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Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure

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Author Info
René van den Brink () (VU University Amsterdam)
Ilya Katsev () (Russian Academy of Sciences)
Gerard van der Laan () (VU University Amsterdam)

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Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the nucleolus. A cooperative game with a permission structure describes a situation in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. The corresponding restricted game takes account of the limited cooperation possibilities by assigning to every coalition the worth of its largest feasible subset. In this paper we provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with permission structure.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-060/1.

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Date of creation: 16 Jun 2008
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Handle: RePEc:dgr:uvatin:20080060

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Related research
Keywords: TU-game; nucleolus; game with permission structure; peer group game; information market game; algorithm; complexity;

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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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References listed on IDEAS
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. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer, vol. 33(3), pages 447-460, 09. [Downloadable!] (restricted)
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  2. 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.
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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!]
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