In this article, we study the problem of Nash equilibrium (NE) seeking of NN -player games with high-order integrator agents over jointly strongly connected networks. The same problem was studied recently over static, undirected, and connected networks. Since a jointly strongly connected network can be directed and disconnected at every time instant, our result strictly includes the existing results as special cases. Moreover, in addition to some analytic conditions on the payoff functions, the existing results also rely on the satisfaction of an inequality involving some Lipschitz constant and the smallest nonzero eigenvalue of the Laplacian of the network graph. By adopting a different approach, our result does not rely on the satisfaction of this inequality. Furthermore, our result can also be extended to the case where the additive disturbances are imposed on the input of each agent. Our design is illustrated by two numerical examples.

中文翻译：

---

联合强连接交换网络上高阶积分器的分布式纳什均衡寻求和抗扰


在本文中，我们研究了联合强连接网络上具有高阶积分代理的神经网络玩家博弈的纳什均衡（NE）寻求问题。最近在静态、无向和连接的网络上研究了同样的问题。由于联合强连接网络可以在每个时刻被引导和断开，因此我们的结果严格包括作为特殊情况的现有结果。此外，除了支付函数上的一些解析条件外，现有结果还依赖于涉及某些Lipschitz常数和网络图拉普拉斯算子的最小非零特征值的不等式的满足。通过采用不同的方法，我们的结果不依赖于这种不平等的满足。此外，我们的结果还可以扩展到对每个智能体的输入施加附加干扰的情况。我们的设计通过两个数值示例进行说明。