This paper formulates infinite dimensional graphon dynamical systems to study the limit problem of linear quadratic Gaussian graphon mean field game (LQG-GMFG). The limit problem is characterized by forward and backward graphon dynamical system equations. Based on this representation, sufficient conditions on the existence of a unique fixed point are established. Furthermore, under the finite rank assumption on the underlying graphon, exact numerical solution methods are presented.

中文翻译：

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LQG Graphon 平均场游戏

本文建立无限维图子动力学系统来研究线性二次高斯图子平均场博弈(LQG-GMFG)的极限问题。极限问题的特点是前向和后向图形动力学系统方程。基于这种表示，建立了唯一不动点存在的充分条件。此外，在基础图形的有限秩假设下，提出了精确的数值求解方法。