Professor Piermarco Cannarsa, Mathematical Analysis at the University of Rome Tor Vergata, Italy

Thursday, December 03, 2020, 15:00

- 18:00

https://kaust.zoom.us/j/99381635220

The theory of Mean Field Games (MFG) has been developed in the last two decades by economists, engineers, and mathematicians in order to study decision making in very large populations of “small" interacting agents. This short course will be focused on deterministic MFG, which are associated with a first order PDE system. We will address the problem assuming that agents are subject to state constraints, when classical PDE techniques are of little help. First, we will show how to prove the existence of solutions by the so-called Lagrangian approach, which interprets equilibria as certain measures on the space of paths that each agent can choose. Then, we will address regularity issues for such generalized solutions, deriving point-wise properties that allow to recover the typical MFG system. Finally, we will study the asymptotic behavior of solutions to the constrained MFG system as time goes to infinity, borrowing ideas from weak KAM theory.