---
title: "Control of Fair Division"
authors:
  - "Haris Aziz"
  - "Ildikó Schlotter"
  - "Toby Walsh"
doi: ""
url: "https://ijcai.org/proceedings/2016/17"
pdf: "https://ijcai.org/proceedings/2016/0017.pdf"
venue: "Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence"
year: 2016
pages: "67-72"
track: ""
keywords:
---

# Control of Fair Division

Haris Aziz, Ildikó Schlotter, Toby Walsh

*Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence*, pages 67-72.

## Abstract

We initiate the study of control actions in fair division problems where a benevolent or malicious central organizer changes the structure of the fair division problem for self-interest or to benefit one, some or all agents. One motivation for such control is to improve fairness by minimally changing the problem. As a case study, we consider the problem of adding or deleting a small number of items to improve fairness. For two agents, we present polynomial-time algorithms for adding or deleting the minimum number of items to achieve ordinal envy-freeness. For three agents, we show that both problems, as well as the more basic problem of checking whether an envy-free allocation exists, are NP-complete. This closes a problem open for over five years. Our framework leads to a number of interesting directions in the area of fair division.