  For a class of finite horizon first order mean field games and associated
N-player games, we give a simple proof of convergence of symmetric N-player
Nash equilibria in distributed open-loop strategies to solutions of the mean
field game in Lagrangian form. Lagrangian solutions are then connected with
those determined by the usual mean field game system of two coupled first order
PDEs, and convergence of Nash equilibria in distributed Markov strategies is
established.

Optimization and Control