LQG Graphon Mean Field Games: Analysis via Graphon-Invariant Subspaces

• 成果类型: Article
• 署名作者: Gao, Shuang; Caines, Peter E.; Huang, Minyi
• 署名单位: McGill University; Carleton University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3281493
• 发表日期: 2023
• 页码: 7482-7497
• 关键词: Complex networks; graphon control; infinite-dimensional systems; large-scale networks; mean field games

摘要

This article studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics' parameters and heterogeneous network couplings within the graphon mean field game framework. A graphon time-varying dynamical system model is first formulated to study the finite and then limit problems of linear quadratic Gaussian graphon mean field games (LQG-GMFGs). The Nash equilibrium of the limit problem is then characterized by two coupled graphon time-varying dynamical systems. Sufficient conditions are established for the existence of a unique solution to the limit LQG-GMFG problem. For the computation of LQG-GMFG solutions, two methods are established and employed where one is based on fixed point analysis and the other on a decoupling operator Riccati equation; furthermore, two corresponding sets of solutions are established based on spectral decompositions. Finally, a set of numerical simulations on networks associated with different types of graphons are presented.