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

In this talk, using examples from communications and finance, we first present the Mean Field Game (MFG) theory of large population systems. Going to the infinite population limit it may be shown that individual agent feedback strategies exist which yield Nash equilibria given by the Mean Field Game equations.

Next we 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 very large populations and very large scale networks.

Du café et des biscuits seront offerts au début du séminaire.
Bienvenue à tous!