Mean Field Games with Parametrized Followers
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AbstractWe 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.
Acceptance Date30/03/2019
All Author(s) ListBensoussan A., Cass T., Chau M. H. M., Yam S. C. P.
Journal nameIEEE Transactions on Automatic Control
Year2020
Month1
Volume Number65
Issue Number1
PublisherIEEE
Place of PublicationUSA
Pages12 - 27
ISSN0018-9286
eISSN1558-2523
LanguagesEnglish-United States
KeywordsGames, Sociology, Statistics, Stochastic processes, Delay effects, Differential equations, Delays

Last updated on 2020-19-10 at 04:12