We consider a communication system consisting of a server that tracks and publishes updates about a time-varying data source or event, and a gossip network of users interested in closely tracking the event. The timeliness of the information is measured through the version age of information. The users wish to have their expected version ages remain below a threshold, and have the option to either rely on gossip from their neighbors or subscribe to the server directly to follow updates about the event if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing the number of subscribers and reducing costs associated with the frequent sampling of the event. We model the problem setup as a Stackelberg game between the server and the users, where the server commits to a frequency of sampling the event, and the users make decisions on whether to subscribe or not. As an initial work, we focus on directed networks with unidirectional flow of information and obtain the optimal equilibrium strategies for all the players. We provide simulation results to confirm the theoretical findings and provide additional insights.

翻译：我们考虑一个通信系统，该系统由一台追踪并发布关于时变数据源或事件更新的服务器，以及一个由关注紧密追踪该事件的用户组成的八卦网络组成。信息的及时性通过信息版本年龄来衡量。用户希望其期望版本年龄保持在阈值以下，并且如果依靠邻居八卦的方式无法满足及时性要求，他们可以选择直接订阅服务器以获取事件更新。服务器旨在通过增加订阅者数量并降低与频繁采样事件相关的成本来最大化其利润。我们将问题模型建模为服务器与用户之间的斯塔克尔伯格博弈，其中服务器承诺一个采样事件的频率，用户则决定是否订阅。作为初步工作，我们专注于具有单向信息流的有向网络，并获得了所有参与者的最优均衡策略。我们提供了仿真结果以证实理论发现并补充更多见解。