On the supply curve of ride-hailing systems

This paper studies the supply curve of ride-hailing systems under different market conditions. The curve defines a relationship between the throughput of trips of the system and the cost of riders it serves. We first focus on isotropic markets by revisiting a matching failure identified recently that matches a requesting rider with an idle driver very far away. The failure will cause the supply curve of an e-hailing market to be backward bending, but it is proved that the backward bend does not arise in the street-hailing market. By constructing a double-ended queuing model, we prove that the supply curve of an e-hailing system with finite matching radius is always backward bending, but a smaller matching radius leads to a weaker bend. We further reveal the possibility of completely avoiding the bend by adaptively adjusting the matching radius. We then turn to the anisotropic markets and identify another type of matching failure due to indiscriminate matching between drivers and riders, which again causes a backward bending supply. Given the prevalence of such a matching failure in real-world operations, we discuss how to avoid it using price or rationing discrimination. A conceptualized two-node network is constructed to facilitate the discussion.