Efficient and Envy Minimal Matching

42 Pages Posted: 6 Aug 2020 Last revised: 4 Jan 2021

See all articles by Atila Abdulkadiroglu

Atila Abdulkadiroglu

Duke University - Department of Economics

Aram Grigoryan

University of California, San Diego

Date Written: June 1, 2020

Abstract

In priority-based matching problems, there is a trade-off between efficiency and
reducing justified-envy. We show that finding an efficient and justified-envy minimal
matching is an NP-hard problem when objects have weak priority rankings. Consequently, we focus on resolving the trade-off in a subclass of efficient mechanisms.
First, we consider the class of efficient and strategyproof mechanisms and show that
no group-strategyproof mechanism minimizes justified-envy in that class. Then, we
restrict attention to the class of hierarchical exchanges and sequential dictatorship
mechanisms, which are widely studied in the literature and applied in real-life resource
allocation problems. We propose justified-envy minimal mechanisms for each of those
classes.

Keywords: priority-based matching, justified-envy minimality, computational complexity, hierarchical exchanges, sequential dictatorship

JEL Classification: C70, D47, D60

Suggested Citation

Abdulkadiroglu, Atila and Grigoryan, Aram, Efficient and Envy Minimal Matching (June 1, 2020). Available at SSRN: https://ssrn.com/abstract=3646475 or http://dx.doi.org/10.2139/ssrn.3646475

Atila Abdulkadiroglu

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

Aram Grigoryan (Contact Author)

University of California, San Diego ( email )

La Jolla, CA
United States
9177562686 (Phone)

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
108
Abstract Views
845
Rank
453,810
PlumX Metrics