The Banzhaf Value in the Presence of Externalities
AbstractWe propose two generalizations of the Banzhaf value for partition function form games. In both cases, our approach is based on probability distributions over the set of possible coalition structures that may arise for any given set of agents. First, we introduce a family of values, one for each collection of the latter probability distributions, defined as the Banzhaf value of an expected coalitional game. Then, we provide two characterization results for this new family of values within the framework of all partition function games. Both results rely on a property of neutrality with respect to am algamation of players. Second, as this collusion transformation fails to be meanin gful for simple games in partition function form, we propose another generalization of the Banzhaf value which also builds on probability distributions of the above type. This latter family is characterized by means of a neutrality property which uses an amalgamation transformation of players for which simple games are close
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 Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics in its series UB Economics Working Papers with number 2014/302.
Length: 20 pages
Date of creation: 2014
Date of revision:
Banzhaf value; Externalities; Games in partition function form; Simplegames.;
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.:
- Kim Hang Pham Do & Henk Norde, 2007.
"The Shapley Value For Partition Function Form Games,"
International Game Theory Review (IGTR),
World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 353-360.
- Pham Do, K.H. & Norde, H.W., 2002. "The Shapley Value for Partition Function Form Games," Discussion Paper 2002-4, Tilburg University, Center for Economic Research.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
- Bolger, E M, 1986. "Power Indices for Multicandidate Voting Games," International Journal of Game Theory, Springer, vol. 15(3), pages 175-86.
- M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
- Bhaskar Dutta & Lars Ehlers & Anirban Kar, 2008.
"Externalities, Potential, Value And Consistency,"
168, Centre for Development Economics, Delhi School of Economics.
- DUTTA, Bhaskar & EHLERS, Lars & KAR, Anirban, 2008. "Externalities, Potential, Value and Consistency," Cahiers de recherche 2008-06, Universite de Montreal, Departement de sciences economiques.
- DUTTA, Bhaskar & EHLERS, Lars & KAR, Anirban, 2008. "Externalities, Potential, Value and Consistency," Cahiers de recherche 06-2008, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Geoffroy de Clippel & Roberto Serrano, 2008.
"Marginal Contributions and Externalities in the Value,"
Econometric Society, vol. 76(6), pages 1413-1436, November.
- Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions and Externalities in the Value," Working Papers 2005-11, Brown University, Department of Economics.
- Geoffroy de Clippel & Roberto Serrano, 2007. "Marginal contributions and externalities in the value," Working Papers 2007-04, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
- Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions And Externalities In The Value," Economics Working Papers we057339, Universidad Carlos III, Departamento de Economía.
- Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
- Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
- Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer, vol. 26(1), pages 137-141.
- Hafalir, Isa E., 2007. "Efficiency in coalition games with externalities," Games and Economic Behavior, Elsevier, vol. 61(2), pages 242-258, November.
- André Casajus, 2012. "Amalgamating players, symmetry, and the Banzhaf value," International Journal of Game Theory, Springer, vol. 41(3), pages 497-515, August.
- Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (UB Economics).
If references are entirely missing, you can add them using this form.