Cominimum Additive Operators
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).
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96-13, Department of Economics, University of Birmingham.
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Levine's Working Paper Archive
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- repec:spr:compst:v:52:y:2000:i:2:p:221-236 is not listed on IDEAS
- Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-69, September.
- repec:ner:tilbur:urn:nbn:nl:ui:12-146635 is not listed on IDEAS
- van den Nouweland, C.G.A.M. & Borm, P.E.M. & Tijs, S.H., 1992. "Allocation rules for hypergraph communication situations," Other publications TiSEM b97fb9dd-2acf-470d-b9eb-a, School of Economics and Management.
- repec:ner:tilbur:urn:nbn:nl:ui:12-84483 is not listed on IDEAS
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