Stable and extremely unequal

TL;DR

This paper explores the inherent conflict between stability and equality in many-to-one matching markets, revealing that stable outcomes tend to be highly unequal, especially when schools' utilities are aligned with students' utilities.

Contribution

It demonstrates that the unique stable matching in such markets inherently results in extreme inequality among matched pairs.

Findings

Stable matchings exhibit extreme inequality.

Aligned preferences lead to unequal utility distributions.

Unique stable allocation favors certain pairs over others.

Abstract

We highlight the tension between stability and equality in non transferable utility matching. We consider many to one matchings and refer to the two sides of the market as students and schools. The latter have aligned preferences, which in this context means that a school's utility is the sum of its students' utilities. We show that the unique stable allocation displays extreme inequality between matched pairs.