# Monotone and Online Fair Division

arXiv: https://arxiv.org/abs/2006.15891 · HTML: https://mlsanity.com/paper/2006.15891/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Online Fair Division for Personalized 2-Value Instances](https://mlsanity.com/paper/2505.22174/) (2025)
- [Online Fair Allocation of Perishable Resources](https://mlsanity.com/paper/2406.02402/) (2024)
- [Credit Fairness: Online Fairness In Shared Resource Pools](https://mlsanity.com/paper/2601.17944/) (2026)

## Abstract (arXiv)

We study a new but simple model for online fair division in which indivisible items arrive one-by-one and agents have monotone utilities over bundles of the items. We consider axiomatic properties of mechanisms for this model such as strategy-proofness, envy-freeness, and Pareto efficiency. We prove a number of impossibility results that justify why we consider relaxations of the properties, as well as why we consider restricted preference domains on which good axiomatic properties can be achieved. We propose two mechanisms that have good axiomatic fairness properties on restricted but common preference domains.