  Today mobile users such as drivers are invited by content providers (e.g.,
Tripadvisor) to sample fresh information of diverse paths to control the age of
information (AoI). However, selfish drivers prefer to travel through the
shortest path instead of the others with extra costs in time and gas. To
motivate drivers to route and sample diverse paths, this paper is the first to
propose online pricing for a provider to economically reward drivers for
diverse routing and control the actual AoI dynamics over time and spatial path
domains. This online pricing optimization problem should be solved without
knowing drivers' costs and even arrivals, and is intractable due to the curse
of dimensionality in both time and space. If there is only one non-shortest
path, we leverage the Markov decision process (MDP) techniques to analyze the
problem. Accordingly, we design a linear-time algorithm for returning optimal
online pricing, where a higher pricing reward is needed for a larger AoI. If
there are a number of non-shortest paths, we prove that pricing one path at a
time is optimal, yet it is not optimal to choose the path with the largest
current AoI. Then we propose a new backward-clustered computation method and
develop an approximation algorithm to alternate different paths to price over
time. Perhaps surprisingly, our analysis of approximation ratio suggests that
our algorithm's performance approaches closer to optimum given more paths.
