IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2106.03272.html
   My bibliography  Save this paper

Signatured Deep Fictitious Play for Mean Field Games with Common Noise

Author

Listed:
  • Ming Min
  • Ruimeng Hu

Abstract

Existing deep learning methods for solving mean-field games (MFGs) with common noise fix the sampling common noise paths and then solve the corresponding MFGs. This leads to a nested-loop structure with millions of simulations of common noise paths in order to produce accurate solutions, which results in prohibitive computational cost and limits the applications to a large extent. In this paper, based on the rough path theory, we propose a novel single-loop algorithm, named signatured deep fictitious play, by which we can work with the unfixed common noise setup to avoid the nested-loop structure and reduce the computational complexity significantly. The proposed algorithm can accurately capture the effect of common uncertainty changes on mean-field equilibria without further training of neural networks, as previously needed in the existing machine learning algorithms. The efficiency is supported by three applications, including linear-quadratic MFGs, mean-field portfolio game, and mean-field game of optimal consumption and investment. Overall, we provide a new point of view from the rough path theory to solve MFGs with common noise with significantly improved efficiency and an extensive range of applications. In addition, we report the first deep learning work to deal with extended MFGs (a mean-field interaction via both the states and controls) with common noise.

Suggested Citation

  • Ming Min & Ruimeng Hu, 2021. "Signatured Deep Fictitious Play for Mean Field Games with Common Noise," Papers 2106.03272, arXiv.org.
    • Handle: RePEc:arx:papers:2106.03272
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2106.03272
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiequn Han & Ruimeng Hu & Jihao Long, 2020. "Convergence of Deep Fictitious Play for Stochastic Differential Games," Papers 2008.05519, arXiv.org, revised Mar 2021.
    2. Ruimeng Hu & Thaleia Zariphopoulou, 2021. "$N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction," Papers 2106.00581, arXiv.org, revised Jun 2021.
    3. Jiequn Han & Ruimeng Hu, 2019. "Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games," Papers 1912.01809, arXiv.org, revised Jun 2020.
    4. Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yichen Feng & Ming Min & Jean-Pierre Fouque, 2022. "Deep Learning for Systemic Risk Measures," Papers 2207.00739, arXiv.org.
    2. Xiaofei Shi & Daran Xu & Zhanhao Zhang, 2023. "Deep learning algorithms for hedging with frictions," Digital Finance, Springer, vol. 5(1), pages 113-147, March.
    3. Ming Min & Tomoyuki Ichiba, 2023. "Convolutional signature for sequential data," Digital Finance, Springer, vol. 5(1), pages 3-28, March.
    4. Erhan Bayraktar & Qi Feng & Zhaoyu Zhang, 2022. "Deep Signature Algorithm for Multi-dimensional Path-Dependent Options," Papers 2211.11691, arXiv.org, revised Jan 2024.
    5. Christa Cuchiero & Philipp Schmocker & Josef Teichmann, 2023. "Global universal approximation of functional input maps on weighted spaces," Papers 2306.03303, arXiv.org, revised Feb 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han, Jiequn & Hu, Ruimeng & Long, Jihao, 2023. "A class of dimension-free metrics for the convergence of empirical measures," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 242-287.
    2. Jiequn Han & Yucheng Yang & Weinan E, 2021. "DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks," Papers 2112.14377, arXiv.org, revised Feb 2022.
    3. Robert Balkin & Hector D. Ceniceros & Ruimeng Hu, 2023. "Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms," Papers 2307.06450, arXiv.org.
    4. Ludovic Tangpi & Xuchen Zhou, 2022. "Optimal Investment in a Large Population of Competitive and Heterogeneous Agents," Papers 2202.11314, arXiv.org, revised Feb 2023.
    5. Guanxing Fu & Chao Zhou, 2021. "Mean Field Portfolio Games," Papers 2106.06185, arXiv.org, revised Apr 2022.
    6. Lijun Bo & Shihua Wang & Xiang Yu, 2022. "A mean field game approach to equilibrium consumption under external habit formation," Papers 2206.13341, arXiv.org, revised Mar 2024.
    7. Lijun Bo & Shihua Wang & Xiang Yu, 2021. "Mean Field Game of Optimal Relative Investment with Jump Risk," Papers 2108.00799, arXiv.org, revised Feb 2023.
    8. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    9. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, June.
    10. Li-Hsien Sun, 2022. "Mean Field Games with Heterogeneous Groups: Application to Banking Systems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 130-167, January.
    11. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    12. Gu Wang & Jiaxuan Ye, 2023. "Fund Managers’ Competition for Investment Flows Based on Relative Performance," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 605-643, August.
    13. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    14. Nicole Bäuerle & Tamara Göll, 2023. "Nash equilibria for relative investors via no-arbitrage arguments," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 1-23, February.
    15. Qian Lei & Chi Seng Pun, 2021. "Nonlocality, Nonlinearity, and Time Inconsistency in Stochastic Differential Games," Papers 2112.14409, arXiv.org, revised Sep 2023.
    16. Guan, Guohui & Liang, Zongxia & Xia, Yi, 2023. "Optimal management of DC pension fund under the relative performance ratio and VaR constraint," European Journal of Operational Research, Elsevier, vol. 305(2), pages 868-886.
    17. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.
    18. Steven Campbell & Yichao Chen & Arvind Shrivats & Sebastian Jaimungal, 2021. "Deep Learning for Principal-Agent Mean Field Games," Papers 2110.01127, arXiv.org.
    19. Michail Anthropelos & Tianran Geng & Thaleia Zariphopoulou, 2020. "Competition in Fund Management and Forward Relative Performance Criteria," Papers 2011.00838, arXiv.org.
    20. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2106.03272. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.