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AM Seminar: Graphon Mean Field Games: A Dynamical Equilibrium Theory for a Networked World

Speaker Name: 
Peter E. Caines
Speaker Title: 
Speaker Organization: 
McGill University
Start Time: 
Monday, February 1, 2021 - 4:00pm
End Time: 
Monday, February 1, 2021 - 5:00pm
via Zoom
Abhishek Halder


The complexity of large population multi-agent dynamical systems, such as those occuring in economics, communication systems, environmental and transportation systems, makes centralized control infeasible and classical game theoretic solutions intractable.

In this talk, we first present the Mean Field Game (MFG) theory of large population systems. Going to the infinite population limit, individual agent feedback strategies exist which yield Nash equilibria. These are given by the MFG equations consisting of (i) a Hamilton-Jacobi-Bellman equation generating the Nash values and the best response control actions, and (ii) a McKean-Vlasov-Fokker-Planck–Kolmogorov equation for the probability distribution of the states of the population, otherwise known as the mean field.

Next we shall introduce Graphon Mean Field Game and Control theory. Very large scale networks linking dynamical agents are now ubiquitous, with examples being given by electrical power grids and social media networks. In this setting, the emergence of the graphon theory of infinite networks has enabled the formulation of the Graphon Mean Field Game equations. Just as for MFG theory, it is the simplicity of the infinite population GMFG strategies which permits their application to otherwise intractable problems involving large populations and networks.


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 Distinguished 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 2009, is a Fellow of IFAC, 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 was republished as a SIAM Classics in Applied Mathematics in June, 2018, and is a Senior Editor of Nonlinear Analysis – Hybrid Systems. His research interests include stochastic systems, mean field games and control theory, systems on complex networks and hybrid systems theory, together with their applications to natural and artificial systems.

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