Matching in Dynamic Imbalanced Markets

65 Pages Posted: 25 Sep 2018 Last revised: 25 May 2019

See all articles by Itai Ashlagi

Itai Ashlagi

Stanford University - Management Science & Engineering

Afshin Nikzad

University of Southern California, Department of Economics

Philipp Strack

Yale, Department of Economics

Date Written: March 10, 2019

Abstract

We study matching policies in a dynamic exchange market with random compatibility, in which some agents are easier to match than others. In steady state this asymmetry creates an endogenous imbalance: hard-to-match agents wait for partners, while easy-to-match agents can match almost immediately upon arrival and leave the market quickly.

A greedy policy, which attempts to match agents upon arrival, does not account for the positive externality waiting agents generate as they make it easier to match agents that arrive in the future, and may result in more unmatched than other policies. While this trade-off between a "thicker market" and quick matching is present in small markets we show that it vanishes in large markets and the greedy policy nevertheless dominates any other dynamic matching policy. As arrival rate increases the greedy policy matches a (weakly) higher fraction of agents than any other policy and leads to (weakly) lower average waiting time than any other policy. We show that in a large market greedy matching strictly outperforms batching policies (e.g., weekly matching) and a patient policy, which attempts to match agents only as they are about to depart the market.

We test our large market predictions with kidney exchange data from the National Kidney Registry (NKR). Numerical simulations show that, in line with our predictions, the greedy policy matches patient-donor pairs significantly faster (roughly 20-30 days) than other commonly used policies and at most 1% percent fewer pairs than the patient policy.

Keywords: Kidney Exchange, Dynamic Matching

JEL Classification: C78, D47

Suggested Citation

Ashlagi, Itai and Nikzad, Afshin and Strack, Philipp, Matching in Dynamic Imbalanced Markets (March 10, 2019). Available at SSRN: https://ssrn.com/abstract=3251632 or http://dx.doi.org/10.2139/ssrn.3251632

Itai Ashlagi

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Afshin Nikzad (Contact Author)

University of Southern California, Department of Economics ( email )

Los Angeles, CA 90066
United States

HOME PAGE: http://afshin-nikzad.com

Philipp Strack

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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