空间匹配中的距离灵活性：集中度的价值

中文摘要 AI 辅助

在空间匹配市场中，供给单元的灵活性通过其服务半径来衡量，即其能够服务需求的最大距离。在维度 $k \geq 2$ 中，我们研究平台应如何在供给节点之间分配服务半径，并受限于其总和的预算。平台在观察供给和需求位置之前做出此选择，目标是最大化预期满足的需求。我们表明，优选分配的形状取决于总预算：在适当条件下，大预算倾向于在优超（majorization）意义上更均匀的分配，而小预算则倾向于集中。我们还刻画了一种在极稀疏情况下渐近最优的非均匀分配，并表明均匀分配在该情况下是次优的。我们的结果为 [ASY26b] 中数值实验提出的半径分配问题提供了理论解释。

英文摘要

In spatial matching markets, a supply unit's flexibility is measured by its service radius, the maximum distance at which it can serve demand. In dimensions $k \geq 2$, we study how a platform should allocate service radii among the supply nodes subject to a budget on their sum. The platform makes this choice before observing supply and demand locations, with the objective of maximizing the expected fulfilled demand. We show that the shape of a preferred allocation depends on the total budget: under suitable conditions, large budgets favor allocations that are more uniform in the sense of majorization, while small budgets favor concentration. We also characterize a non-uniform allocation that is asymptotically optimal for a very-sparse regime, and show that the uniform allocation is suboptimal in this regime. Our results provide theoretical explanations for the radius allocation questions raised by the numerical experiments in [ASY26b].

发表机构

• Carnegie Mellon University（卡内基梅隆大学）
• University of Pennsylvania（宾夕法尼亚大学）

机构由 AI 辅助整理，请以论文原文为准。