Reforming an Unfair Allocation by Exchanging Goods
Abstract
Abstract Fairly allocating indivisible goods is a frequently occurring task in everyday life. Given an initial allocation of the goods, we consider the problem of reforming it via a sequence of exchanges to attain fairness in the form of envy-freeness up to one good (EF1). We present a vast array of results on the complexity of determining whether it is possible to reach an EF1 allocation from the initial allocation and, if so, the minimum number of exchanges required. In particular, we uncover several distinctions based on the number of agents involved and their utility functions. Furthermore, we derive essentially tight bounds on the worst-case number of exchanges needed to achieve EF1 when the initial allocation is balanced.
Fields of Study & Subjects
EU Law and Policy Analysis
Taxation and Legal Issues
Publication details
- Journal / source
- Algorithmica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 88
- Issue
- 4
- Publication date
- 29 June 2026
- Language
- EN