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On Concavity and Supermodularity

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  • Massimo Marinacci
  • Luigi Montrucchio

Abstract

Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [2] and Konig [5].

Suggested Citation

  • Massimo Marinacci & Luigi Montrucchio, 2006. "On Concavity and Supermodularity," Carlo Alberto Notebooks 5, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:5
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    References listed on IDEAS

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    1. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
    2. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
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    Cited by:

    1. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Complete Monotone Quasiconcave Duality," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 321-339, May.
    2. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.

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    More about this item

    Keywords

    Concavity; Supermodularity;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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