An Algorithm for Computing the Nucleolus of Disjunctive Additive Games with An Acyclic Permission Structure
AbstractA 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 consider the class of non-negative additive games with an acyclic permission structure. This class generalizes the so-called peer group games being non-negative additive games on a permission tree. We provide a polynomial time algorithm for computing the nucleolus of every restricted game corresponding to some disjunctive non-negative additive game with an acyclic permission structure. We discuss an application to market situations where sellers can sell objects to buyers through a directed network of intermediaries.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-104/1.
Date of creation: 31 Oct 2008
Date of revision:
Contact details of provider:
Web page: http://www.tinbergen.nl
TU-game; additive game; acyclic permission structure; disjunctive approach; peer group game; nucleolus; algorithm; complexity;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
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.:
- 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.
- Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991.
"Games with permission structures: The conjunctive approach,"
1991-14, Tilburg University, Center for Economic Research.
- Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
- Muto, Shigeo & Potters, Jos & Tijs, Stef, 1989. "Information Market Games," International Journal of Game Theory, Springer, vol. 18(2), pages 209-26.
- RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, vol. 26(1), pages 27-43.
- van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
- Arin, J. & Feltkamp, V., 1994.
"The nucleolus and kernel of veto-rich transferable utility games,"
1994-40, Tilburg University, Center for Economic Research.
- 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.
- Brânzei, R. & Solymosi, T. & Tijs, S.H., 2003.
"Strongly Essential Coalitions and the Nucleolus of Peer Group Games,"
2003-19, Tilburg University, Center for Economic Research.
- 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.
- Muto, S. & Potters, J.A.M. & Tijs, S.H., 1989. "Information market games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154244, Tilburg University.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).
If references are entirely missing, you can add them using this form.