Ergodic behavior of control and mean field games problems depending on acceleration
P Cardaliaguet, C Mendico - Nonlinear Analysis, 2021 - Elsevier
The goal of this paper is to study the long time behavior of solutions of the first-order mean
field game (MFG) systems with a control on the acceleration. The main issue for this is the
lack of small time controllability of the problem, which prevents to define the associated
ergodic mean field game problem in the standard way. To overcome this issue, we first study
the long-time average of optimal control problems with control on the acceleration: we prove
that the time average of the value function converges to an ergodic constant and represent …
field game (MFG) systems with a control on the acceleration. The main issue for this is the
lack of small time controllability of the problem, which prevents to define the associated
ergodic mean field game problem in the standard way. To overcome this issue, we first study
the long-time average of optimal control problems with control on the acceleration: we prove
that the time average of the value function converges to an ergodic constant and represent …
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