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|
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- Pedro Miranda & Michel Grabisch & Pedro Gil, 2006.
"Dominance of capacities by k-additive belief functions,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- 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.
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Springer;Game Theory Society, vol. 20(3), pages 255-268.
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- Chateauneuf, Alain & Rebille, Yann, 2004. "A Yosida-Hewitt decomposition for totally monotone games," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 1-9, July.
- Eichberger, J. & Kelsey, D., 1996.
"E-Capacities and the Ellsberg Paradox,"
96-13, Department of Economics, University of Birmingham.
- Gilboa, Itzhak, 1989.
"Expectation and Variation in Multi-period Decisions,"
Econometric Society, vol. 57(5), pages 1153-1169, September.
- Itzhak Gilboa, 1989. "Expectation and Variation in Multi-Period Decisions," Post-Print hal-00753240, HAL.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-587, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
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