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The convexity-cone approach to comparative risk and downside risk

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  • Massimo Marinacci
  • Luigi Montrucchio

Abstract

We establish a calculus characterization of the core of supermodular games, which reduces the description of the core to the computation of suitable Gateaux derivatives of the Choquet integrals associated with the game. Our result generalizes to infinite games a classic result of Shapley (1971). As a secondary contribution, we provide a fairly complete analysis of the Gateaux and Frechet differentiability of the Choquet integrals of supermodular measure games.

Suggested Citation

  • Massimo Marinacci & Luigi Montrucchio, 2002. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 18-2002, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:18-2002
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    References listed on IDEAS

    as
    1. Epstein, Larry G. & Marinacci, Massimo, 2001. "The Core of Large Differentiable TU Games," Journal of Economic Theory, Elsevier, vol. 100(2), pages 235-273, October.
    2. Marinacci, Massimo & Montrucchio, Luigi, 2003. "Subcalculus for set functions and cores of TU games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 1-25, February.
    3. Massimo Marinacci, 1996. "Decomposition and Representation of Coalitional Games," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 1000-1015, November.
    4. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
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