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Computer Science > Computer Science and Game Theory

arXiv:2211.03883 (cs)
[Submitted on 7 Nov 2022 (v1), last revised 13 Aug 2024 (this version, v3)]

Title:Approximating Nash Social Welfare by Matching and Local Search

Authors:Jugal Garg, Edin Husić, Wenzheng Li, László A. Végh, Jan Vondrák
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Abstract:For any $\eps>0$, we give a simple, deterministic $(4+\eps)$-approximation algorithm for the Nash social welfare (NSW) problem under submodular valuations. We also consider the asymmetric variant of the problem, where the objective is to maximize the weighted geometric mean of agents' valuations, and give an $(\omega + 2 + \eps) \ee$-approximation if the ratio between the largest weight and the average weight is at most $\omega$.
We also show that the $\nfrac12$-EFX envy-freeness property can be attained simultaneously with a constant-factor approximation. More precisely, we can find an allocation in polynomial time that is both $\nfrac12$-EFX and a $(8+\eps)$-approximation to the symmetric NSW problem under submodular valuations.
Comments: 27 pages. Appeared in STOC 2023. This version improves the proofs and gives a new FPT result
Subjects: Computer Science and Game Theory (cs.GT); Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2211.03883 [cs.GT]
  (or arXiv:2211.03883v3 [cs.GT] for this version)
  https://doi.org/10.48550/arXiv.2211.03883

Submission history

From: Edin Husic [view email]
[v1] Mon, 7 Nov 2022 22:06:16 UTC (438 KB)
[v2] Wed, 29 Mar 2023 09:38:02 UTC (437 KB)
[v3] Tue, 13 Aug 2024 19:16:46 UTC (71 KB)
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