# Fair Division of Indivisible Goods: Recent Progress and Open Questions

arXiv: https://arxiv.org/abs/2208.08782 · HTML: https://mlsanity.com/paper/2208.08782/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2022.

## Built on by (most cited first, 21 of 21)

- [Virtual Agent Economies](https://mlsanity.com/paper/2509.10147/) (2025)
- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Online Fair Division with Additional Information](https://mlsanity.com/paper/2505.24503/) (2025)
- [Pushing the Frontier on Approximate EFX Allocations](https://mlsanity.com/paper/2406.12413/) (2024)
- [Online Fair Division for Personalized 2-Value Instances](https://mlsanity.com/paper/2505.22174/) (2025)
- [Fairness Aware Reinforcement Learning via Proximal Policy Optimization](https://mlsanity.com/paper/2502.03953/) (2025)
- [Fair Allocation in Dynamic Mechanism Design](https://mlsanity.com/paper/2406.00147/) (2024)
- [On the existence of EFX allocations in multigraphs](https://mlsanity.com/paper/2502.09777/) (2025)
- [Simultaneously Fair Allocation of Indivisible Items Across Multiple Dimensions](https://mlsanity.com/paper/2506.21727/) (2025)
- [The Cost of EFX: Generalized-Mean Welfare and Complexity Dichotomies with Few Surplus Items](https://mlsanity.com/paper/2601.12849/) (2026)
- [Constrained Serial Dictatorships can be Fair](https://mlsanity.com/paper/2301.06086/) (2023)
- [Using Protected Attributes to Consider Fairness in Multi-Agent Systems](https://mlsanity.com/paper/2410.12889/) (2024)
- [Learning Fair and Preferable Allocations through Neural Network](https://mlsanity.com/paper/2410.17500/) (2024)
- [Probing EFX via PMMS: (Non-)Existence Results in Discrete Fair Division](https://mlsanity.com/paper/2507.14957/) (2025)
- [Envy-Free Allocation of Indivisible Goods via Noisy Queries](https://mlsanity.com/paper/2602.06361/) (2026)
- [Divide-and-Denoise: A Game-Theoretic Method for Fairly Composing Diffusion Models](https://mlsanity.com/paper/2606.14756/) (2026)
- [Fair Division with Strictly Increasing Valuations: A Tight Threshold for Two-Agent EF1 and PO](https://mlsanity.com/paper/2607.23367/) (2026)
- [Simultaneous Envy and Equitability Guarantees](https://mlsanity.com/paper/2608.26410/) (2026)
- [Settling the Computational Complexity of Max-Min Allocation with Ternary Valuations](https://mlsanity.com/paper/2610.05237/) (2026)
- [Improving the Bounds on Approximating Weighted Maximin Share for Chores](https://mlsanity.com/paper/2610.15520/) (2026)
- [Exact Cut Complexity of Equal-Length Proportional Cake Cutting](https://mlsanity.com/paper/2610.19733/) (2026)

## Abstract (arXiv)

Allocating resources to individuals in a fair manner has been a topic of interest since ancient times, with most of the early mathematical work on the problem focusing on resources that are infinitely divisible. Over the last decade, there has been a surge of papers studying computational questions regarding the indivisible case, for which exact fairness notions such as envy-freeness and proportionality are hard to satisfy. One main theme in the recent research agenda is to investigate the extent to which their relaxations, like maximin share fairness (MMS) and envy-freeness up to any good (EFX), can be achieved. In this survey, we present a comprehensive review of the recent progress made in the related literature by highlighting different ways to relax fairness notions, common algorithm design techniques, and the most interesting questions for future research.