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arXiv · 1005.4540

Optimal Partitions in Additively Separable Hedonic Games

Haris Aziz·Felix Brandt·Hans Georg Seedig
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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 $\Sigma_{2}^{p}$-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.

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Haris Aziz, Felix Brandt, Hans Georg Seedig. 2010-05-25. Optimal Partitions in Additively Separable Hedonic Games. https://doi.org/10.1016/j.artint.2012.09.006

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