  Ridesharing platforms match drivers and riders to trips, using dynamic prices
to balance supply and demand. A challenge is to set prices that are
appropriately smooth in space and time, so that drivers with the flexibility to
decide how to work will nevertheless choose to accept their dispatched trips,
rather than drive to another area or wait for higher prices or a better trip.
In this work, we propose a complete information model that is simple yet rich
enough to incorporate spatial imbalance and temporal variations in supply and
demand -- conditions that lead to market failures in today's platforms. We
introduce the Spatio-Temporal Pricing (STP) mechanism. The mechanism is
incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to
always accept their trip dispatches. From any history onward, the equilibrium
outcome of the STP mechanism is welfare-optimal, envy-free, individually
rational, budget balanced, and core-selecting. We also prove the impossibility
of achieving the same economic properties in a dominant-strategy equilibrium.
Simulation results show that the STP mechanism can achieve substantially
improved social welfare and earning equity than a myopic mechanism.
