2019/12/04 by Jiequn Han, Ruimeng Hu, Han, Jiequn +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Forecasting Techniques and Applications #Machine Learning (cs.LG) #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Sports Analytics and Performance #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1912.01809
openalex publication_date 2019/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.