Modularity and Monotonicity of Games
The purpose of this paper is twofold. First, we generalize Kajii et al. (2007), and provide a condition under which for a game v, its Mobius inversion is equal to zero within the framework of the k-modularity of v for k >= 2. This condition is more general than that in Kajii et al. (2007). Second, we provide a condition under which for a game v for k >= 2, its Mobius inversion takes non-negative values, and not just zero. This paper relates the study of totally monotone games to that of kmonotone games. Furthermore, the modularity of a game can be related to k-additive capacities proposed by Grabisch (1997). As applications of our results to economics, this paper shows that a Gini index representation of Ben-Porath and Gilboa (1994) can be characterized by using our results directly. Our results can also be applied to potential functions proposed by Hart and Mas-Colell (1989) and further analyzed by Ui et al. (2011). *>= is greater than or equal to.
|Date of creation:||Jun 2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.kier.kyoto-u.ac.jp/eng/index.html
More information through EDIRC
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.:
- Miranda, Pedro & Grabisch, Michel & Gil, Pedro, 2006.
"Dominance of capacities by k-additive belief functions,"
European Journal of Operational Research,
Elsevier, vol. 175(2), pages 912-930, December.
- Pedro Miranda & Michel Grabisch & Pedro Gil, 2006. "Dominance of capacities by k-additive belief functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00186905, HAL.
- Eichberger, J. & Kelsey, D., 1996.
"E-Capacities and the Ellsberg Paradox,"
96-13, Department of Economics, University of Birmingham.
- van den Nouweland, C.G.A.M. & Borm, P.E.M. & Tijs, S.H., 1992. "Allocation rules for hypergraph communication situations," Other publications TiSEM b97fb9dd-2acf-470d-b9eb-a, Tilburg University, School of Economics and Management.
- Chateauneuf, Alain & Rebille, Yann, 2004. "A Yosida-Hewitt decomposition for totally monotone games," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 1-9, July.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer, vol. 20(3), pages 255-68.
- repec:ner:tilbur:urn:nbn:nl:ui:12-146635 is not listed on IDEAS
- Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-69, September.
When requesting a correction, please mention this item's handle: RePEc:kyo:wpaper:871. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ryo Okui)
If references are entirely missing, you can add them using this form.