Ε-Nash mean-field games for general linear-quadratic systems with applications. (April 2020)

• Record Type: Journal Article
• Authors: Xu, Ruimin; Zhang, Feng
• Is Part Of: Automatica. Volume 114(2020)
• Publication Date: 2020-04
• Subjects: Mean-field game -- Linear-quadratic problem -- Large population -- ϵ-Nash equilibrium; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2020.108835
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper is concerned with general mean-field (MF) linear-quadratic (LQ) games of stochastic large-population system, where the individual diffusion coefficient can depend on both the state and the control of the agent. Moreover, the control weight in the cost functional could be indefinite. The asymptotic suboptimality property (namely, ϵ -Nash equilibrium) of the decentralized strategies for the LQ games is derived through the consistency condition. The impact of the population's collective behaviors and the consistency of the mean field estimation are illustrated by the numerical results. A pricing problem is also studied, for which the decentralized suboptimal price is obtained.