2024/01/17 by Dexuan Xu, Xu, De-xuan, Zhun Gou +5 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2401.09030
openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies linear quadratic graphon mean field games (LQ-GMFGs) with common noise, in which a large number of agents are coupled via a weighted undirected graph. One special feature, compared with the well-studied graphon mean field games, is that the states of agents are described by the dynamic systems with the idiosyncratic noises and common noise. The limit LQ-GMFGs with common noise are formulated based on the assumption that these graphs lie in a sequence converging to a limit graphon. By applying the spectral decomposition method, the existence of solution for the formulated limit LQ-GMFGs is derived. Moreover, based on the adequate convergence assumptions, a set of ε-Nash equilibrium strategies for the finite large population problem is constructed.