  Stochastic differential games have been used extensively to model agents'
competitions in Finance, for instance, in P2P lending platforms from the
Fintech industry, the banking system for systemic risk, and insurance markets.
The recently proposed machine learning algorithm, deep fictitious play,
provides a novel efficient tool for finding Markovian Nash equilibrium of large
$N$-player asymmetric stochastic differential games [J. Han and R. Hu,
Mathematical and Scientific Machine Learning Conference, pages 221-245, PMLR,
2020]. By incorporating the idea of fictitious play, the algorithm decouples
the game into $N$ sub-optimization problems, and identifies each player's
optimal strategy with the deep backward stochastic differential equation (BSDE)
method parallelly and repeatedly. In this paper, we prove the convergence of
deep fictitious play (DFP) to the true Nash equilibrium. We can also show that
the strategy based on DFP forms an $\eps$-Nash equilibrium. We generalize the
algorithm by proposing a new approach to decouple the games, and present
numerical results of large population games showing the empirical convergence
of the algorithm beyond the technical assumptions in the theorems.
