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

2021/03/19 by J. Frédéric Bonnans, Bonnans, Joseph Frédéric, Justina Gianatti +3 · 3 citations
Economics, Econometrics and Finance · #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.2103.10743

openalex publication_date 2021/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Approximately optimal distributed controls for high-dimensional stochastic systems with pairwise interaction through controls
• Mean-Field Games with Constraints
• Quantitative convergence for displacement monotone Mean Field Games of control

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