Introduction

This chapter provides a background on recent advances in the theory of mean field games (MFGs). MFGs has met an amazing success since pioneering works of more than ten years ago. It gives a self-contained study of the so-called master equation and an answer to the convergence problem. MFGs should be understood as games with a continuum of players, each of them interacting with the whole statistical distribution of the population. In this regard, they are expected to provide an asymptotic formulation for games with finitely many players with mean field interaction. This chapter focuses on the converse problem, which may be formulated by confirming whether the equilibria of the finite games converge to a solution of the corresponding MFG as the number of players becomes very large.