  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.
