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Expected utility theory with ”small worlds”


  • Jacob Gyntelberg

    (Nordea Bank, Copenhagen)

  • Frank Hansen

    (Institute of Economics, University of Copenhagen)


We formulate a new theory of expected utility under uncertainty based on the notion of an event-lattice, which is a natural generalization of a Savage state space. The modelling of uncertainty is based on the idea that the decision maker for each group of related decisions to be taken creates a ”small world” which functions as a local state space. We introduce a set of preference axioms similar in spirit to the Savage axioms, and show that they lead to a generalization of the standard von Neumann-Savage theory of expected utility. The generalization allows for an intuitive distinction between risk and uncertainty. In each ”small world” risk is described by an additive probability measure; and these local risk measures all appear as restrictions of a common integrated additive expectation functional which is defined on the ”grand world”, thereby providing numerical expressions to the notion of uncertainty. We illustrate the use of the theory for the Ellsberg paradox and for some portfolio decisions which cannot be captured by the standard von Neumann-Savage theory.

Suggested Citation

  • Jacob Gyntelberg & Frank Hansen, 2004. "Expected utility theory with ”small worlds”," Discussion Papers 04-20, University of Copenhagen. Department of Economics, revised Jan 2005.
  • Handle: RePEc:kud:kuiedp:0420

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    Cited by:

    1. Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2007. "Non-classical expected utility theory with application to type indeterminacy," PSE Working Papers halshs-00587721, HAL.
    2. Hammond, Peter J., 2011. "Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space," Economic Research Papers 270755, University of Warwick - Department of Economics.
    3. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    4. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    5. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
    6. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    7. Ehud Lehrer & Eran Shmaya, 2005. "A Subjective Approach to Quantum Probability," Game Theory and Information 0503002, University Library of Munich, Germany.

    More about this item


    expected utility; decision making under uncertainty;

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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