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Size Monotonicity and Stability of the Core in Hedonic Games

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  • 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.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2011.52.

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Date of creation: Jul 2011
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Handle: RePEc:fem:femwpa:2011.52

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Keywords: Core; Hedonic Games; Monotonicity; Stable Sets;

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  1. Ichiishi, T, 1990. "Comparative Cooperative Game Theory," International Journal of Game Theory, Springer, vol. 19(2), pages 139-52.
  2. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Chin Sung, 2004. "Simple Priorities and Core Stability in Hedonic Games," Working Papers 2004.51, Fondazione Eni Enrico Mattei.
  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. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
  5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  6. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  7. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
  8. 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.
  9. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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