Learning controls in mean field games: the fictitious play and related gradient descent
Abstract
We investigate two learning procedures and their relationship to the formation of equilibrium in potential mean field games (MFGs). The first one is a version of the fictitious play in which players observe directly the actions (controls) of other players and learn the distribution of the MFG through an update rules on controls. This leads to a new iterative procedure which converges for a wide class of potential MFGs of controls, even in the presence of common noise. On the other hand we also consider the learning procedure of a principal agent trying to solve a mean field control problem with only local gradient information. We prove that under very general assumption, the gradient descent of such agent converges to a solution of the associated potential MFG.
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BibTeX
@misc{meynard2026learning,
title = {{Learning controls in mean field games: the fictitious play and related gradient descent}},
author = {Charles Meynard},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06292},
eprint = {2610.06292},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05773855v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning controls in mean field games: the fictitious play and related gradient descent
AU - Charles Meynard
PY - 2026
DA - 2026/10/01
PB - HAL
DO - 10.48550/arxiv.2610.06292
UR - https://hal.science/hal-05773855v1
AB - We investigate two learning procedures and their relationship to the formation of equilibrium in potential mean field games (MFGs). The first one is a version of the fictitious play in which players observe directly the actions (controls) of other players and learn the distribution of the MFG through an update rules on controls. This leads to a new iterative procedure which converges for a wide class of potential MFGs of controls, even in the presence of common noise. On the other hand we also consider the learning procedure of a principal agent trying to solve a mean field control problem with only local gradient information. We prove that under very general assumption, the gradient descent of such agent converges to a solution of the associated potential MFG.
ER -