Modularity and Monotonicity of Games
Takao Asano () and
Hiroyuki Kojima ()
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Takao Asano: Faculty of Economics, Okayama University
Hiroyuki Kojima: Department of Economics, Teikyo University
No 871, KIER Working Papers from Kyoto University, Institute of Economic Research
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.
Keywords: Belief Functions; Mobius Inversion; Totally Monotone Games; k-additive capacities; Gini Index; Potential Functions (search for similar items in EconPapers)
JEL-codes: C71 D81 D90 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:kyo:wpaper:871
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