English

An Improved Lower Bound for Maximin Share Allocations of Goods

Computer Science and Game Theory 2022-10-26 v2

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 nn players and mm goods if mn+4m \leq n+4. We extend this guarantee to the case of m=n+5m = n+5 and show that the same guarantee fails for m=n+6m = n+6.

Keywords

Cite

@article{arxiv.2209.06330,
  title  = {An Improved Lower Bound for Maximin Share Allocations of Goods},
  author = {Kevin Hsu},
  journal= {arXiv preprint arXiv:2209.06330},
  year   = {2022}
}

Comments

It has come to the attention of the author that the same result has already been published. Please refer to Feige, Uriel, Ariel Sapir, and Laliv Tauber. "A tight negative example for MMS fair allocations." International Conference on Web and Internet Economics. Springer, Cham, 2021