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 and efficient tool for finding Markovian Nash equilibrium of large
The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number (
 Award ID(s):
 1761622
 Publication Date:
 NSFPAR ID:
 10340146
 Journal Name:
 Foundations of Data Science
 Volume:
 3
 Issue:
 3
 Page Range or eLocationID:
 543
 ISSN:
 26398001
 Sponsoring Org:
 National Science Foundation
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player asymmetric stochastic differential games [J. Han and R. Hu, Mathematical and Scientific Machine Learning Conference, pages 221245, PMLR, 2020]. By incorporating the idea of fictitious play, the algorithm decouples the game into\begin{document}$ N $\end{document} suboptimization problems, and identifies each player's optimal strategy with the deep backward stochastic differential equation (BSDE) method parallelly and repeatedly. In this paper, we prove the convergence of deep fictitious play (DFP) to the true Nash equilibrium. We can also show that the strategy based on DFP forms an\begin{document}$ N $\end{document} Nash equilibrium. We generalize the algorithm by proposing a new approach to decouple the games, and present numerical results of large population games showing the empirical convergence of the algorithm beyond the technical assumptions in the theorems.\begin{document}$ \epsilon $\end{document} 
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