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

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 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)
Pages: 23pages
Date: 2013-06
New Economics Papers: this item is included in nep-gth and nep-mic
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