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A Radon-Nikodym approach to measure information

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  • Yann Rébillé

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

Abstract

We consider a decision maker facing uncertainty which behaves as a subjective expected utility maximizer. The value of information is traditionnaly captured as a greater expected utility the decision maker can achieve by selecting a best strategy as information arrives. We deal with the limit process of being better informed and introduce an information density function depending soley on the states that gives an exact least upper bound to being more informed. This information density function is given by a Radon-Nikodym's type theorem for set functions and is explicitely computed for the countable case.

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  • Yann Rébillé, 2010. "A Radon-Nikodym approach to measure information," Working Papers hal-00526251, HAL.
    • Handle: RePEc:hal:wpaper:hal-00526251
    Note: View the original document on HAL open archive server: https://hal.science/hal-00526251
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    References listed on IDEAS

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    1. Lehrer, Ehud & Rosenberg, Dinah, 2006. "What restrictions do Bayesian games impose on the value of information?," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 343-357, June.
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    4. Kennan, John, 1981. "The Existence of Expected Utility Maximizing Decisions When Utility Is Unbounded," Econometrica, Econometric Society, vol. 49(1), pages 215-218, January.
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    Keywords

    Decision making under uncertainty; value of information; expected utility; capacity; Radon-Nikodyn derivative;
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