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Expected utility theory under non-classical uncertainty

Author

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  • V. Danilov

    ()

  • A. Lambert-Mogiliansky

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Abstract

In this article, Savage's theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.
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Suggested Citation

  • V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
  • Handle: RePEc:kap:theord:v:68:y:2010:i:1:p:25-47
    DOI: 10.1007/s11238-009-9142-6
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    References listed on IDEAS

    as
    1. Danilov, V.I. & Lambert-Mogiliansky, A., 2008. "Measurable systems and behavioral sciences," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 315-340, May.
    2. Jacob Gyntelberg & Frank Hansen, 2004. "Expected Utility Theory with “Small Worlds”," FRU Working Papers 2004/04, University of Copenhagen. Department of Economics. Finance Research Unit.
    3. Ariane Lambert Mogiliansky & Shmuel Zamir & Herve Zwirn, 2003. "Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man," Discussion Paper Series dp343, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Ehud Lehrer & Eran Shmaya, 2005. "A Subjective Approach to Quantum Probability," Game Theory and Information 0503002, EconWPA.
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    Citations

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    Cited by:

    1. Vladimir Danilov & Ariane Lambert-Mogiliansky, 2017. "Preparing a (quantum) belief system," Post-Print halshs-01631568, HAL.
    2. Dino Borie, 2013. "Expected utility theory with non-commutative probability theory," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(2), pages 295-315, October.
    3. V. I. Yukalov & D. Sornette, 2012. "Quantum decision making by social agents," Papers 1202.4918, arXiv.org, revised Oct 2015.
    4. Ariane Lambert-Mogiliansky & Jerome Busemeyer, 2012. "Quantum Type Indeterminacy in Dynamic Decision-Making: Self-Control through Identity Management," Games, MDPI, Open Access Journal, vol. 3(2), pages 1-22, May.
    5. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Transparency in Public Life. A Quantum Cognition Perspective," PSE Working Papers halshs-01064980, HAL.
    6. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    7. Hammond, Peter J, 2011. "Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space," The Warwick Economics Research Paper Series (TWERPS) 969, University of Warwick, Department of Economics.
    8. Jérôme Busemeyer & Ariane Lambert-Mogiliansky, 2012. "Quantum Type Indeterminacy in Dynamic Decision-Making: Self-control Through Identity Management," Working Papers halshs-00692024, HAL.
    9. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Our (represented) World: A Quantum-Like Object," PSE Working Papers halshs-01152332, HAL.
    10. Boyer-Kassem, Thomas & Duchêne, Sébastien & Guerci, Eric, 2016. "Testing quantum-like models of judgment for question order effect," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 33-46.
    11. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    12. Haven, Emmanuel & Sozzo, Sandro, 2016. "A generalized probability framework to model economic agents' decisions under uncertainty," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 297-303.

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