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Strongly essential coalitions and the nucleolus of peer group games

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Author Info
Tijs, S.
Branzei, R.
Solymosi, T. (Tilburg University, Center for Economic Research)

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Abstract

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespeci ed collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n - 1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n-1. We propose an algorithm that computes the nucleolus of an n-player peer group game in O(n2) time directly from the data of the underlying peer group situation.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 19.

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Date of creation: 2003
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Handle: RePEc:dgr:kubcen:200319

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Related research
Keywords: peer games;

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. D. Granot & F. Granot & W. R. Zhu, 1998. "Characterization sets for the nucleolus," International Journal of Game Theory, Springer, vol. 27(3), pages 359-374. [Downloadable!] (restricted)
  2. Bondareva O. N. & Driessen T. S. H., 1994. "Extensive Coverings and Exact Core Bounds," Games and Economic Behavior, Elsevier, vol. 6(2), pages 212-219, March. [Downloadable!] (restricted)
  3. Branzei, R. & Fragnelli, V. & Tijs, S., 2000. "Tree-connected peer group situations and peer group games," Discussion Paper 117, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Vincent Feltkamp & Javier Arin, 1997. "The Nucleolus and Kernel of Veto-Rich Transferable Utility Games," International Journal of Game Theory, Springer, vol. 26(1), pages 61-73.
  5. Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer, vol. 21(1), pages 85-106.
  6. Reijnierse, Hans & Potters, Jos, 1998. "The -Nucleolus of TU-Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 77-96, July. [Downloadable!] (restricted)
  7. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, vol. 20(4), pages 419-27.
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  8. Solymosi, Tamas & Raghavan, T. E. S. & Tijs, Stef, 2005. "Computing the nucleolus of cyclic permutation games," European Journal of Operational Research, Elsevier, vol. 162(1), pages 270-280, April. [Downloadable!] (restricted)
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Cited by:
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  1. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure," Tinbergen Institute Discussion Papers 08-104/1, Tinbergen Institute. [Downloadable!]
  2. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure," Tinbergen Institute Discussion Papers 08-060/1, Tinbergen Institute. [Downloadable!]
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