NDLI: Modularity and monotonicity of games

Content Provider	Springer Nature Link
Author	Asa, Takao Kojima, Hiroyuki
Copyright Year	2014
Abstract	The purpose of this paper is twofold. First, we generalize Kajii et al. (J Math Econ 43:218–230, 2007) and provide a condition under which for a game $$v$$ , its Möbius inverse is equal to zero within the framework of the $$k$$ -modularity of $$v$$ for $$k \ge 2$$ . This condition is more general than that in Kajii et al. (J Math Econ 43:218–230, 2007). Second, we provide a condition under which for a game $$v$$ , its Möbius inverse takes non-negative values, and not just zero. This paper relates the study of totally monotone games to that of $$k$$ -monotone games. Furthermore, this paper shows that the modularity of a game is related to $$k$$ -additive capacities proposed by Grabisch (Fuzzy Sets Syst 92:167–189, 1997). To illustrate its application in the field of economics, we use these results to characterize a Gini index representation of Ben-Porath and Gilboa (J Econ Theory 64:443–467, 1994). Our results can also be applied to potential functions proposed by Hart and Mas-Colell (Econometrica 57:589–614, 1989) and further analyzed by Ui et al. (Math Methods Oper Res 74:427–443, 2011).
Starting Page	29
Ending Page	46
Page Count	18
File Format	PDF
ISSN	14322994
Journal	Mathematical Methods of Operations Research
Volume Number	80
Issue Number	1
e-ISSN	14325217
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-04-23
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Möbius inverse Totally monotone games $$k$$ -Additive capacities Gini index Potential functions Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory Business/Management Science
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research Mathematics Software

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