On Matching and Thickness in Heterogeneous Dynamic Markets

78 Pages Posted: 16 Nov 2017 Last revised: 12 May 2018

See all articles by Itai Ashlagi

Itai Ashlagi

Stanford University - Management Science & Engineering

Maximilien Burq

Massachusetts Institute of Technology (MIT) - Operations Research Center

Patrick Jaillet

Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science

Vahideh Manshadi

Yale School of Management

Date Written: May 7, 2018

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 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.

Further, somewhat surprisingly, we find that in a heterogeneous market and under bilateral matching, increasing the arrival rate of hard-to-match agents has a non-monotone effect on waiting times. This behavior is in contrast with that of a homogeneous dynamic market, where increasing arrival rate always improves waiting time, and it highlights fundamental differences between heterogeneous and homogeneous dynamic markets.

Keywords: Matching Markets, Stochastic Networks, Kidney Exchange

JEL Classification: C78, C44, C61

Suggested Citation

Ashlagi, Itai and Burq, Maximilien and Jaillet, Patrick and Manshadi, Vahideh, On Matching and Thickness in Heterogeneous Dynamic Markets (May 7, 2018). Available at SSRN: https://ssrn.com/abstract=3067596 or http://dx.doi.org/10.2139/ssrn.3067596

Itai Ashlagi

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Maximilien Burq

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

Patrick Jaillet

Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science ( email )

77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States

Vahideh Manshadi (Contact Author)

Yale School of Management ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

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