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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- Gilboa, Itzhak, 1989.
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"Subjective Probability and Expected Utility without Additivity,"
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- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992.
"Allocation Rules for Hypergraph Communication Situations,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 20(3), pages 255-68.
- 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, Tilburg University, School of Economics and Management.
- Jürgen Eichberger & David Kelsey, 1999.
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