Optimal partitions in additively separable hedonic games

Authors:
Haris Aziz;Felix Brandt;Hans Georg Seedig
Affiliations:
Department of Informatics, Technische Universität München, München, Germany;Department of Informatics, Technische Universität München, München, Germany;Department of Informatics, Technische Universität München, München, Germany
Venue:
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Year:
2011

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Abstract

We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitarian social welfare or one which is both Pareto optimal and individually rational is NP-hard. We also prove that checking whether there exists a partition which is both Pareto optimal and envy-free is Σ2p-complete. Even though an envy-free partition and a Nash stable partition are both guaranteed to exist for symmetric preferences, checking whether there exists a partition which is both envy-free and Nash stable is NP-complete.