Mean field games for multiagent systems in a Markov environment

In this paper, distributed games for large population multiagent systems in a Markov environment are investigated. To reduce the computational complexity, the mean field approach is adopted to construct distributed strategies. The population aggregate effect is provided by analyzing the consistency equation system which is obtained by the parameterized method. A set of distributed strategies is given from the population aggregate effect and the solution of a Markov jump tracking problem. It is shown that the closed-loop system is uniformly stable, and the distributed strategies are asymptotically optimal in the sense of Nash equilibrium, as the number of agents grows to infinity.