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A new integral for capacities

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  • Ehud Lehrer

    (Tel Aviv University)

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://128.118.178.162/eps/game/papers/0504/0504004.pdf
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Bibliographic 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://128.118.178.162

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

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References

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  9. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA.
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Cited by:
  1. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer, vol. 56(1), pages 33-58, May.
  2. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.
  3. Ehud Lehrer & Roee Tepper, 2013. "Concave Expected Utility and Event Separability," Levine's Working Paper Archive 786969000000000809, David K. Levine.

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