Distinguished Lecture, Short Course - Lecture 1: On Mean Field Games

Pierre-Louis Lions
Université de Paris IX (Paris-Dauphine)

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.

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