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Deep Neural Network Solution for Finite State Mean Field Game with Error Estimation

Author

Listed:
  • Jialiang Luo

    (Imperial College)

  • Harry Zheng

    (Imperial College)

Abstract

We discuss the numerical solution to a class of continuous time finite state mean field games. We apply the deep neural network (DNN) approach to solving the fully coupled forward and backward ordinary differential equation system that characterizes the equilibrium value function and probability measure of the finite state mean field game. We prove that the error between the true solution and the approximate solution is linear to the square root of DNN loss function. We give an example of applying the DNN method to solve the optimal market making problem with terminal rank-based trading volume reward.

Suggested Citation

  • Jialiang Luo & Harry Zheng, 2023. "Deep Neural Network Solution for Finite State Mean Field Game with Error Estimation," Dynamic Games and Applications, Springer, vol. 13(3), pages 859-896, September.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00477-5
    DOI: 10.1007/s13235-022-00477-5
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    References listed on IDEAS

    as
    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
    2. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Finite state mean field game; Forward backward ODE; Deep neural network; Error estimation;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • G1 - Financial Economics - - General Financial Markets

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