  Ridesharing markets are complex: drivers are strategic, rider demand and
driver availability are stochastic, and complex city-scale phenomena like
weather induce large scale correlation across space and time. At the same time,
past work has focused on a subset of these challenges. We propose a model of
ridesharing networks with strategic drivers, spatiotemporal dynamics, and
stochasticity. Supporting both computational tractability and better modeling
flexibility than classical fluid limits, we use a two-level stochastic model
that allows correlated shocks caused by weather or large public events.
  Using this model, we propose a novel pricing mechanism: stochastic
spatiotemporal pricing (SSP). We show that the SSP mechanism is asymptotically
incentive-compatible and that all (approximate) equilibria of the resulting
game are asymptotically welfare-maximizing when the market is large enough. The
SSP mechanism iteratively recomputes prices based on realized demand and
supply, and in this sense prices dynamically. We show that this is critical:
while a static variant of the SSP mechanism (whose prices vary with the
market-level stochastic scenario but not individual rider and driver decisions)
has a sequence of asymptotically welfare-optimal approximate equilibria, we
demonstrate that it also has other equilibria producing extremely low social
welfare. Thus, we argue that dynamic pricing is important for ensuring
robustness in stochastic ride-sharing networks.
