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Dynamic Games and Applications Seminar

Mean-Field Games Through Monotone Methods

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Nov 10, 2022   11:00 AM — 12:00 PM

Rita Ferreira King Abdullah University of Science and Technology, Saudi Arabia

Rita Ferreira

Presentation on YouTube

In this talk, we address the study of mean-field games (MFGs) using monotonicity techniques. MFGs model the limit of differential games with a large population as the number of agents tends to infinity. In these models, each agent is rational and optimizes a cost functional, and often comprise a system of two equations, a Hamilton–Jacobi equation and a Fokker–Planck equation, which can be associated with a monotone operator. This structure is key to establish the uniqueness of solutions, as used by Lasry and Lions. A main difficulty in the MFG theory is to establish the existence of solutions. While Hamilton–Jacobi and Fokker–Planck equations are extremely well understood, the coupling between these two equations presents substantial difficulties. Our main purpose is to discuss how monotone operators ideas enable a unified approach to address existence of weak solutions to a wide class of MFGs, including stationary problems with periodic or Dirichlet boundary conditions, time-dependent problems, and planning problems with congestion.

Georges Zaccour organizer
Can Baris Cetin organizer

Location

Online meeting
Zoom
Montréal Québec
Canada

Associated organization

Research Axis