TY - GEN
T1 - On Optimal Tradeoffs between EFX and Nash Welfare
AU - Feldman, Michal
AU - Mauras, Simon
AU - Ponitka, Tomasz
N1 - Publisher Copyright: Copyright © 2024, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
PY - 2024/3/25
Y1 - 2024/3/25
N2 - A major problem in fair division is how to allocate a set of indivisible resources among agents fairly and efficiently. The goal of this work is to characterize the tradeoffs between two well-studied measures of fairness and efficiency - envy freeness up to any item (EFX) for fairness, and Nash welfare for efficiency - by saying, for given constants α and β, whether there exists an α-EFX allocation that guarantees a β-fraction of the maximum Nash welfare (β-MNW). For additive valuations, we show that for any α ∈ [0, 1], there exists a partial allocation that is α-EFX and α+11 -MNW. This tradeoff turns out to be tight (for every α) as demonstrated by an impossibility result that we give. We also show that for α ∈ [0, φ−1 ≈ 0.618] these partial allocations can be turned into complete allocations where all items are assigned. Furthermore, for any α ∈ [0, 1/2], we show that the tight tradeoff of α-EFX and α+11 -MNW with complete allocations holds for the more general setting of subadditive valuations. Our results improve upon the current state of the art, for both additive and subadditive valuations, and match the best-known approximations of EFX under complete allocations, regardless of Nash welfare guarantees. Notably, our constructions for additive valuations also provide EF1 and constant approximations for maximin share guarantees.
AB - A major problem in fair division is how to allocate a set of indivisible resources among agents fairly and efficiently. The goal of this work is to characterize the tradeoffs between two well-studied measures of fairness and efficiency - envy freeness up to any item (EFX) for fairness, and Nash welfare for efficiency - by saying, for given constants α and β, whether there exists an α-EFX allocation that guarantees a β-fraction of the maximum Nash welfare (β-MNW). For additive valuations, we show that for any α ∈ [0, 1], there exists a partial allocation that is α-EFX and α+11 -MNW. This tradeoff turns out to be tight (for every α) as demonstrated by an impossibility result that we give. We also show that for α ∈ [0, φ−1 ≈ 0.618] these partial allocations can be turned into complete allocations where all items are assigned. Furthermore, for any α ∈ [0, 1/2], we show that the tight tradeoff of α-EFX and α+11 -MNW with complete allocations holds for the more general setting of subadditive valuations. Our results improve upon the current state of the art, for both additive and subadditive valuations, and match the best-known approximations of EFX under complete allocations, regardless of Nash welfare guarantees. Notably, our constructions for additive valuations also provide EF1 and constant approximations for maximin share guarantees.
UR - http://www.scopus.com/inward/record.url?scp=85189335277&partnerID=8YFLogxK
U2 - https://doi.org/10.1609/aaai.v38i9.28826
DO - https://doi.org/10.1609/aaai.v38i9.28826
M3 - منشور من مؤتمر
T3 - Proceedings of the AAAI Conference on Artificial Intelligence
SP - 9688
EP - 9695
BT - Technical Tracks 14
A2 - Wooldridge, Michael
A2 - Dy, Jennifer
A2 - Natarajan, Sriraam
T2 - 38th AAAI Conference on Artificial Intelligence, AAAI 2024
Y2 - 20 February 2024 through 27 February 2024
ER -