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Hedonic Coalition Formation Games with Variable Populations: Core Characterizations and (Im)Possibilities

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  • Mehmet Karakaya
  • Bettina Klaus

Abstract

We consider hedonic coalition formation games with variable sets of agents and extend the properties competition sensitivity and resource sensitivity (introduced by Klaus, 2011, for roomate markets) to hedonic coalition formation games. Then, we show that on the domain of solvable hedonic coalition formation games, the Core is characterized by coalitional unanimity and Maskin monotonicity (see also Takamiya, 2010, Theorem 1). Next, we characterize the Core for solvable hedonic coalition formation games by unanimity, Maskin monotonicity, and either competition sensitivity or resource sensitivity (Corollary 2). Finally, and in contrast to roommate markets, we show that on the domain of solvable hedonic coalition formation games, there exists a solution not equal to the Core that satisfies coalitional unanimity, consistency, competition sensitivity, and resource sensitivity (Example 2).

Suggested Citation

  • Mehmet Karakaya & Bettina Klaus, 2015. "Hedonic Coalition Formation Games with Variable Populations: Core Characterizations and (Im)Possibilities," Cahiers de Recherches Economiques du Département d'économie 15.01, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:15.01
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    References listed on IDEAS

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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. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
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    6. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    7. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
    8. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    9. Burak Can & Bettina Klaus, 2013. "Consistency and population sensitivity properties in marriage and roommate markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 835-862, October.
    10. Dimitrov, Dinko & Sung, Shao Chin, 2007. "On top responsiveness and strict core stability," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 130-134, February.
    11. Klaus, Bettina, 2011. "Competition and resource sensitivity in marriage and roommate markets," Games and Economic Behavior, Elsevier, vol. 72(1), pages 172-186, May.
    12. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    13. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    14. 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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    17. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
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    Citations

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    Cited by:

    1. Andrew J. Collins & Sheida Etemadidavan & Wael Khallouli, 2020. "Generating Empirical Core Size Distributions of Hedonic Games using a Monte Carlo Method," Papers 2007.12127, arXiv.org.
    2. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2023. "A Core-Partition Ranking Solution to Coalitional Ranking Problems," Group Decision and Negotiation, Springer, vol. 32(4), pages 965-985, August.
    3. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    4. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.
    5. Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2021. "A Core-partition solution for coalitional rankings with a variable population domain," Working Papers 2021-06, CRESE.
    6. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.

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    More about this item

    Keywords

    Coalitional Unanimity; Competition Sensitivity; Consistency; Core; Hedonic Coalition Formation; Maskin Monotonicity; Resource Sensitivity;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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