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Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity

Bouveret, Sylvain; Lang, Jérôme (2008), Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity, The Journal of Artificial Intelligence Research, 32, p. 525-564. http://dx.doi.org/10.1613/jair.2467

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Type
Article accepté pour publication ou publié
Date
2008
Nom de la revue
The Journal of Artificial Intelligence Research
Volume
32
Éditeur
AI Access Foundation
Pages
525-564
Identifiant publication
Métadonnées
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Auteur(s)
Bouveret, Sylvain cc
Lang, Jérôme
Résumé (EN)
We consider the problem of allocating fairly a set of indivisible goods among agents from the point of view of compact representation and computational complexity. We start by assuming that agents have dichotomous preferences expressed by propositional formulae. We express efficiency and envy-freeness in a logical setting, which reveals unexpected connections to nonmonotonic reasoning. Then we identify the complexity of determining whether there exists an efficient and envy-free allocation, for several notions of efficiency, when preferences are represented in a succinct way (as well as restrictions of this problem). We first study the problem under the assumption that preferences are dichotomous, and then in the general case.
Mots-clés
allocation of resources; Complexity; nonmonotonic reasoning