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Integral with Respect to Non-additive Measure in Economics

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Non-Additive Measures

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 310))

Abstract

This chapter surveys the use of non-additive measures in economics, focusing on their use in preference theory. In economics, the risky situation where the probability measure is known and the uncertain situation where even the probability measure is unknown had tended not to be distinguished. This is mainly because of Savage’s theorem which states that if an agent complies with some set of behavioral axioms, she may be regarded as trying to maximize the expected utility with respect to some probability measure. This is called subjective expected utility (SEU) theory. However, the plausible and robust preference patterns which cannot be explained by SEU is known. The most famous one among them is Ellsberg’s paradox. The attempts to resolve these anomalies by using non-additive measures were initiated by D. Schmeidler and I. Gilboa in 1980’s. The main purpose of this chapter is to explain their theories, emphasizing representation theorems by means of non-additive measures. We will see that their models nicely resolve Ellsberg’s paradox.

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Author information

Authors and Affiliations

  1. Faculty of Economics, Keio University, Keio, Japan

    Hiroyuki Ozaki

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  1. Hiroyuki Ozaki
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Editor information

Editors and Affiliations

  1. IIIA-CSIC, Bellaterra, Spain

    Vicenc Torra

  2. Toho Gakuen, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. European Centre for Soft Computing, Mieres, Spain

    Michio Sugeno

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Ozaki, H. (2014). Integral with Respect to Non-additive Measure in Economics. In: Torra, V., Narukawa, Y., Sugeno, M. (eds) Non-Additive Measures. Studies in Fuzziness and Soft Computing, vol 310. Springer, Cham. https://doi.org/10.1007/978-3-319-03155-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-03155-2_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03154-5

  • Online ISBN: 978-3-319-03155-2

  • eBook Packages: EngineeringEngineering (R0)

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