Optimal cancellation penalty for competing ride-sourcing platforms under waiting time uncertainty

•Nash equilibrium of ride-sourcing duopoly encapsulating waiting time uncertainty.•Derivation of order cancellation probability under different waiting time perceptions.•Comparison of leveraging cancellation penalty under heterogenous road conditions.•The punishing effect and blocking effect of cancellation penalty. This paper investigates the optimal fare and penalty strategy of ride-sourcing platforms in a competing market. When ordering ride-sourcing services, passengers encounter waiting time variability due to the uncertainty in the matching and pickup processes. In some scenarios, some passengers order ride-sourcing services from multiple platforms to save waiting time, which results in subsequent order cancellations. To capture the behavior of order cancellation, this paper derives the cancellation probability based on the perceived inhomogeneous Poisson process. In view of the punishing effect and blocking effect of order cancellation penalty, this paper investigates the impact of order cancellation penalties on market equilibrium and platform revenue. We formulate a game-theoretic framework and obtain the duopoly market equilibrium to explore the optimal pricing (including penalties and fares) of different platforms. By incorporating passenger perceptions into the order cancellation behavior, this study produces insightful pricing schemes for the ride-sourcing platforms.