Topics on mean field games with application

This talk starts by introducing the interacting particle
 system approach for modeling large scale decision problems involving
 many agents and mean field coupling. A central issue is to design low
 complexity individual strategies. This has led to the development of
 mean field game theory via consistent mean field approximations as
 inspired by ideas from statistical physics. I will describe the
 fundamental procedure to solve such problems and show a so-called
 epsilon-Nash equilibrium theorem. An application to stochastic economic
 growth, for both discrete and continuous time, will be presented.
 Further generalization of the theory will be discussed (major players,
 social optimization, robustness, etc.)