Dynamic Pricing for On-Demand Ride-Sharing: A Continuous Approach

Abstract

We investigate the dynamic pricing problem in on-demand ride-sharing using a continuous-time continuous-space approach. A ride-sharing platform controls two sides of the market, supply (vacant vehicles) and demand (customers' trip requests) via setting dynamic prices and commissions with the objective of maximizing its expected revenue in the infinite horizon. The dynamic model of supply is described by the multi-population traffic flow with an intergroup transfer (a system of hyperbolic stochastic partial differential equations); the demand subjects to independent stochastic processes. This continuous setting allows solving the revenue maximization by optimal control without treating combinatorial explosions. The demand-supply-based pricing is smooth in space and the traffic congestion resulted from control is also considered. This work provides a macroscopic perspective in handling the complicated spatiotemporal pricing problem in ride-sharing and similar matching markets.

Keywords: dynamic pricing, continuous approach, optimal control, ride-sharing, two-sided market