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A new integral for capacities

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Author Info
Ehud Lehrer (Tel Aviv University)

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Abstract

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.

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File URL: http://129.3.20.41/eps/game/papers/0504/0504004.pdf
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Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0504004.

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Length: 17 pages
Date of creation: 10 Apr 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0504004

Note: Type of Document - pdf; pages: 17
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Web page: http://129.3.20.41

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Related research
Keywords: new integral; capacity; choquet integral; fuzzy capacity; concavity;

Other versions of this item:

Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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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.:
  1. 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. [Downloadable!] (restricted)
  2. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February. [Downloadable!] (restricted)
  3. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November. [Downloadable!] (restricted)
  4. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA. [Downloadable!]
  5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  6. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February. [Downloadable!] (restricted)
  7. Ebbe Groes & Hans JÛrgen Jacobsen & Birgitte Sloth & Torben TranÖs, 1998. "Axiomatic characterizations of the Choquet integral," Economic Theory, Springer, vol. 12(2), pages 441-448. [Downloadable!] (restricted)
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  8. 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. [Downloadable!]
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