| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 1863 - 1892 | |
| DOI | https://doi.org/10.1051/m2an/2023026 | |
| Published online | 03 July 2023 | |
A fictitious-play finite-difference method for linearly solvable mean field games
1
Toyota Central R&D Labs., Inc., Bunkyo-ku, Tokyo 112-0004, Japan
2
Toyota Central R&D Labs., Inc. Nagakute, Aichi 480-1192, Japan
3
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
* Corresponding author: daisuke-inoue@mosk.tytlabs.co.jp
Received:
28
April
2022
Accepted:
14
March
2023
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf transformation and iterative computation using fictitious play are introduced. This leads to an implementation-friendly algorithm that iteratively solves explicit schemes. The convergence properties of the proposed scheme are mathematically proved by tracking the error of the variable through iterations. Numerical calculations show that the proposed method works stably for both one- and two-dimensional control problems.
Mathematics Subject Classification: 49N80 / 49M25 / 65M06
Key words: Mean field games / Finite difference methods / fictitious play / Cole-Hopf transformation
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.