Public Lecture: On Mean Field Games
Presented by Pierre-Louis Lions, Collége de France and Ecole Polytechnique

Tuesday Jan. 5, 2010, 4:30 pm
Moore Hall, Room 100
Reception in the IPAM building immediately following the lecture.

Abstract: This talk will be a general presentation of Mean Field Games (MFG in short), a new class of mathematical models and problems introduced and studied in collaboration with Jean- Michel Lasry. Roughly speaking, MFG are mathematical models that aim to describe the behavior of a very large number of “agents” who optimize their decisions while taking into account and interacting with the other agents. The derivation of MFG, which can be justified rigorously from Nash equilibria for N players games, letting N go to infinity, leads to new nonlinear systems involving ordinary differential equations or partial differential equations. Many classical systems are particular cases of MFG like, for example, compressible Euler equations, Hartree equations, porous media equations, semilinear elliptic equations, Hamilton-Jacobi-Bellman equations, Vlasov-Boltzmann models ... In this talk we shall explain in a very simple example how MFG models are derived and present some overview of the theory, its connections with many other fields and its applications.

The Speaker: Pierre-Louis Lions is a French mathematician who was awarded the Fields Medal in 1994 for his work on partial differential equations. Lions earned a doctorate from the University of Paris VI in 1979. He is a member of the French Academy of Sciences and Professor at the College de France. For his outstanding contributions to mathematics and its applications, he has received many prestigious awards, including the Doistau-Blutet Foundation Prize, the Ampère Prize, the IBM Prize and the Philip Morris Prize.