EF1 for Mixed Manna with Unequal Entitlements

TL;DR

This paper addresses fair division of indivisible mixed items among agents with unequal entitlements, proposing relaxations and algorithms to achieve approximate fairness efficiently.

Contribution

It introduces a relaxation of WEF1 called WEF1T and provides polynomial-time algorithms for achieving it, including a generalization of Fisher markets for mixed manna.

Findings

Polynomial-time algorithm for WEF1T

Generalized Fisher markets for mixed manna

Efficient fair division with unequal entitlements

Abstract

We study fair division of indivisible mixed manna when agents have unequal entitlements, with weighted envy-freeness up to one item (WEF1) as our primary notion of fairness. We identify several shortcomings of existing techniques to achieve WEF1. Hence, we relax WEF1 to weighted envy-freeness up to 1 transfer (WEF1T), and give a polynomial-time algorithm for achieving it. We also generalize Fisher markets to the mixed manna setting, and use them to get a polynomial-time algorithm for two agents that outputs a WEF1 allocation.