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Today many mobile users in various zones are invited to sense and send backreal-time useful information (e.g., traffic observation and sensor data) tokeep the freshness of the content updates in such zones. However, due to thesampling cost in sensing and transmission, a user may not have the incentive tocontribute the real-time information to help reduce the age of information(AoI). We propose dynamic pricing for each zone to offer age-dependent monetaryreturns and encourage users to sample information at different rates over time.This dynamic pricing design problem needs to well balance the monetary paymentsas rewards to users and the AoI evolution over time, and is challenging tosolve especially under the incomplete information about users' arrivals andtheir private sampling costs. After formulating the problem as a nonlinearconstrained dynamic program, to avoid the curse of dimensionality, we firstpropose to approximate the dynamic AoI reduction as a time-average term andsuccessfully solve the approximate dynamic pricing in closed-form. Further, byproviding the steady-state analysis for an infinite time horizon, we show thatthe pricing scheme (though in closed-form) can be further simplified to an$\varepsilon$-optimal version without recursive computing over time. Finally,we extend the AoI control from a single zone to many zones with heterogeneoususer arrival rates and initial ages, where each zone cares not only its own AoIdynamics but also the average AoI of all the zones in a mean field game systemto provide a holistic service. Accordingly, we propose decentralized mean fieldpricing for each zone to self-operate by using a mean field term to estimatethe average age dynamics of all the zones, which does not even require manyzones to exchange their local data with each other.

Dynamic Pricing and Mean Field Analysis for Controlling Age of Information