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Coextrema Additive Operators

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Author Info

  • Atsushi Kajii

    ()
    (Institute of Economic Research, Kyoto University)

  • Hiroyuki Kojima

    ()
    (Department of Economics, Teikyo University)

  • Takashi Ui

    ()
    (Faculty of Economics, Yokohama National University)

Abstract

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space Ω, which include additivity and comonotonic additivity as extreme cases. Let E ⊆ 2Ω be a collection of subsets of Ω. Two functions x and y on Ω are E-coextrema if, for each E ∈ E, the set of minimizers of x restricted on E and that of y have a common element, and the set of maximizers of x restricted on E and that of y have a common element as well. An operator I on the set of functions on Ω is E-coextrema additive if I(x+y) = I(x)+I(y) whenever x and y are E-coextrema. The main result characterizes homogeneous E-coextrema additive operators.

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Bibliographic Info

Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 631.

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Length: 20pages
Date of creation: May 2007
Date of revision:
Handle: RePEc:kyo:wpaper:631

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Related research

Keywords: Choquet integral; comonotonicity; non-additive probabilities; capacities;

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