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arXiv · 1509.02333

Precise Complexity of the Core in Dichotomous and Additive Hedonic Games

Dominik Peters
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Abstract

Hedonic games provide a general model of coalition formation, in which a set of agents is partitioned into coalitions, with each agent having preferences over which other players are in her coalition. We prove that with additively separable preferences, it is $\Sigma_2^p$-complete to decide whether a core- or strict-core-stable partition exists, extending a result of Woeginger (2013). Our result holds even if valuations are symmetric and non-zero only for a constant number of other agents. We also establish $\Sigma_2^p$-completeness of deciding non-emptiness of the strict core for hedonic games with dichotomous preferences. Such results establish that the core is much less tractable than solution concepts such as individual stability.

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Dominik Peters. 2015-09-08. Precise Complexity of the Core in Dichotomous and Additive Hedonic Games. https://arxiv.org/abs/1509.02333

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