How to Price Fresh Data

We introduce the concept of a fresh data market, in which a destination user requests, and pays for, fresh data updates from a source provider. Data freshness is captured by the {\it age of information} (AoI) metric, defined as the time elapsed since the latest update has reached the destination. The source incurs an operational cost, modeled as an increasing convex function of the number of updates. The destination incurs an age-related cost, modeled as an increasing convex function of the AoI. The source charges the destination for each update and designs a pricing mechanism to maximize its profit; the destination on the other hand chooses a data update schedule to minimize the summation of its payments to the source and its age-related cost. The interaction among the source and destination is hence game-theoretic. Motivated by the existing pricing literature, we first study a time-dependent pricing scheme, in which the price for each update depends on when it is requested. We show in this case that the game equilibrium leads to only one data update, which does not yield the maximum profit to the source. This motivates us to consider a quantity-based pricing scheme, in which the price of each update depends on how many updates have been previously requested. We show that among all pricing schemes in which the price of an update may vary according to both time and quantity, the quantity-based pricing scheme performs best: it maximizes the source's profit and minimizes the social cost of the system, defined as the aggregate source's operational cost and the destination's age-related cost. Numerical results show that the optimal quantity-based pricing can be 27% more profitable for the source and incurs 54% less social cost, compared with the optimal time-dependent pricing.