A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints
Optimization and Control
2022-01-19 v2
Abstract
The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the distributions of the optimal strategies. Moreover, final state and mixed state-control constraints are considered, the dynamics being nonlinear and affine with respect to the control. The existence of equilibria is obtained by Kakutani's theorem, applied to a fixed point formulation of the problem. Finally, uniqueness results are shown under monotonicity assumptions.
Keywords
Cite
@article{arxiv.2103.10743,
title = {A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints},
author = {Joseph Frédéric Bonnans and Justina Gianatti and Laurent Pfeiffer},
journal= {arXiv preprint arXiv:2103.10743},
year = {2022}
}