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Size Monotonicity and Stability of the Core in Hedonic Games

Author

Listed:
  • Dinko Dimitrov

    (Chair of Economic Theory, Saarland University)

  • Shao Chin Sung

    (Department of Industrial and Systems Engineering, Aoyama Gakuin University)

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

  • Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2011.52
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    References listed on IDEAS

    as
    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. Ichiishi, T, 1990. "Comparative Cooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 139-152.
    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. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    5. 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.
    6. 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.
    7. ICHIISHI, Tatsuro, 1990. "Comparative cooperative game theory," LIDAM Reprints CORE 903, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    9. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    10. 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.
    11. 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.
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    JEL classification:

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

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