Mean Field Game Systems with Common and Latent Processes

Many interacting systems contain latent (i.e. exogenous) processes that affect their dynamics, yet which cannot themselves be directly observed. This paper studies a class of (non-cooperative) stochastic games with major and minor agents interacting in a system that is modulated by a latent Markov chain. Moreover, the agents' cost functionals are permitted to couple with the latent process. A novel convex analysis is developed to (i) solve the mean field game (MFG) limit of the problem, (ii) demonstrate that the best response strategies generate an ε-Nash equilibrium for the finite player game, and (iii) obtain explicit characterisations of the best response strategies.