# Repeatedly Matching Items to Agents Fairly and Efficiently

arXiv: https://arxiv.org/abs/2207.01589 · HTML: https://mlsanity.com/paper/2207.01589/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2022.

## Built on by (most cited first, 8 of 8)

- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [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)
- [Resource Sharing Through Multi-Round Matchings](https://mlsanity.com/paper/2211.17199/) (2022)
- [Fairness in Repeated Matching: A Maximin Perspective](https://mlsanity.com/paper/2510.04624/) (2025)
- [Resource Allocation under the Latin Square Constraint](https://mlsanity.com/paper/2501.06506/) (2025)
- [Temporal Panel Selection in Ongoing Citizens' Assemblies](https://mlsanity.com/paper/2602.16194/) (2026)
- [Online Fair Division with Budget Constraints](https://mlsanity.com/paper/2607.23310/) (2026)

## Abstract (arXiv)

We consider a novel setting where a set of items are matched to the same set of agents repeatedly over multiple rounds. Each agent gets exactly one item per round, which brings interesting challenges to finding efficient and/or fair em repeated matchings. A particular feature of our model is that the value of an agent for an item in some round depends on the number of rounds in which the item has been used by the agent in the past. We present a set of positive and negative results about the efficiency and fairness of repeated matchings. For example, when items are goods, a variation of the well-studied fairness notion of envy-freeness up to one good (EF1) can be satisfied under certain conditions. Furthermore, it is intractable to achieve fairness and (approximate) efficiency simultaneously, even though they are achievable separately. For mixed items, which can be goods for some agents and chores for others, we propose and study a new notion of fairness that we call em swap envy-freeness (swapEF).