In this article, we study the asymptotic behavior of deterministic, continuous-time imitation dynamics for population games over networks. The basic assumption of this learning mechanism—encompassing the replicator dynamics—is that players belonging to a single population exchange information through pairwise interactions, where they become aware of the actions played by the other players and the corresponding rewards. Using this information, they can revise their current action, imitating one of the players they interact with. The pattern of interactions regulating the learning process is determined by a community structure. First, the set of equilibrium points of such network imitation dynamics is characterized. Second, for the class of potential games and for undirected and connected community networks, global asymptotic convergence is proved. In particular, our results guarantee convergence to a Nash equilibrium from every fully supported initial population state in the special case when the Nash equilibria are isolated and fully supported. Examples and numerical simulations are offered to validate the theoretical results, and counterexamples are discussed for scenarios when the assumptions on the community structure are not verified.

中文翻译：

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社区网络中人口游戏的模仿动力学

在本文中，我们研究网络上人口博弈的确定性，连续时间模仿动力学的渐近行为。这种学习机制的基本假设（包括复制者的动力学）是，属于单个种群的参与者通过成对互动来交换信息，在此他们意识到其他参与者所扮演的动作和相应的奖励。利用这些信息，他们可以模仿与之互动的玩家之一，从而修改当前的动作。调节学习过程的互动方式由社区结构决定。首先，表征这种网络模仿动力学的平衡点集。其次，对于一类潜在的游戏以及无定向和连接的社区网络，证明了全局渐近收敛。特别是，当孤立和完全支持纳什均衡时，在特殊情况下，我们的结果可确保从每个完全支持的初始种群状态收敛到纳什均衡。提供了实例和数值模拟来验证理论结果，并讨论了未验证社区结构假设的情况下的反例。