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Extendable Cooperative Games

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Author Info

  • YARON AZRIELI
  • EHUD LEHRER

Abstract

A (TU) cooperative game is extendable if every core allocation of each subgame can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its subgames can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core. Further, we characterize extendability in terms of an extension of the balanced cover of the game. It is also shown how this extension can unify the analysis of many families of games under one roof. Copyright 2007 Blackwell Publishing, Inc..

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9779.2007.00345.x
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Bibliographic Info

Article provided by Association for Public Economic Theory in its journal Journal of Public Economic Theory.

Volume (Year): 9 (2007)
Issue (Month): 6 (December)
Pages: 1069-1078

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Handle: RePEc:bla:jpbect:v:9:y:2007:i:6:p:1069-1078

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Cited by:
  1. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
  2. Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December.
  3. Arantza Estevez-Fernandez, 2011. "New Characterizations for Largeness of the Core," Tinbergen Institute Discussion Papers 11-086/1, Tinbergen Institute.
  4. Yaron Azrieli & Ehud Lehrer, 2007. "On some families of cooperative fuzzy games," International Journal of Game Theory, Springer, vol. 36(1), pages 1-15, September.
  5. Evan Shellshear, 2009. "Characterizing core stability with fuzzy games," Working Papers 410, Bielefeld University, Center for Mathematical Economics.
  6. Chateauneuf, Alain & Ventura, Caroline, 2011. "Partial probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 22-28, January.
  7. Brânzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Discussion Paper 2008-55, Tilburg University, Center for Economic Research.
  8. Evan Shellshear, 2007. "On core stability and extendability," Working Papers 387, Bielefeld University, Center for Mathematical Economics.
  9. Ehud Lehrer, 2009. "A new integral for capacities," Economic Theory, Springer, vol. 39(1), pages 157-176, April.
  10. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.
  11. Arantza Estevez-Fernandez, 2011. "New Characterizations for Largeness of the Core," Tinbergen Institute Discussion Papers 11-086/1, Tinbergen Institute.
  12. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Discussion Paper 2007-54, Tilburg University, Center for Economic Research.

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