Optimizing Profitability in Timely Gossip Networks

We consider a communication system where a group of users, interconnected in a bidirectional gossip network, wishes to follow a time-varying source, e.g., updates on an event, in real-time. The users wish to maintain their expected version ages below a threshold, and can either rely on gossip from their neighbors or directly subscribe to a server publishing about the event, if the former option does not meet the timeliness requirements. The server wishes to maximize its profit by increasing subscriptions from users and minimizing event sampling frequency to reduce costs. This leads to a Stackelberg game between the server and the users where the sender is the leader deciding its sampling frequency and the users are the followers deciding their subscription strategies. We investigate equilibrium strategies for low-connectivity and high-connectivity topologies.