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
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games
We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large ๐-player stochastic differential games. Following the idea of fictitious play, we recast the ๐-player game into ๐ 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 ๐-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.
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- Award ID(s):
- 1953035
- PAR ID:
- 10253642
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 107
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 221-245
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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