  This paper studies spatiotemporal pricing and fleet management for autonomous
mobility-on-demand (AMoD) systems while taking elastic demand into account. We
consider a platform that offers ride-hailing services using a fleet of
autonomous vehicles and makes pricing, rebalancing, and fleet sizing decisions
in response to demand fluctuations. A network flow model is developed to
characterize the evolution of system states over space and time, which captures
the vehicle-passenger matching process and demand elasticity with respect to
price and waiting time. The platform's objective of maximizing profit is
formulated as a constrained optimal control problem, which is highly nonconvex
due to the nonlinear demand model and complex supply-demand interdependence. To
address this challenge, an integrated decomposition and dynamic programming
approach is proposed, where we first relax the problem through a change of
variable, then separate the relaxed problem into a few small-scale subproblems
via dual decomposition, and finally solve each subproblem using dynamic
programming. Despite the nonconvexity, our approach establishes a theoretical
upper bound to evaluate the solution optimality. The proposed model and
methodology are validated in numerical studies for Manhattan. We find that
compared to the benchmark case, the proposed upper bound is significantly
tighter. We also find that compared to pricing alone, joint pricing and fleet
rebalancing can only offer a minor profit improvement when demand can be
accurately predicted. However, during unanticipated demand surges, joint
pricing and rebalancing can lead to substantially improved profits, and the
impacts of demand shocks, despite being more widespread, can dissipate faster.
