论文标题
Graphon平均现场游戏和GMFG方程
Graphon Mean Field Games and the GMFG Equations
论文作者
论文摘要
大型网络及其无限限制的图形理论的出现使得分布在渐近无限网络上的动态系统的集中控制理论（Gao and Caines，IEEE CDC 2017，2017）。此外，在（Caines and Huang，IEEE CDC 2018，2019）中启动了对此类系统的分散控制的研究，在该研究中，Graphon平均野战游戏（GMFG）和GMFG方程式是为无块网络上非合件动态游戏的分析而制定的。在这项工作中，引入了GMFG方程的存在和唯一性结果，以及用于GMFG系统的Epsilon-Nash理论，该理论将无限人口平衡与无限网络相关联，以在有限网络上有限人口平衡。这些结果在本文中是严格确定的。
The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks (Gao and Caines, IEEE CDC 2017, 2018). Furthermore, the study of the decentralized control of such systems was initiated in (Caines and Huang, IEEE CDC 2018, 2019), where Graphon Mean Field Games (GMFG) and the GMFG equations were formulated for the analysis of non-cooperative dynamic games on unbounded networks. In that work, existence and uniqueness results were introduced for the GMFG equations, together with an epsilon-Nash theory for GMFG systems which relates infinite population equilibria on infinite networks to finite population equilibria on finite networks. Those results are rigorously established in this paper.
