Maximin-Aware Allocations of Indivisible Chores with Symmetric and Asymmetric Agents

TL;DR

This paper extends the concept of maximin-awareness fairness to the allocation of indivisible chores among weighted agents, exploring existence, computation, and relaxations of such fair allocations.

Contribution

It adapts and generalizes maximin-awareness to chores and weighted agents, providing new results on existence, computation, and relaxations.

Findings

Existence results for MMA allocations with chores and weights

Algorithms for computing MMA and relaxed allocations

Connections between MMA and existing fairness concepts

Abstract

The real-world deployment of fair allocation algorithms usually involves a heterogeneous population of users, which makes it challenging for the users to get complete knowledge of the allocation except for their own bundles. Chan et al. [IJCAI 2019] proposed a new fairness notion, maximin-awareness (MMA), which guarantees that every agent is not the worst-off one, no matter how the items that are not allocated to her are distributed. We adapt and generalize this notion to the case of indivisible chores and when the agents may have arbitrary weights. Due to the inherent difficulty of MMA, we also consider its up to one and up to any relaxations. A string of results on the existence and computation of MMA related fair allocations, and their connections to existing fairness concepts is given.