[论文解读] The Costs and Benefits of Ridesharing: Sequential Individual Rationality and Sequential Fairness.

Ragavendran Gopalakrishnan, Koyel Mukherjee+1 more|arXiv (Cornell University)|Jul 25, 2016

Transportation and Mobility Innovations参考文献 28被引用 13

一句话总结

本文引入了顺序个体理性（SIR）和顺序公平性（SF），以确保拼车系统在稳定与公平，其中现有乘客不会因新乘客的加入而处境变差。它通过次线性绕行距离上限刻画了SIR可行路线，并提出了公平补偿乘客因绕行而产生的不便的成本分摊方案，揭示了动态拼车中结构性限制与算法挑战。

ABSTRACT

In designing dynamic shared service systems that incentivize customers to opt for shared rather than exclusive service, the traditional notion of individual rationality may be insufficient, as a customer's estimated utility could fluctuate arbitrarily during their time in the shared system, as long as their realized utility at service completion is not worse than that for exclusive service. In this work, within a model that explicitly considers the costs incurred by customers due to sharing, we introduce the notion of sequential individual rationality (SIR) that requires that the disutility of existing customers is nonincreasing as the system state changes due to new customer arrivals. Next, under SIR, we observe that cost sharing can also be viewed as benefit sharing, which inspires a natural definition of sequential fairness (SF) - the total incremental benefit due to a new customer is shared among existing customers in proportion to the incremental inconvenience suffered. We demonstrate the effectiveness of these notions by applying them to a ridesharing system, where unexpected detours to pick up subsequent passengers inconvenience the existing passengers. Imposing SIR and SF reveals interesting and surprising results, including: (a) natural limits on the incremental detours permissible, (b) exact characterization of SIR-feasible routes, which boast sublinear upper and lower bounds on the fractional detours, (c) exact characterization of sequentially fair cost sharing schemes, which includes a strong requirement that passengers must compensate each other for the detour inconveniences that they cause, and (d) new algorithmic problems related to and motivated by SIR.

研究动机与目标

• 为解决传统个体理性在动态拼车中因服务过程中客户效用不可预测波动而导致的不稳定性问题。
• 定义更强的公平性准则——顺序个体理性（SIR），确保新乘客加入时，现有乘客的不悦感不会增加。
• 将成本分摊视为收益共享，从而提出一种新的公平性概念：顺序公平性（SF），即新乘客带来的收益按其对现有乘客造成的额外不便程度成比例分配。
• 刻画具有绕行导致不悦感的拼车系统中SIR可行路线与SF合规成本分摊机制的特性。
• 揭示在实时共享出行系统中强制实施SIR时产生的结构性约束与算法挑战。

提出的方法

• 提出顺序个体理性（SIR）作为动态激励条件，要求在每次新客户加入时，现有乘客的不悦感非递增。
• 将绕行视为不悦感的来源，并推导出保持SIR的分数绕行距离的边界，建立允许绕行的次线上限与下限。
• 通过按新乘客带来的增量收益与其对现有乘客造成的增量不便成比例分配，引入顺序公平性（SF）。
• 通过路线几何与绕行比率的数学约束，精确刻画SIR可行路线。
• 设计乘客之间相互补偿绕行导致不便的成本分摊机制，确保SF合规。
• 识别出在SIR约束下，特别是实时动态系统中，路线选择与成本分配方面出现的新算法问题。

实验结果

研究问题

• RQ1 在拼车系统中，为保持顺序个体理性（SIR），绕行长度的结构性限制是什么？
• RQ2 如何设计成本分摊机制，以同时反映新乘客带来的收益与造成的不便，从而确保顺序公平性（SF）？
• RQ3 路线满足SIR可行性的必要与充分条件是什么？这些条件如何约束路线设计？
• RQ4 乘客之间相互补偿的要求如何影响成本分摊方案的可行性与结构？
• RQ5 在动态实时拼车环境中强制实施SIR时，会涌现出哪些新的算法挑战？

主要发现

• SIR对增量绕行施加了自然限制，分数绕行距离受总行程长度的次线性函数约束。
• SIR可行路线被精确刻画为确保现有乘客不悦感在新乘客加入时不增加的约束条件。
• 顺序公平性（SF）要求乘客相互补偿因绕行导致的不便，从而在成本分摊中形成强有力的公平性条件。
• 本文识别出一类同时满足SIR与SF的成本分摊方案，其显式公式基于增量不便与增量收益。
• 分析表明，SIR对共享出行系统中的路线规划与动态分配施加了非平凡的算法约束。
• 结果表明，若不显式建立绕行导致不悦感的补偿机制，拼车系统中的公平与稳定无法实现。