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NP-Hardness of Approximating Nash Social Welfare with Supermodular Valuations

Computer Science and Game Theory 2025-10-31 v1
Authors: Alon Bebchuk
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Abstract

We study the problem of allocating a set of indivisible items to agents with supermodular utilities to maximize the Nash social welfare. We show that the problem is NP-hard for any approximation factor.

Keywords

Nash social welfare supermodular valuations NP-hardness approximation indivisible items

Cite

@article{arxiv.2510.26055,
  title  = {NP-Hardness of Approximating Nash Social Welfare with Supermodular Valuations},
  author = {Alon Bebchuk},
  journal= {arXiv preprint arXiv:2510.26055},
  year   = {2025}
}

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