The paper considers a communication system where a group of users, interconnected in a bidirectional gossip network, wish to track a time-varying source (e.g., updates on an event) in real-time. The users want 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.
The server's goal is 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 server is the leader deciding its sampling frequency and the users are the followers deciding their subscription strategies.
The authors investigate equilibrium strategies for low-connectivity (bidirectional line) and high-connectivity (fully-connected) network topologies. For the bidirectional line network, multiple Stackelberg equilibrium solutions exist, with higher plausible periodicity of subscribers under frequent server sampling. In contrast, the fully-connected network gives a single equilibrium solution and fewer subscribers, as the deep network connectivity disincentivizes users from subscribing.
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