Abstract
We derive two hardness results on stable winning coalitions in Gamson’s game. First, it is coNP-complete to decide whether there exists a stable winning coalition that is connected. Secondly, it is \(\Delta _2\)P-complete to decide whether there exists a stable winning coalition that includes a weakest player. Our results precisely pinpoint the computational complexity of both problems, and they indicate a negative answer to a recent question of Le Breton et al. (2008, Soc Choice Welf 30:57–67).
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Acknowledgments
We thank two reviewers for a careful reading of the text and for providing many helpful comments that improved the presentation of the paper. Part of this research was conducted while the authors were visiting TU Graz, and both authors acknowledge support by the Doctoral College in Discrete Mathematics (grant W1230, Austrian Science Fund FWF). Vladimir Deineko acknowledges support by Warwick University’s Centre for Discrete Mathematics and Its Applications (DIMAP). Gerhard Woeginger acknowledges support by DIAMANT (a mathematics cluster of the Netherlands Organization for Scientific Research NWO), and by the Alexander von Humboldt Foundation, Bonn, Germany.
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Deineko, V.G., Woeginger, G.J. Two hardness results for Gamson’s game. Soc Choice Welf 43, 963–972 (2014). https://doi.org/10.1007/s00355-014-0819-6
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DOI: https://doi.org/10.1007/s00355-014-0819-6