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

Jialiang Luo () and Harry Zheng ()
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Jialiang Luo: Imperial College
Harry Zheng: Imperial College

Dynamic Games and Applications, 2023, vol. 13, issue 3, No 8, 859-896

Abstract: 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.

Keywords: Finite state mean field game; Forward backward ODE; Deep neural network; Error estimation; 93E20; 90C39 (search for similar items in EconPapers)
JEL-codes: C7 G1 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13235-022-00477-5

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