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Modularity and Monotonicity of Games

  • Takao Asano

    ()

    (Faculty of Economics, Okayama University)

  • Hiroyuki Kojima

    ()

    (Department of Economics, Teikyo University)

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    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.

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP871.pdf
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    Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 871.

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    Length: 23pages
    Date of creation: Jun 2013
    Date of revision:
    Handle: RePEc:kyo:wpaper:871
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    1. Miranda, Pedro & Grabisch, Michel & Gil, Pedro, 2006. "Dominance of capacities by k-additive belief functions," European Journal of Operational Research, Elsevier, vol. 175(2), pages 912-930, December.
    2. Eichberger, J. & Kelsey, D., 1996. "E-Capacities and the Ellsberg Paradox," Discussion Papers 96-13, Department of Economics, University of Birmingham.
    3. van den Nouweland, C.G.A.M. & Borm, P.E.M. & Tijs, S.H., 1992. "Allocation rules for hypergraph communication situations," Other publications TiSEM b97fb9dd-2acf-470d-b9eb-a, Tilburg University, School of Economics and Management.
    4. Chateauneuf, Alain & Rebille, Yann, 2004. "A Yosida-Hewitt decomposition for totally monotone games," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 1-9, July.
    5. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    6. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer, vol. 20(3), pages 255-68.
    7. repec:ner:tilbur:urn:nbn:nl:ui:12-146635 is not listed on IDEAS
    8. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-69, September.
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