| Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
|
|
|---|---|---|
| Page(s) | 953 - 990 | |
| DOI | https://doi.org/10.1051/m2an/2023019 | |
| Published online | 07 April 2023 | |
Linear programming fictitious play algorithm for mean field games with optimal stopping and absorption
1
Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom
2
CREST, ENSAE, Institut Polytechnique de Paris, 5 avenue Henry Le Chatelier, 91120 Palaiseau, France
* Corresponding author: peter.tankov@ensae.fr
Received:
2
March
2022
Accepted:
20
February
2023
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean field game population dynamics without computing the value function by solving linear programming problems associated with the distributions of the players still in the game and their stopping times/controls. We show the convergence of the algorithm using the topology of convergence in measure in the space of subprobability measures, which is needed to deal with the lack of continuity of the flows of measures. Numerical examples are provided to illustrate the convergence of the algorithm.
Mathematics Subject Classification: 91A55 / 91A13 / 60G40
Key words: Mean-field games / Optimal stopping / Continuous control / Absorption / Infinite-dimensional linear programming / Fictitious play
© 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.