Two hardness results for Gamson’s game

Vladimir Deineko () and Gerhard Woeginger ()

Social Choice and Welfare, 2014, vol. 43, issue 4, 963-972

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 $$\Delta _2$$ Δ 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). Copyright Springer-Verlag Berlin Heidelberg 2014

Date: 2014
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DOI: 10.1007/s00355-014-0819-6

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