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Coextrema Additive Operators

Atsushi Kajii, Hiroyuki Kojima () and Takashi Ui
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Hiroyuki Kojima: Department of Economics, Teikyo University

No 631, KIER Working Papers from Kyoto University, Institute of Economic Research

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.

Keywords: Choquet integral; comonotonicity; non-additive probabilities; capacities (search for similar items in EconPapers)
JEL-codes: C71 D81 D90 (search for similar items in EconPapers)
Pages: 20pages
Date: 2007-05
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Persistent link: https://EconPapers.repec.org/RePEc:kyo:wpaper:631

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