On Matching and Thickness in Heterogeneous Dynamic Markets

TL;DR

This paper analyzes dynamic matching in markets with heterogeneous agents, examining how market composition and matching technology affect agents' waiting times and efficiency, with implications for real-world applications like kidney exchanges.

Contribution

It provides a novel asymptotic analysis of waiting times in heterogeneous dynamic markets, highlighting the impact of market composition and matching technology on efficiency and policy implications.

Findings

Bilateral matching is nearly as efficient as chain matching when hard-to-match agents are less frequent.

Prioritizing hard-to-match agents reduces their waiting times in certain market conditions.

Increasing arrival rates can non-monotonically affect waiting times due to market competition effects.

Abstract

We study dynamic matching in an infinite-horizon stochastic market. While all agents are potentially compatible with each other, some are hard-to-match and others are easy-to-match. Agents prefer to be matched as soon as possible and matches are formed either bilaterally or indirectly through chains. We adopt an asymptotic approach and compute tight bounds on the limit of waiting time of agents under myopic policies that differ in matching technology and prioritization. We find that the market composition is a key factor in the desired matching technology and prioritization level. When hard-to-match agents arrive less frequently than easy-to-match ones (i) bilateral matching is almost as efficient as chains (waiting times scale similarly under both, though chains always outperform bilateral matching by a constant factor), and (ii) assigning priorities to hard-to-match agents improves their waiting times. When hard-to-match agents arrive more frequently, chains are much more efficient than bilateral matching and prioritization has no impact. We further conduct comparative statics on arrival rates. Somewhat surprisingly, we find that in a heterogeneous market and under bilateral matching, increasing arrival rate has a non-monotone effect on waiting times, due to the fact that, under some market compositions, there is an adverse effect of competition. Our comparative statics shed light on the impact of merging markets and attracting altruistic agents (that initiate chains) or easy-to-match agents. This work uncovers fundamental differences between heterogeneous and homogeneous dynamic markets, and potentially helps policy makers to generate insights on the operations of matching markets such as kidney exchange programs.