This was part of Distributed Solutions to Complex Societal Problems Reunion Workshop

Deterministic mean field games with control on the acceleration and state constraints

Yves Achdou, Universite Paris Cité
Tuesday, February 21, 2023

Abstract: We consider deterministic mean field games in which the agents control their accelerationand are constrained to remain in a region of R^n. After recalling previous results on the unconstrained problem, we study relaxed equilibria in the Lagrangian setting; they are described by a probability measure on trajectories. The main results concern the existence of relaxed equilibria undersuitable assumptions. The fact that the optimal trajectories of the related optimal control problem solved by the agents do not form a compact set brings a difficulty in the proof of existence.The proof also requires closed graph properties of the map which associates to initial conditions the set of optimal trajectories.