Distance flexibility in spatial matching: the value of concentration
Abstract
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 ≥ 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].
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BibTeX
@misc{ameen2026distance,
title = {{Distance flexibility in spatial matching: the value of concentration}},
author = {Taha Ameen and Sophie H. Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36361},
eprint = {2609.36361},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36361},
}
RIS
TY - UNPB
TI - Distance flexibility in spatial matching: the value of concentration
AU - Taha Ameen
AU - Sophie H. Yu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36361
UR - https://arxiv.org/abs/2609.36361
AB - 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 ≥ 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].
ER -