Allocation problem in cross-platform ride-hail integration

Abstract

We consider a ride-hail system in which a third-party integrator receives ride requests and allocates them to ride service platforms. The ride allocation problem (RAP) is modeled as a Stackelberg game. The integrator, as the leader, chooses the allocation that maximizes its profit, by pricing the rides such that no platform (i.e., follower) can find a more profitable allocation. In pursuit of self-interest, the integrator may refuse to match as many rides as the platforms are willing to serve, thereby injecting an artificial scarcity into the system. To protect the platforms from over exploitation, an exogenous reserve price is introduced to bound their per capita profit from below. We formulate RAP as a bilevel pricing problem, and convert it to a single-level problem by dualizing the lower level. When artificial scarcity is eliminated and all reserve prices are set to zero, we prove the single-level problem can be turned into a mixed integer-linear program that equals its linear relaxation, thus becoming polynomially solvable. Moreover, this version of RAP is shown to be related to cooperative assignment games. Numerical experiments confirm that artificial scarcity negatively affects matching productivity and social welfare. The integrator is favored to take most profits, and leveraging artificial scarcity strengthens its dominance. Moreover, the tighter the supply, the more the integrator benefit from artificial scarcity. The reserve price helps redistribute benefits from the integrator to the platforms. However, demanding an excessively large reserve price may depress the platforms’ profits, while undermining system efficiency.