论文标题
随机网络上的线性季度随机差异游戏
Linear-Quadratic Stochastic Differential Games on Random Directed Networks
论文作者
论文摘要
在Feng，Fouque \＆Ichiba \ Cite {Fengfouquequeichiba2020linearearquadratic}的Feng启动了有指导网络上线性 - 二次随机差异游戏的研究。在这项工作中，定义了带有有限或无限玩家的定向链上的游戏以及确定性的有向树上的游戏，并计算了他们的Nash Equilibria。当前的工作通过首先开发一个随机的定向链结构来继续进行分析，假设每两个邻居之间的相互作用是随机的。我们明确解决了该系统的开环NASH平衡，我们发现平衡下的动力学是由\ cite {fengfouquequeichiba2020202020llinearearquadratic}引入的加泰罗尼亚马尔可夫链描述的无限维高斯过程。关于随机差异游戏的讨论扩展到了随机的双向定向链和随机的定向树结构。
The study of linear-quadratic stochastic differential games on directed networks was initiated in Feng, Fouque \& Ichiba \cite{fengFouqueIchiba2020linearquadratic}. In that work, the game on a directed chain with finite or infinite players was defined as well as the game on a deterministic directed tree, and their Nash equilibria were computed. The current work continues the analysis by first developing a random directed chain structure by assuming the interaction between every two neighbors is random. We solve explicitly for an open-loop Nash equilibrium for the system and we find that the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain introduced in \cite{fengFouqueIchiba2020linearquadratic}. The discussion about stochastic differential games is extended to a random two-sided directed chain and a random directed tree structure.
