Envy-freeness in 3D hedonic games

McKay, M and Cseh, Ágnes and Manlove, D (2024) Envy-freeness in 3D hedonic games. AUTONOMOUS AGENTS AND MULTI-AGENT SYSTEMS, 38 (2). ISSN 1387-2532

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Abstract

We study the problem of fairly partitioning a set of agents into coalitions based on the agents’ additively separable preferences, which can also be viewed as a hedonic game. We study three successively weaker solution concepts, related to envy, weakly justified envy, and justified envy. In a model in which coalitions may have any size, trivial solutions exist for these concepts, which provides a strong motivation for placing restrictions on coalition size. In this paper, we require feasible coalitions to have size three. We study the existence of partitions that are envy-free, weakly justified envy-free, and justified envy-free, and the computational complexity of finding such partitions, if they exist. We impose various restrictions on the agents’ preferences and present a complete complexity classification in terms of these restrictions.

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