Work

Reforming an Unfair Allocation by Exchanging Goods

Year: 2026

Type: article

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.

Source: Algorithmica

DOI: 10.1007/s00453-026-01401-8

Authors: Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, Warut Suksompong

Institutions: National University of Singapore, The University of Tokyo, Kyushu University

Language: English

Topic: Game Theory and Voting Systems

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,290