  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.
