Superiority of Instantaneous Decisions in Thin Dynamic Matching Markets

TL;DR

This paper demonstrates that in thin dynamic matching markets, simple instantaneous matching policies with a fixed sojourn time can nearly maximize matches and minimize waiting times, challenging the belief that market thickness is essential.

Contribution

It introduces the idea that agent sojourn behavior can be as effective as market thickness for optimal matching performance, with new proof techniques for Markov processes.

Findings

Instantaneous matching with fixed sojourn time is nearly optimal.

Agent sojourn behavior can substitute market thickness.

The policy minimizes waiting time effectively.

Abstract

We study a dynamic matching setting where homogeneous agents arrive at random according to a Poisson process and randomly form edges yielding a sparse market. Agents stay in the market according to a certain sojourn time and wait to be matched with a compatible agent by a matching algorithm. When their maximum sojourn time is reached, they perish unmatched. The primary objective is to maximize the number of matched agents. Our main result is to show that a uniformly guaranteed sojourn time suffices to get almost optimal performance of instantaneous matching. Interestingly, this matching policy essentially keeps as few agents in the market as possible. Hence, in contrast to the common paradigm that market thickness is the crucial property for obtaining strong matching performance, we show that the agents' sojourn behavior can be an equally powerful factor. In addition, instantaneous matching is close to optimal with respect to minimizing waiting time. We develop new techniques for proving our results going beyond commonly adopted methods for Markov processes.