Distance flexibility in spatial matching: the value of concentration

2026-09-28

AI Summary

This study addresses how platforms can optimize service radius allocation under budget constraints to maximize demand fulfillment in spatial matching markets. Leveraging stochastic geometry and majorization theory, the authors analyze the impact of uniform versus concentrated configurations on expected fulfillment rates in multidimensional spaces, employing asymptotic analysis to characterize optimal strategies. The work reveals that large budgets favor uniform allocation while small budgets favor concentrated allocation. Furthermore, it proposes an asymptotically optimal non-uniform allocation scheme for sparse scenarios and rigorously proves the suboptimality of uniform allocation in extremely sparse regimes. These theoretical findings provide a solid foundation for related numerical experiments.

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 $k \geq 2$, 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].

Problem

• spatial matching markets
• service radius allocation
• distance flexibility
• budget constraint
• demand fulfillment

Innovation

• spatial matching markets
• service radius allocation
• majorization
• asymptotic optimality
• sparse regime