Computational complexity of necessary envy-freeness

Haris Aziz, Ildikó Schlotter and Toby Walsh

Mathematical Social Sciences, 2024, vol. 127, issue C, 86-98

Abstract: We consider the fundamental problem of fairly allocating indivisible items when agents have strict ordinal preferences over individual items. We focus on the well-studied fairness criterion of necessary envy-freeness. For a constant number of agents, the computational complexity of the deciding whether there exists an allocation that satisfies necessary envy-freeness has been open for several years. We settle this question by showing that the problem is NP-complete even for three agents. Considering that the problem is polynomial-time solvable for the case of two agents, we provide a clear understanding of the complexity of the problem with respect to the number of agents.

Keywords: Fair division; Envy-freeness (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:127:y:2024:i:c:p:86-98

DOI: 10.1016/j.mathsocsci.2023.08.002

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