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Size Monotonicity and Stability of the Core in Hedonic Games

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  • Dimitrov, Dinko
  • Chin Sung, Shao

Abstract

We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games.

Suggested Citation

  • Dimitrov, Dinko & Chin Sung, Shao, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Climate Change and Sustainable Development 115722, Fondazione Eni Enrico Mattei (FEEM).
    • Handle: RePEc:ags:feemcl:115722
    DOI: 10.22004/ag.econ.115722
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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. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    3. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    4. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    5. Anindya Bhattacharya & Amit K. Biswas, 2002. "Stability Of The Core In A Class Of Ntu Games: A Characterization," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 165-172.
    6. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    7. Ichiishi, T, 1990. "Comparative Cooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 139-152.
    8. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    9. 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.
    10. Peleg, Bezalel, 1986. "A proof that the core of an ordinal convex game is a von Neumann-Morgenstern solution," Mathematical Social Sciences, Elsevier, vol. 11(1), pages 83-87, February.
    11. ICHIISHI, Tatsuro, 1990. "Comparative cooperative game theory," LIDAM Reprints CORE 903, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    More about this item

    Keywords

    Research Methods/ Statistical Methods;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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