In this talk we give a short introduction to mean-field games.
These problems arise in the study of differential games with infinitely
many indistinguishable players. A number of very interesting new partial
differential equations and systems arise naturally. These include systems
of Hamilton-Jacobi and transport of Fokker-Planck equations, systems of
hyperbolic conservation laws, infinite dimensional partial differential
equations in spaces of probability measures or random variables, to name
just a few. We will discuss a number of new results as well as open
problems.