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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References listed on IDEAS
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- Jürgen Eichberger & David Kelsey, 1999.
"E-Capacities and the Ellsberg Paradox,"
Theory and Decision,
Springer, vol. 46(2), pages 107-138, April.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- 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, vol. 20(3), pages 255-68.
- E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer, vol. 52(2), pages 221-236, November.
- 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.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- 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.
- Algaba, A. & Bilbao, J.M. & Borm, P.E.M. & Lopez, J., 2000. "The position value for union stable systems," Other publications TiSEM f7ea939d-770c-43ed-92ae-1, Tilburg University, School of Economics and Management.
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