  We propose a deep neural network-based algorithm to identify the Markovian
Nash equilibrium of general large $N$-player stochastic differential games.
Following the idea of fictitious play, we recast the $N$-player game into $N$
decoupled decision problems (one for each player) and solve them iteratively.
The individual decision problem is characterized by a semilinear
Hamilton-Jacobi-Bellman equation, to solve which we employ the recently
developed deep BSDE method. The resulted algorithm can solve large $N$-player
games for which conventional numerical methods would suffer from the curse of
dimensionality. Multiple numerical examples involving identical or
heterogeneous agents, with risk-neutral or risk-sensitive objectives, are
tested to validate the accuracy of the proposed algorithm in large group games.
Even for a fifty-player game with the presence of common noise, the proposed
algorithm still finds the approximate Nash equilibrium accurately, which, to
our best knowledge, is difficult to achieve by other numerical algorithms.
