  Over the past few years, ride-sharing has emerged as an effective way to
relieve traffic congestion. A key problem for these platforms is to come up
with a revenue-optimal (or GMV-optimal) pricing scheme and an induced vehicle
dispatching policy that incorporate geographic and temporal information. In
this paper, we aim to tackle this problem via an economic approach.
  Modeled naively, the underlying optimization problem may be non-convex and
thus hard to compute. To this end, we use a so-called "ironing" technique to
convert the problem into an equivalent convex optimization one via a clean
Markov decision process (MDP) formulation, where the states are the driver
distributions and the decision variables are the prices for each pair of
locations. Our main finding is an efficient algorithm that computes the exact
revenue-optimal (or GMV-optimal) randomized pricing schemes. We characterize
the optimal solution of the MDP by a primal-dual analysis of a corresponding
convex program. We also conduct empirical evaluations of our solution through
real data of a major ride-sharing platform and show its advantages over fixed
pricing schemes as well as several prevalent surge-based pricing schemes.
