Linear quadratic mean field games with a major player: The multi-scale approach. (March 2020)

• Record Type: Journal Article
• Authors: Ma, Yan; Huang, Minyi
• Is Part Of: Automatica. Volume 113(2020)
• Publication Date: 2020-03
• Subjects: Asymptotic solvability -- Linear quadratic -- Mean field game -- Major and minor players -- Re-scaling -- Riccati differential equation; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108774
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper considers linear quadratic (LQ) mean field games with a major player and analyzes an asymptotic solvability problem. It starts with a large-scale system of coupled dynamic programming equations and applies a re-scaling technique introduced in Huang and Zhou (2018) and Huang and Zhou (2020) to derive a set of Riccati equations in lower dimensions, the solvability of which determines the necessary and sufficient condition for asymptotic solvability. We next derive the mean field limit of the strategies and the value functions. Finally, we show that the two decentralized strategies can be interpreted as the best responses of a major player and a representative minor player embedded in an infinite population, which have the property of consistent mean field approximations.