Before revision:  We modify the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium . There is a unique equilibrium in N-player games and mean field games with mild conditions on the equity market.
After revision:  We modify the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium , we show a unique equilibrium in N-player games and mean field games with mild conditions on the equity market.