decision process with common noise

We investigate propagation of chaos for mean field Markov Decision Process with common noise (CMKV-MDP), and when the optimization is performed over randomized open-loop controls on infinite horizon. first state a rate convergence order MNγ, where MN in Wasserstein distance empirical measure, γ ∈ (0,1] an explicit constant, limit value functions N-agent control problem asymmetric controls, towards function CMKV-MDP. Furthermore, we show how to explicitly construct (ϵ+O(MNγ))-optimal policies model from ϵ-optimal Our approach relies sharp comparison between Bellman operators CMKV-MDP, fine coupling measures.