A new look at the role of players’ weights in the weighted Shapley value
Abstracteveral new families of semivalues for weighted n-person transferable utility games are axiomatically constructed and discussed under increasing collections of axioms, where the weighted Shapley value arises as the resulting one member family. A more general approach to such weighted games defined in the form of two components, a weight vector λ and a classical TU-game v, is provided. The proposed axiomatizations are done both in terms of λ and v. Several new axioms related to the weight vector λ are discussed, including the so-called “amalgamating payoffs” axiom, which characterizes the value of a weighted game in terms of another game with a smaller number of players. They allow for a new look at the role of players’ weights in the context of the weighted Shapley value for the model of weighted games, giving new properties of it. Besides, another simple formula for the weighted Shapley value is found and examples illustrating some surprising behavior of it in the context of players’ weights are given. The paper contains a wide discussion of the results obtained.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 223 (2012)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/eor
Game theory; n-Person game; TU-game; Weighted cooperative game; Weighted semivalue; Weighted Shapley value;
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.:
- Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
- Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
- Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008.
"Dividends and Weighted Values in Games with Externalities,"
UFAE and IAE Working Papers
758.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2010. "Dividends and weighted values in games with externalities," International Journal of Game Theory, Springer, vol. 39(1), pages 177-184, March.
- Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008. "Dividends and Weighted Values in Games with Externalities," Working Papers 366, Barcelona Graduate School of Economics.
- Ines Macho-Stadler & David Perez-Castrillo & David Wettstein, 2009. "Dividends and Weighted Values in Games with Externalities," Working Papers 0906, Ben-Gurion University of the Negev, Department of Economics.
- Gómez-Rúa, María & Vidal-Puga, Juan, 2010.
"The axiomatic approach to three values in games with coalition structure,"
European Journal of Operational Research,
Elsevier, vol. 207(2), pages 795-806, December.
- Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "The axiomatic approach to three values in games with coalition structure," MPRA Paper 8904, University Library of Munich, Germany.
- Haeringer, Guillaume, 2006.
"A new weight scheme for the Shapley value,"
Mathematical Social Sciences,
Elsevier, vol. 52(1), pages 88-98, July.
- Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
- Pierre Dehez, 2011. "Allocation of fixed costs: characterization of the (dual) weighted Shapley value," Working Papers of BETA 2011-03, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
- Valeri Vasil'Ev, 2007. "Weber Polyhedron And Weighted Shapley Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 139-150.
- Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer, vol. 20(2), pages 183-90.
- Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer, vol. 35(3), pages 523-538, June.
- E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer, vol. 29(1), pages 1-9.
- Bergantinos, Gustavo & Lorenzo-Freire, Silvia, 2008. ""Optimistic" weighted Shapley rules in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 289-298, February.
- Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Preserving or removing special players: what keeps your payoff unchanged in TU-games?," Working Papers 2013-09, CRESE.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.