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3:20-3:40 : Title : Mean Field Game Theory for Partially Observed Nonlinear Systems with a Major Agent Speaker : Nevroz Sen, McGill University Abstract : Mean field game (MFG) theory with a major player and many minor players (MM-MFG) considers the situation where the major player has a significant influence, i.e., asymptotically non-vanishing, on any minor agent. A distinct feature of such games is that the mean field term becomes stochastic and, as a result, the best response control actions of the minor agents depend on the state of the major agent as well as the stochastic mean field. In this work, we consider MM-MFG systems under the assumption that this information is partially available to the minor agents and develop MFG theory for such systems. The first step of such a theory requires one to develop an estimation theory for partially observed stochastic dynamical systems whose state equations are of McKean-Vlasov (MV) type stochastic differential equations and hence contain a measure term corresponding to the distribution of the solution of the state process. It should however be observed that in this setup it is required to jointly estimate the state process and a stochastic measure term. Consequently, nonlinear filtering equations are first developed on the joint space of a metric space and the space of probability distributions on that metric space. We then consider the MFG problem with partial observations on the minor agents and complete observation at the major agent. The approach to the problem for MM-MFG systems adopted in this work is to follow the procedure of constructing the associated completely observed system via the application of nonlinear filtering theory. The existence and uniqueness of Nash equilibria is then analysed in this setting. This is a joint work with Peter E. Caines.. 1