Cominimum Additive Operators

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

No 601, 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 \omega, which include additivity and comonotonic additivity as extreme cases. Let \epsilon be a collection of subsets of \omega. Two functions x and y on \omega are \epsilon-cominimum if, for each E \subseteq \epsilon, the set of minimizers of x restricted on E and that of y have a common element. An operator I on the set of functions on is E- cominimum additive if I(x+y) = I(x)+I(y) whenever x and y are \epsilon-cominimum. The main result characterizes homogeneous E-cominimum additive operators in terms of the Choquet integrals and the corresponding non-additive signed measures. As applications, this paper gives an alternative proof for the characterization of the E-capacity expected utility model of Eichberger and Kelsey (1999) and that of the multi-period decision model of Gilboa (1989).

Keywords: Choquet integral; comonotonicity; non-additive probabilities; capacities; cooperative games (search for similar items in EconPapers)
JEL-codes: C71 D81 D90 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2005-02
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Cominimum additive operators (2007)
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