Guaranteeing MMS for All but One Agent When Allocating Indivisible Chores

Fuente: arXiv
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Main Authors: Qiu, Jiawei, Wu, Xiaowei, Zhang, Cong, Zhou, Shengwei
Format: Preprint
Published: 2024
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author Qiu, Jiawei
Wu, Xiaowei
Zhang, Cong
Zhou, Shengwei
author_facet Qiu, Jiawei
Wu, Xiaowei
Zhang, Cong
Zhou, Shengwei
contents We study the problem of allocating $m$ indivisible chores to $n$ agents with additive cost functions under the fairness notion of maximin share (MMS). In this work, we propose a notion called $α$-approximate all-but-one maximin share ($α$-AMMS) which is a stronger version of $α$-approximate MMS. An allocation is called $α$-AMMS if $n-1$ agents are guaranteed their MMS values and the remaining agent is guaranteed $α$-approximation of her MMS value. We show that there exist $α$-AMMS allocations, with $α= 9/8$ for three agents; $α= 4/3$ for four agents; and $α= (n+1)^2/4n$ for $n\geq 5$ agents.
format Preprint
id arxiv_https___arxiv_org_abs_2410_12347
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Guaranteeing MMS for All but One Agent When Allocating Indivisible Chores
Qiu, Jiawei
Wu, Xiaowei
Zhang, Cong
Zhou, Shengwei
Computer Science and Game Theory
We study the problem of allocating $m$ indivisible chores to $n$ agents with additive cost functions under the fairness notion of maximin share (MMS). In this work, we propose a notion called $α$-approximate all-but-one maximin share ($α$-AMMS) which is a stronger version of $α$-approximate MMS. An allocation is called $α$-AMMS if $n-1$ agents are guaranteed their MMS values and the remaining agent is guaranteed $α$-approximation of her MMS value. We show that there exist $α$-AMMS allocations, with $α= 9/8$ for three agents; $α= 4/3$ for four agents; and $α= (n+1)^2/4n$ for $n\geq 5$ agents.
title Guaranteeing MMS for All but One Agent When Allocating Indivisible Chores
topic Computer Science and Game Theory
url https://arxiv.org/abs/2410.12347