The Value of Excess Supply in Spatial Matching Markets

TL;DR

This paper analyzes how a slight excess of supply in spatial matching markets significantly reduces matching costs, showing that having just a bit more drivers than riders enables near-optimal, low-cost matching algorithms.

Contribution

It quantifies the benefit of excess supply in spatial matching, demonstrating that even a small surplus of drivers drastically improves matching efficiency and cost performance.

Findings

Greedy matching algorithm achieves $O( ext{log}^3(n))$ cost with slight excess supply.

Equal supply yields a minimum matching cost of $ heta( ext{sqrt}(n))$, even optimally.

Small excess supply dramatically reduces matching costs in spatial markets.

Abstract

We study dynamic matching in a spatial setting. Drivers are distributed at random on some interval. Riders arrive in some (possibly adversarial) order at randomly drawn points. The platform observes the location of the drivers, and can match newly arrived riders immediately, or can wait for more riders to arrive. Unmatched riders incur a waiting cost $c$ per period. The platform can match riders and drivers, irrevocably. The cost of matching a driver to a rider is equal to the distance between them. We quantify the value of slightly increasing supply. We prove that when there are $(1+\epsilon)$ drivers per rider (for any $\epsilon > 0$), the cost of matching returned by a simple greedy algorithm which pairs each arriving rider to the closest available driver is $O(\log^3(n))$, where $n$ is the number of riders. On the other hand, with equal number of drivers and riders, even the \emph{ex post} optimal matching does not have a cost less than $\Theta(\sqrt{n})$. Our results shed light on the important role of (small) excess supply in spatial matching markets.