A rank based mean field game in the strong formulation
  We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence. 
Erhan Bayraktar and Yuchong Zhang
math.PR math.OC q-fin.MF