Precise Complexity of the Core in Dichotomous and Additive Hedonic Games

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.

ADT-2017, 15 pages in LNCS style

References in corpus (3)

• Stable partitions in additively separable hedonic games
• Optimal Partitions in Additively Separable Hedonic Games
• Simple Causes of Complexity in Hedonic Games