Mean field games: a bridge between Hamilton-Jacobi and transport-diffusion equations

Abstract: Mean field game theory was developed since 2006 by J.‑M. Lasry and P.‑L. Lions in order to adapt the concept of Nash equilibria to differential games with infinitely many players. In this context, the value function of any small player depends on the distribution law of the dynamical state of the system. This model leads to systems of PDEs coupling Hamilton–Jacobi with Fokker–Planck (or continuity) equations. In this talk I will describe some features of mean field game systems and their connection with optimal control and optimal transport, pointing out the role played by weak solutions, renormalized formulations, convex analysis and adjoint methods.

analysis of PDEs

Audience: researchers in the topic

Rio de Janeiro webinar on analysis and partial differential equations

Series comments: Talks are held twice a month; start time and day of the week may vary, according to the speaker time zone. A link to join each webinar will be made available in due time here and at sites.google.com/view/webinarpde/home