Mean field games for large population stochastic multi-agent systems with Markov jumps

In the paper, we investigate decentralized games of large population stochastic multi-agent systems with Markov jumps. The agents are coupled via their individual indices, and their structure parameters are time-varying, which can be characterized by a sequence of independent and identically distributed (i.i.d) Markov chains. We use the mean field approach to prove that there exist two deterministic functions which can be used to approximate the coupled terms in the indices, and design constructively a decentralized control law. Under some mild conditions, the closed-loop system is shown to be uniform stable and sub-optimal in Nash equilibrium sense, as the number of agents grows to infinity.