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arXiv · 2106.14816

Nash Social Welfare for 2-value Instances

Hannaneh Akrami·Bhaskar Ray Chaudhury·Kurt Mehlhorn·Golnoosh Shahkarami·Quentin Vermande
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Abstract

This paper is merged with arXiv:2107.08965v2. We refer the reader to the full and updated version. We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an allocation with maximum Nash social welfare, i.e., the geometric mean of the valuations of the agents. We give a polynomial-time algorithm to find a Nash social welfare maximizing allocation when the valuation functions are integrally 2-valued, i.e., each agent has a value either $1$ or $p$ for each good, for some positive integer $p$. We then extend our algorithm to find a better approximation factor for general 2-value instances.

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Hannaneh Akrami, Bhaskar Ray Chaudhury, Kurt Mehlhorn, Golnoosh Shahkarami, Quentin Vermande. 2021-06-28. Nash Social Welfare for 2-value Instances. https://arxiv.org/abs/2106.14816

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