Modularity and Monotonicity of Games
AbstractThe 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.
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Bibliographic InfoPaper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 871.
Date of creation: Jun 2013
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More information through EDIRC
Belief Functions; Mobius Inversion; Totally Monotone Games; k-additive capacities; Gini Index; Potential Functions;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- D90 - Microeconomics - - Intertemporal Choice - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-06-30 (All new papers)
- NEP-GTH-2013-06-30 (Game Theory)
- NEP-MIC-2013-06-30 (Microeconomics)
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