Efficient and Envy Minimal Matching
42 Pages Posted: 6 Aug 2020 Last revised: 4 Jan 2021
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: Suggested Citation