A new integral for capacities
A new integral for capacities, different from the Choquet integral, is introduced and characterized. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is then extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also when there is information only about a few events and not about all of them.
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.:
- Weber, Robert J., 1994. "Games in coalitional form," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 36, pages 1285-1303 Elsevier.
- Ehud Kalai & Eitan Zemel, 1980. "Generalized Network Problems Yielding Totally Balanced Games," Discussion Papers 425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
- Ebbe Groes & Hans JÛrgen Jacobsen & Birgitte Sloth & Torben TranÖs, 1998.
"Axiomatic characterizations of the Choquet integral,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 441-448.
- Ebbe Groes & Hans Jørgen Jacobsen & Birgitte Sloth & Torben Tranæs, 1996. "Axiomatic Characterizations of the Choquet Integral," Discussion Papers 96-19, University of Copenhagen. Department of Economics.
- Dow James & Werlang Sergio Ribeiro Da Costa, 1994.
"Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction,"
Journal of Economic Theory,
Elsevier, vol. 64(2), pages 305-324, December.
- Dow, James & Werlang, Sérgio Ribeiro da Costa, 1992. "Nash equilibrium under knightian uncertainty: breaking-down backward induction," Economics Working Papers (Ensaios Economicos da EPGE) 186, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
- Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
- Itzhak Gilboa, 1987.
"Expected Utility with Purely Subjective Non-Additive Probabilities,"
- Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
- Yaron Azrieli & Ehud Lehrer, 2007. "Market Games in Large Economies with a Finite Number of Types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 327-342, May.
- Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-1272, November.
- Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
- Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0504004. 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: (EconWPA)
If references are entirely missing, you can add them using this form.