Abstract
We consider mean field games between a dominant leader and many followers, such that each follower is subject to a heterogeneous delay effect from the leader's action, who in turn can exercise governance on the population through this influence. The delay effects are assumed to be discretely distributed among the followers. Given regular enough coefficients, we describe a necessary condition for the existence of a solution for the equilibrium by a system of coupled forward–backward stochastic differential equations and stochastic partial differential equations. We provide a thorough study for the particular linear quadratic case. By adopting a functional approach, we obtain the time-independent sufficient condition, which warrants the unique existence of the solution of the whole mean field game problem. Several numerical illustrations with different time horizons and populations are demonstrated.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.