Volume 57, Number 2, March-April 2023
|Page(s)||953 - 990|
|Published online||07 April 2023|
Linear programming fictitious play algorithm for mean field games with optimal stopping and absorption
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: email@example.com
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
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