Strategic Profit Generation in Age-Based Systems

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-Nash game between the server and the users, where the server is the leader deciding its frequency of sampling the event, and the users are the followers deciding whether to subscribe or not. We first focus on directed networks with unidirectional flow of information and obtain the optimal equilibrium strategies for all the players, and later extend to the general case of undirected networks with bidirectional flow of information on inter-node links. We finally provide simulation results to confirm our theoretical findings and provide additional insights.