2020/08/12 by Jiequn Han, Ruimeng Hu, Han, Jiequn +3 · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Machine Learning (cs.LG) #Mathematical Biology Tumor Growth #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Stochastic processes and financial applications #cs.GT #cs.LG #math.OC #q-fin.MF
paper · pdf · doi:10.48550/arxiv.2008.05519
openalex publication_date 2020/08/12 · arxiv created 2021/03/21 · arxiv updated 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.