Pierre-Louis Lions
Collège de
France, París.
“On Mean Field Games”
Jueves
28 de mayo
11:30
hr., C-XV-520
Resumen:
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.