Mean Field Game (MFG) theory establishes the existence of Nash equilibria for games involving a large number of agents modeled by controlled stochastic dynamical systems. In this talk we shall explain how the power of the formulation arises from the tractability of a game’s infinite population McKean-Vlasov (MV) Hamilton-Jacobi-Bellman and MV-Fokker-Planck-Kolmogorov PDEs, where these are linked by the distribution of the state of a generic agent, otherwise known as the system's mean field. The resulting infinite population decentralized feedback controls depend only upon an agent’s state and the mean field, and approximate Nash equilibria are obtained when they are applied in the otherwise intractable finite population setting. The potential applications of MFG theory are numerous and in the latter part of the talk applications to communications and finance will be presented. Finally, the theory’s generalizations to infinite networks as expressed by the Graphon-Network MFG equations will be sketched.
Peter E. Caines received the BA in mathematics from Oxford University in 1967 and the PhD in systems and control theory in 1970 from Imperial College, University of London, supervised by David Q. Mayne, FRS. In 1980, he joined McGill University, Montreal, where he is James McGill Professor and Macdonald Chair in the Department of Electrical and Computer Engineering. In 2000, his paper on adaptive control with G. C. Goodwin and P. J. Ramadge (IEEE TAC, 1980) was recognized by the IEEE Control Systems Society as one of the 25 seminal control theory papers of the 20th century. He received the IEEE Control Systems Society Bode Lecture Prize in 2013, is a Fellow of CIFAR, SIAM, IEEE, the IMA (UK) and the Royal Society of Canada (2003), and is a member of Professional Engineers Ontario. Peter Caines is the author of Linear Stochastic Systems (Wiley,1988) which is to be republished as a SIAM Classic and is a Senior Editor of Nonlinear Analysis – Hybrid Systems. His research interests include stochastic, mean field game, and networked and hybrid systems theory together with their applications to natural and artificial systems.