Graphon Mean Field Games and Their Equations
Graphon Mean Field Games and Their Equations
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Graphon 平均场游戏及其方程
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Minyi Huang
中科院分区：
文献类型：
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作者：
P. Caines;Minyi Huang
大网络及其无限极限的图形理论的出现，使得在渐近无限网络上分布的动力系统的集中控制理论得以形成（Gao和Caines， IEEE CDC 2017,2018）。此外，在（Caines and Huang, IEEE CDC 2018, 2019）中开始了对这类系统的分散控制的研究，其中制定了Graphon Mean Field Games （GMFG）和GMFG方程，用于分析无界网络上的非合作动态博弈。在该工作中，引入了GMFG方程的存在唯一性结果，以及GMFG系统的epsilon-Nash理论，该理论将无限网络上的无限种群均衡与有限网络上的有限种群均衡联系起来。这些结果在本文中得到了严格的证实。
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.