Fair Division with Two-Sided Preferences
Ayumi Igarashi, Yasushi Kawase, Warut Suksompong, Hanna Sumita
TL;DR
The paper studies fair division with two-sided preferences, where teams possess additive valuations over participants and participants have preferences over teams. It proves that one can efficiently compute allocations that are $EF1$ for teams together with swap stability and individual stability even when team valuations are mixed in sign, and it establishes $EF1$ plus PO existence for nonnegative participants, with efficient results in binary valuations and special multi-team cases. It also reveals hardness barriers by showing coNP-hardness for PO decision under certain constraints and NP-hardness for justified envy-freeness existence, while providing polynomial-time algorithms in two-team scenarios via generalized adjusted winner and related constructions. The findings advance practical fair division models for sports teams, supervisor-student allocations, and other two-sided matching applications, offering both algorithmic procedures and complexity boundaries. The work suggests future exploration of MMS approximations, variable entitlements, and broader stability notions within two-sided fair division.
Abstract
We study a fair division setting in which participants are to be fairly distributed among teams, where not only do the teams have preferences over the participants as in the canonical fair division setting, but the participants also have preferences over the teams. We focus on guaranteeing envy-freeness up to one participant (EF1) for the teams together with a stability condition for both sides. We show that an allocation satisfying EF1, swap stability, and individual stability always exists and can be computed in polynomial time, even when teams may have positive or negative values for participants. When teams have nonnegative values for participants, we prove that an EF1 and Pareto optimal allocation exists and, if the valuations are binary, can be found in polynomial time. We also show that an EF1 and justified envy-free allocation does not necessarily exist, and deciding whether such an allocation exists is computationally difficult.