Joint Pricing and Matching in Ride-Sharing Systems

Ride-sharing firms use pricing and matching decisions to control the ride-sharing platforms. Those decisions can be made jointly or interchangeably, which raises the following questions: Is matching optimization necessary? Specifically, is fixing the matching decisions to a simple rule and optimizing only the pricing decisions enough to achieve the optimal performance? In order to answer these questions, we study the interplay between pricing and matching decisions of a ride-sharing firm. There are many studies in the ride-sharing literature that optimize the pricing decisions under an assumed matching policy. However, we show that ignoring matching optimization can result in subpar overall performance. We formulate a stylized ride-sharing model that captures customer and driver behaviors and geospatial nature of the system. Customers are both price and delay sensitive, and drivers are strategic and self-scheduling. We prove that optimizing the matching decisions have first-order effect on the system performance. We show that fixing the matching decisions and optimizing only the pricing decisions does not maximize the number of matchings in general. Similarly, we show that fixing the pricing decisions and optimizing only the matching decisions is not optimal in general. Finally, we show that optimizing in only one dimension (either pricing or matching) has no benefit to the firm under some conditions, whereas joint pricing and matching optimization can lead to a significant performance increase