Dynamic Matching: Characterizing and Achieving Constant Regret

54 Pages Posted: 12 Apr 2021 Last revised: 14 Sep 2022

See all articles by Süleyman Kerimov

Süleyman Kerimov

Jesse H. Jones Graduate School of Business, Rice University

Itai Ashlagi

Stanford University - Department of Management Science & Engineering

Itai Gurvich

Northwestern University

Date Written: April 10, 2021

Abstract

We study how to optimally match agents in a dynamic matching market with heterogeneous match cardinalities and values. A network topology determines the feasible matches in the market. In general, a fundamental trade-off exists between short-term value---which calls for performing matches frequently---and long-term value---which calls, sometimes, for delaying match decisions in order to perform better matches.

We find that in networks that satisfy a general position condition, the tension between short- and long-term value is limited, and a simple periodic clearing policy (nearly) maximizes the total match value simultaneously at all times. Central to our results is the general position gap ε; a proxy for capacity slack in the market. With the exception of trivial cases, no policy can achieve an all-time regret that is smaller, in terms of order, than 1/ε. We achieve this lower bound with a policy, which periodically resolves a natural matching integer linear program, provided that the delay between resolving periods is of the order of 1/ε. Examples illustrate the necessity of some delay to alleviate the tension between short- and long-term value.

Keywords: dynamic matching, queueing, optimal control

JEL Classification: C44, C61, C78

Suggested Citation

Kerimov, Süleyman and Ashlagi, Itai and Gurvich, Itai, Dynamic Matching: Characterizing and Achieving Constant Regret (April 10, 2021). Available at SSRN: https://ssrn.com/abstract=3824407 or http://dx.doi.org/10.2139/ssrn.3824407

Süleyman Kerimov (Contact Author)

Jesse H. Jones Graduate School of Business, Rice University ( email )

6100 South Main Street
P.O. Box 1892
Houston, TX 77005-1892
United States

Itai Ashlagi

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Itai Gurvich

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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