论文标题
LQG Graphon平均现场游戏：通过Graphon不变子空间进行分析
LQG Graphon Mean Field Games: Analysis via Graphon Invariant Subspaces
论文作者
论文摘要
本文研究了具有均匀的节点动力学参数的大规模线性二次随机游戏的解决方案，以及在[2] - [4]中的Graphon平均场游戏框架内的均值均值网络耦合。 Graphon时变动力系统模型首先是为了研究有限的，然后限制线性二次高斯图形均值野外游戏（LQG-GMFG）的问题。然后，极限问题的NASH平衡以两个耦合的Graphon时变动力系统为特征。建立了足够的条件，以解决极限LQG-GMFG问题的独特解决方案。为了计算LQG-GMFG解决方案，建立了两种方法，并使用一种方法基于固定点迭代，而另一一种方法是基于解耦操作员Riccati方程的两种方法；此外，基于光谱分解建立了两组相应的溶液集。最后，介绍了与不同类型的图形相关联的网络上的一组数值模拟。
This paper 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 in [2]-[4]. 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-GMFG). 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 iterations 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.
