How to Make Money From Fresh Data: Subscription Strategies in Age-Based Systems

TL;DR

This work addresses monetizing freshness in a time-varying data service by formulating a Stackelberg game where a server selects a sampling rate $\beta$ and users decide to subscribe based on an age-of-information constraint in a gossip network. Using discrete-time analysis, the authors derive closed-form aging expressions $x_R=\dfrac{p_e}{\beta}$ and $x_S= p_e\left(\beta^{-1}+1\right)$, define AC-stability, and characterize equilibrium subscriptions for directed line, tree, and star topologies. Key results show an inverse relationship between subscriber fraction and both gossiping and sampling rates, with line networks supporting periodic AC-stable subscriptions, trees yielding exponential decay in subscribers, and star networks exhibiting threshold-based regimes governed by $\beta_c$ and $\beta_r$. The findings illuminate how network structure and pricing interact to determine profitability and subscriber reach in real-time information services.

Abstract

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.

Figures (7)

• Figure 1: System model consisting of a server and user nodes. Here, the event process is updated with probability $\!p_e$ and the server gets updates with rate $\!\beta\!$.
• Figure 2: Directed line network where the users are subscribing to the server's information in every $K$ users.
• Figure 3: $F_S$ and $K$ values at different $\beta$.
• Figure 4: Directed tree network with $K=2$ levels.
• Figure 5: Equilibrium subscription strategies on star network as function of $\beta$.

Theorems & Definitions (2)

• Definition 1
• Remark 1