In the Mean Field Games (MFG) framework where there is an agent (so-called Major) which has asymptotically non-vanishing influence on any other agent (so-called Minor), the best response control actions of the Minor agents depend on the state of the Major agent as well as on the stochastic mean field. The theory of MFG with a Major agent (MM-MFG) is well understood when the observations of the Minor agents are complete. In this work we analyze the MM-MFG problem when the Major agent's state is partially observed by the Minor agents. We first develop Nonlinear Filtering Theory for partially observed stochastic dynamical systems described by McKean-Vlasov (MV) stochastic state equations. Next, applying the standard separation methodology, we analyze the associated completely observed system. The existence and uniqueness of the solutions of the stochastic MFG system as well as the epsilon-Nash equilibria property of such a solution are presented in this setting.
This is joint work with Peter E. Caines
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