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, whereby they get aware of the actions played by the other players and the corresponding rewards. Using this information, they can revise their current action, imitating the 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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社区网络人口博弈中的模仿动态

我们研究了网络上人口游戏的确定性、连续时间模仿动态的渐近行为。这种学习机制的基本假设——包括复制动力学——是属于单个群体的玩家通过成对交互交换信息，从而他们了解其他玩家的行为和相应的奖励。使用这些信息，他们可以修改他们当前的动作，模仿与他们互动的玩家之一。调节学习过程的交互模式由社区结构决定。首先，描述了这种网络模仿动力学的平衡点集。其次，对于潜在博弈类和无向和连接的社区网络，证明了全局渐近收敛。特别是，在纳什均衡被隔离和完全支持的特殊情况下，我们的结果保证从每个完全支持的初始种群状态收敛到纳什均衡。提供了示例和数值模拟来验证理论结果，并针对未验证社区结构假设的情况讨论了反例。