A characterization of sub-game perfect Nash equilibria for SDEs of mean   field type
  We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is extended to a mean field game to construct decentralized strategies and obtain an estimate of their performance. 
Boualem Djehiche and Minyi Huang
math.OC math.PR