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Mean Field Games and the Control of Large Scale Systems: An Overview

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Mean Field Game (MFG) theory provides tractable strategies for the decentralized control of large scale systems. The power of the formulation arises from the relative tractability of its infinite population McKean-Vlasov (MV) Hamilton-Jacobi-Bellman equations and the associated MV-Fokker-Planck-Kolmogorov equations, where these are linked by the distribution of the state of a generic agent, otherwise known as the system’s mean field. The resulting decentralized feedback controls yield approximate Nash equilibria and depend only upon an agent’s state and the mean field. Applications of MFG theory are being investigated within engineering, finance, economics and social dynamics, while theoretical developments include existence and uniqueness theory for solutions to the MFG equations, major-minor (MM) agent systems containing asymptotically non-negligible agents, non-linear estimation theory for MM-MFG systems, and the comparison of centralized (optimal) control and MFG control performance.

This talk is part of the CUED Control Group Seminars series.

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