ダウンロード数: 326
タイトル: | Modularity and Monotonicity of Games |
著者: | Asano, Takao Kojima, Hiroyuki |
キーワード: | Belief Functions Möbius Inversion Totally Monotone Games k-additive capacities Gini Index Potential Functions |
発行日: | Jun-2013 |
出版者: | Institute of Economic Research, Kyoto University |
誌名: | KIER Discussion Paper |
巻: | 871 |
抄録: | 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). |
URI: | http://hdl.handle.net/2433/175276 |
出現コレクション: | KIER Discussion Paper (英文版) |
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