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A hardness result for core stability in additive hedonic games

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  • Woeginger, Gerhard J.

Abstract

We investigate the computational complexity of a decision problem in hedonic coalition formation games. We prove that core stability in additive hedonic games is complete for the second level of the polynomial hierarchy.

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  • Woeginger, Gerhard J., 2013. "A hardness result for core stability in additive hedonic games," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 101-104.
    • Handle: RePEc:eee:matsoc:v:65:y:2013:i:2:p:101-104
    DOI: 10.1016/j.mathsocsci.2012.10.001
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    1. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    2. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
    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.
    5. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    6. Sung, Shao Chin & Dimitrov, Dinko, 2011. "On core membership testing for hedonic coalition formation games," Center for Mathematical Economics Working Papers 374, Center for Mathematical Economics, Bielefeld University.
    7. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
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    Cited by:

    1. Martin Gairing & Rahul Savani, 2019. "Computing Stable Outcomes in Symmetric Additively Separable Hedonic Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1101-1121, August.
    2. Kondor, Gábor, 2022. "Egyoldali párosítási piacok nehézségi eredményei magasabb dimenzióban [Hardness results of one-sided matching markets in higher dimensions]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 825-840.
    3. Rothe, Jörg & Schadrack, Hilmar & Schend, Lena, 2018. "Borda-induced hedonic games with friends, enemies, and neutral players," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 21-36.
    4. Sheida Etemadidavan & Andrew J. Collins, 2021. "An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games," SN Operations Research Forum, Springer, vol. 2(4), pages 1-20, December.

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