Abstract In the rapidly evolving ride-sourcing market, emerging third-party integrators offer passengers the convenience of accessing services from multiple platforms simultaneously. This innovative business model allows a third-party integrator to send ride service requests from passengers to multiple ride-sourcing platforms, ultimately selecting the most desirable one from the ones that respond. In this study, we address the integrator’s platform assignment problem in a ride-sourcing market, taking into account the stochastic nature of passenger waiting times influenced by factors such as the random locations of idle vehicles. Our findings reveal that a third-party integrator, using minimum waiting time as a criterion for platform assignment, can effectively reduce passengers’ generalized trip costs and increase both passenger demand and social welfare under specific moderate conditions. Furthermore, we demonstrate that when the waiting time on each platform follows the Weibull distribution with the scale parameter linearly dependent on the number of idle vehicles, the passenger waiting time with an integrator follows the same distribution as merging all platforms into one. Additionally, the probability of a platform being assigned to passengers equals the proportion of its idle vehicles across the entire integrated market under this distribution type. Moreover, we extend the proposed integrator platform assignment model to a scenario where the integrator makes assignments among selected options for passengers. Numerical examples demonstrate that when platforms have identical fares, platforms with smaller fleet sizes are more likely to benefit from integration, while those with larger fleet sizes may experience losses. We further demonstrate that platform competition for trip fares decreases passenger demand and social welfare if passengers cannot choose platform options. However, in cases where passengers have the freedom to select platform options, platform competition increases passenger demand and social welfare.

Highlights • Order assignment in a ride-sourcing market with a third-party integrator is modeled. • Integration conditionally leads to higher passenger demand and social welfare. • Platforms’ portions of idle vehicles in the market are critical for market shares. • Platforms with smaller fleet sizes are more likely to benefit from the integration. • Platforms with larger fleet sizes may lose from the integration.