Dynamic Spatial Matching

TL;DR

This paper studies dynamic spatial matching in online platforms, showing that with effective algorithms, the expected matching cost can nearly match the ideal case with known future arrivals, across various dimensions and scenarios.

Contribution

The paper characterizes the scaling behavior of matching costs in dynamic spatial settings and provides concrete algorithms that achieve near-optimal costs.

Findings

Matching cost scales with system size and dimension.

Algorithms achieve near-ideal costs comparable to known future locations.

Cost reduction is significant when only demand is dynamic in one dimension.

Abstract

Motivated by a variety of online matching platforms, we consider demand and supply units which are located i.i.d. in [0,1]^d, and each demand unit needs to be matched with a supply unit. The goal is to minimize the expected average distance between matched pairs (the "cost"). We model dynamic arrivals of one or both of demand and supply with uncertain locations of future arrivals, and characterize the scaling behavior of the achievable cost in terms of system size (number of supply units), as a function of the dimension d. Our achievability results are backed by concrete matching algorithms. Across cases, we find that the platform can achieve cost (nearly) as low as that achievable if the locations of future arrivals had been known beforehand. Furthermore, in all cases except one, cost nearly as low in terms of scaling as the expected distance to the nearest neighboring supply unit is achievable, i.e., the matching constraint does not cause an increase in cost either. The aberrant case is where only demand arrivals are dynamic, and d=1; excess supply significantly reduces cost in this case.