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arXiv · 2209.06330

An Improved Lower Bound for Maximin Share Allocations of Goods

Kevin Hsu
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Abstract

The problem of fair division of indivisible goods has been receiving much attention recently. The prominent metric of envy-freeness can always be satisfied in the divisible goods setting (see for example \cite{BT95}), but often cannot be satisfied in the indivisible goods setting. This has led to many relaxations thereof being introduced. We study the existence of {\em maximin share (MMS)} allocations, which is one such relaxation. Previous work has shown that MMS allocations are guaranteed to exist for all instances with $n$ players and $m$ goods if $m \leq n+4$. We extend this guarantee to the case of $m = n+5$ and show that the same guarantee fails for $m = n+6$.

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Kevin Hsu. 2022-09-13. An Improved Lower Bound for Maximin Share Allocations of Goods. https://arxiv.org/abs/2209.06330

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