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Two hardness results for Gamson’s game

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  • Vladimir Deineko
  • Gerhard Woeginger

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

Suggested Citation

  • Vladimir Deineko & Gerhard Woeginger, 2014. "Two hardness results for Gamson’s game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 963-972, December.
    • Handle: RePEc:spr:sochwe:v:43:y:2014:i:4:p:963-972
    DOI: 10.1007/s00355-014-0819-6
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    1. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
    2. Michel Breton & Ignacio Ortuño-Ortin & Shlomo Weber, 2008. "Gamson’s law and hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(1), pages 57-67, January.
    3. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    4. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
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