A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles SIAM Journal on Control and Optimization Year : 2023

A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints

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.
Fichier principal
Vignette du fichier
Bonnans-Gianatti-Pfeiffer-preprint.pdf (407.9 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03174167 , version 1 (18-03-2021)
hal-03174167 , version 2 (17-01-2022)

Licence

Attribution

Identifiers

Cite

J. Frédéric Bonnans, Justina Gianatti, Laurent Pfeiffer. A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints. SIAM Journal on Control and Optimization, 2023, 61 (1), pp.105-134. ⟨10.1137/21M1407720⟩. ⟨hal-03174167v2⟩
110 View
204 Download

Altmetric

Share

Gmail Facebook X LinkedIn More