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.

提出了一种基于深度神经网络的算法来识别一般大型$N$人随机微分博弈的马尔可夫纳什均衡，该算法的核心思想是将$N$人游戏重塑为$N$个解耦决策问题，并通过迭代解决。

深度虚拟博弈对多智能体游戏中马尔科夫纳什均衡的寻找