We consider a ride-hail system in which a third-party integrator receives ride requests and allocates them to ride service platforms. The ride allocation problem (RAP) is modeled as a Stackelberg game. The integrator, as the leader, chooses the allocation that maximizes its profit, by pricing the rides such that no platform (i.e., follower) can find a more profitable allocation. In pursuit of self-interest, the integrator may refuse to match as many rides as the platforms are willing to serve, thereby injecting an artificial scarcity into the system. To protect the platforms from over exploitation, an exogenous reserve price is introduced to bound their per capita profit from below. We formulate RAP as a bilevel pricing problem, and convert it to a single-level problem by dualizing the lower level. When artificial scarcity is eliminated and all reserve prices are set to zero, we prove the single-level problem can be turned into a mixed integer-linear program that equals its linear relaxation, thus becoming polynomially solvable. Moreover, this version of RAP is shown to be related to cooperative assignment games. Numerical experiments confirm that artificial scarcity negatively affects matching productivity and social welfare. The integrator is favored to take most profits, and leveraging artificial scarcity strengthens its dominance. Moreover, the tighter the supply, the more the integrator benefit from artificial scarcity. The reserve price helps redistribute benefits from the integrator to the platforms. However, demanding an excessively large reserve price may depress the platforms’ profits, while undermining system efficiency.

中文翻译：

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跨平台网约车整合中的分配问题


我们考虑一个叫车系统，其中第三方集成商接收乘车请求并将其分配给乘车服务平台。乘车分配问题 (RAP) 被建模为 Stackelberg 博弈。作为领导者的集成商通过对游乐设施进行定价来选择最大化其利润的分配，使得没有平台（即追随者）能够找到更有利可图的分配。为了追求自身利益，集成商可能会拒绝匹配平台愿意提供的尽可能多的游乐设施，从而人为地向系统注入稀缺性。为了保护平台免遭过度剥削，引入了外生底价以限制其人均利润。我们将 RAP 表述为双层定价问题，并通过对较低层进行对偶将其转换为单层问题。当人为稀缺性被消除并且所有底价都设置为零时，我们证明单水平问题可以转化为等于其线性松弛的混合整数线性规划，从而变得多项式可解。此外，该版本的 RAP 被证明与合作分配游戏有关。数值实验证实，人为稀缺会对匹配的生产力和社会福利产生负面影响。整合者倾向于获取大部分利润，而利用人为的稀缺性加强了其主导地位。此外，供应越紧张，集成商从人为稀缺中受益就越大。底价有助于将利益从集成商重新分配给平台。然而，要求过高的底价可能会压低平台的利润，同时损害系统效率。