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.

本文研究了不同市场条件下的乘车系统的供应曲线。曲线定义了系统行程的吞吐量与所服务的骑手成本之间的关系。我们首先关注各向同性市场，方法是重新审视最近发现的匹配故障，该匹配故障将请求驾驶员与非常空闲的驾驶员相匹配。失败将导致电子叫卖市场的供应曲线向后弯曲，但事实证明，在街头叫卖市场中不会出现向后弯曲。通过构建双端排队模型，我们证明了具有有限匹配半径的电子叫车系统的供应曲线总是向后弯曲，但是较小的匹配半径会导致较弱的弯曲。我们进一步揭示了通过自适应地调整匹配半径来完全避免弯曲的可能性。然后，我们转向各向异性市场，找出另一种类型的匹配失败，原因是驾驶员和骑手之间的不分青红皂白的匹配，这又导致供应向后弯曲。鉴于在实际操作中这种匹配失败的普遍性，我们讨论了如何使用价格或定量歧视来避免这种情况。构建了概念化的两节点网络以促进讨论。