Fair Division of Indivisible Goods: A Survey

TL;DR

This survey reviews recent advances in fair division of indivisible goods, highlighting key results, computational challenges, and progress made in the last decade on fairness notions like MMS and EFX.

Contribution

It provides a comprehensive overview of the latest research developments in discrete fair division, emphasizing computational aspects and recent breakthroughs.

Findings

Significant progress in algorithms for MMS and EFX fairness

New hardness results for fair division problems

Improved approximation algorithms for indivisible goods

Abstract

Allocating resources to individuals in a fair manner has been a topic of interest since the ancient times, with most of the early rigorous mathematical work on the problem focusing on infinitely divisible resources. Recently, there has been a surge of papers studying computational questions regarding various different notions of fairness for the indivisible case, like maximin share fairness (MMS) and envy-freeness up to any good (EFX). We survey the most important results in the discrete fair division literature, focusing on the case of additive valuation functions and paying particular attention to the progress made in the last 10 years.