# On Fair Division of Indivisible Items

arXiv: https://arxiv.org/abs/1805.06232 · HTML: https://mlsanity.com/paper/1805.06232/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2018.

## Built on by (most cited first, 2 of 2)

- [Fair and Efficient Resource Allocation with Partial Information](https://mlsanity.com/paper/2105.10064/) (2021)
- [Constrained Serial Dictatorships can be Fair](https://mlsanity.com/paper/2301.06086/) (2023)

## Abstract (arXiv)

We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of e^1/e ≈ 1.445. The computed allocation is Pareto-optimal and approximates envy-freeness up to one item up to a factor of 2 + eps