Two-Sided Matching Meets Fair Division

TL;DR

This paper introduces a novel two-sided matching model incorporating fairness notions from fair division, such as envy-freeness and maximin share guarantees, and analyzes their achievability under various conditions.

Contribution

It proposes new fairness concepts for two-sided matchings, explores their theoretical limitations, and identifies cases where these fairness notions can be achieved.

Findings

DEF1 cannot always be achieved.

Round-robin algorithm achieves DEF1 when preferences are identical.

DMMS cannot be achieved even with identical preferences.

Abstract

We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.