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Reforming an Unfair Allocation by Exchanging Goods

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

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ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Problems, reductions and completeness
Keywords
  • fair division
  • indivisible goods
  • envy-freeness
  • exchanges

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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.

Cite As Get BibTex

Sheung Man Yuen, Ayumi Igarashi, Naoyuki Kamiyama, and Warut Suksompong. Reforming an Unfair Allocation by Exchanging Goods. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.54

Author Details

Sheung Man Yuen
  • National University of Singapore, Singapore
Ayumi Igarashi
  • University of Tokyo, Japan
Naoyuki Kamiyama
  • Kyushu University, Fukuoka, Japan
Warut Suksompong
  • National University of Singapore, Singapore

Funding

This work was partially supported by the Singapore Ministry of Education under grant number MOE-T2EP20221-0001, by JST PRESTO under grant number JPMJPR20C1, by JSPS KAKENHI under grant number JP20H05795, by JST ERATO under grant number JPMJER2301, and by an NUS Start-up Grant.

Acknowledgements

We would like to thank the anonymous reviewers for their valuable comments.

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