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

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

Transportation and Mobility Innovations被引用 4

一句话总结

本文引入了顺序个体理性（SIR）与顺序公平性（SF），以确保在拼车等共享服务系统中实现动态公平，其中新乘客的加入不会导致现有乘客的不满程度上升。研究证明，SIR可行路线等价于哈密顿路径，而SF要求乘客之间对绕路造成的不便进行补偿，从而导致具有次线性绕路边界约束的NP难优化问题。

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 "inconvenience 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

• 解决由于新乘客到达导致个体效用波动的共享服务中的动态公平性问题。
• 形式化顺序个体理性（SIR），确保现有客户在新乘客到达后其不满程度不会上升。
• 定义顺序公平性（SF），即新客户带来的收益按其造成不便的程度成比例分配。
• 将这些概念应用于拼车服务，将绕路建模为不便成本。
• 从算法角度刻画满足SIR可行性和SF合规性的路线及成本分摊方案集合。

提出的方法

• 提出一种效用损失模型，结合货币成本与共享使用带来的不便成本。
• 将顺序个体理性（SIR）定义为约束条件，要求在每次新乘客到达后，效用损失非递增。
• 提出顺序公平性（SF）作为收益分摊机制，其分摊比例与新乘客带来的增量不便程度成正比。
• 将SIR可行性问题简化为图中寻找哈密顿路径的问题，从而确立其NP难性。
• 通过从度量路径TSP（Metric-Path-TSP）到Opt-SIR-Route的度量化约化，证明最优SIR合规路线选择的NP难性。
• 使用整数流分解来建模网络约化中的路径不相交路由，将其与最小费用流问题关联。

实验结果

研究问题

• RQ1 在拼车系统中，何种条件可确保现有乘客因新乘客到达而不会出现不满程度上升？
• RQ2 如何在服务持续期间动态地而非仅在服务结束时实现公平性？
• RQ3 满足顺序个体理性（SIR）的路线具有何种结构与算法特性？
• RQ4 能否形式化顺序公平性，使得新乘客带来的收益按其造成的不便程度成比例分配？
• RQ5 在拼车系统中，寻找最优SIR合规与SF合规路线的计算复杂度如何？

主要发现

• 拼车系统中SIR可行路线与底层图中的哈密顿路径一一对应，建立了精确对应关系。
• 任何SIR可行路线的分数绕路长度被限制在次线性上下界之间，具体为第j段路程的O(1/j)。
• 顺序公平性要求乘客之间对绕路造成的不便进行相互补偿，导致成本分摊方案之间存在强依赖关系。
• 寻找最优SIR合规路线的问题是NP难的，因为其可约化为度量路径TSP问题。
• 在Opt-SIR-Route的构造实例中，所有n!条可能的路线在适当的距离与成本设置下均可为SIR可行，凸显其结构灵活性。
• 从哈密顿路径到SIR可行性的约化证实，判断SIR可行性问题是NP完全的。