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).
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Itzhak Gilboa, 1989.
"Expectation and Variation in Multi-Period Decisions,"
- Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-69, September.
- Jürgen Eichberger & David Kelsey, 1999.
"E-Capacities and the Ellsberg Paradox,"
Theory and Decision,
Springer, vol. 46(2), pages 107-138, April.
- repec:spr:compst:v:52:y:2000:i:2:p:221-236 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- Algaba, A. & Bilbao, J.M. & Borm, P.E.M. & Lopez, J., 1998. "The position value for union stable systems," Research Memorandum FEW 768, Tilburg University, School of Economics and Management.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:218-230. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.