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Coextrema Additive Operators

Author

Listed:
  • 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.

Suggested Citation

  • Atsushi Kajii & Hiroyuki Kojima & Takashi Ui, 2007. "Coextrema Additive Operators," KIER Working Papers 631, Kyoto University, Institute of Economic Research.
  • Handle: RePEc:kyo:wpaper:631
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP631.pdf
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    More about this item

    Keywords

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

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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