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Title: Modularity and Monotonicity of Games
Authors: Asano, Takao
Kojima, Hiroyuki
Keywords: Belief Functions
Möbius Inversion
Totally Monotone Games
k-additive capacities
Gini Index
Potential Functions
Issue Date: Jun-2013
Publisher: Institute of Economic Research, Kyoto University
Journal title: KIER Discussion Paper
Volume: 871
Abstract: 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 Möbius 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 Möbius inversion takes non-negative values, and not just zero. This paper relates the study of totally monotone games to that of k-monotone 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).
Appears in Collections:KIER Discussion Paper (English)

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