On Matching and Thickness in Heterogeneous Dynamic Markets

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 nonmonotone 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.

Matching in Dynamic Imbalanced Markets

“…27 We also examined weighted optimization using various weights and found no any qualitative differences. This is consistent with Ashlagi et al (2019), which found that prioritization is negligible when there are more hard-to-match We also compute the average matching time and waiting time for different types of pairs. match only with over-demanded pairs.…”

“…waiting time, as the compatibility probability tends to zero. 11 Ashlagi et al (2016) add asymmetric types to this random compatibility model where one type has a non-vanishing probability of being matched with any other agent. In particular, in contrast to our model, any two types can potentially match.…”

Quick or Cheap? Breaking Points in Dynamic Markets

“…We identified a unique breaking point where a stark reduction in matching cost compared to a stark increase in waiting cost occurs. In line with recent works by Ashlagi et al (2017), Ashlagi et al (2018) and many others, we focused on a concrete class of social welfare functions that weigh costs from waiting versus matching on a comparable scale and identify the optimal clearing schedule, namely, the clearing schedule that matches the k-th couple when Θ( √ k(log k) 1/3 ) players are on the short side of the market.…”

“…Emek et al (2019) obtain sharper results for a two-location model. There are also other extensions such as allowing for a stochastic graph (Anderson et al, 2015;Ashlagi et al, 2018).…”

Dynamically Stable Matching

“…Related literature The paper contributes mainly to three strands of the literature. The first strand is the literature on market design, which studies dynamic matching markets such as those in this paper, but from the point of view of optimality instead of stability (Ünver (2010), Leshno (2017), Akbarpour et al (2017), Anderson et al (2015), Schummer (2015), Bloch and Cantala (2017), Ashlagi et al (2018), Arnosti and Shi (2018), Baccara et al (2019), Thakral (2019)). The present study of stability is important because stability is considered a key property for the success of algorithms (Roth (1991)) and because it highlights the potential issues in applying the static notions of stability to dynamic matching markets.…”