Fairness Concepts for Indivisible Items with Externalities

TL;DR

This paper introduces new fairness concepts and algorithms for allocating indivisible items with externalities, extending existing fairness notions to account for external effects among agents.

Contribution

It proposes new fairness notions like GFS and extends EF1 and EFX to settings with externalities, along with algorithms for fair allocation.

Findings

Extended EF1 and EFX to externalities setting

Introduced the GFS fairness concept

Developed algorithms for fair allocations

Abstract

We study a fair allocation problem of indivisible items under additive externalities in which each agent also receives values from items that are assigned to other agents. We propose several new fairness concepts. We extend the well-studied envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) to this setting, and we propose a new fairness concept called general fair share (GFS). We undertake a detailed study and present algorithms for finding fair allocations.