Download Mean Field Game Theory for Partially Observed Nonlinear Systems

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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..
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