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Expected utility theory under non-classical uncertainty

Author

Listed:
  • Vladimir Ivanovitch Danilov

    (CEMI - Central Economic Mathematical Institute - RAS - Russian Academy of Sciences [Moscow])

  • Ariane Lambert-Mogiliansky

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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.

Suggested Citation

  • Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Post-Print halshs-00754482, HAL.
    • Handle: RePEc:hal:journl:halshs-00754482
    DOI: 10.1007/s11238-009-9142-6
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    Cited by:

    1. Danilov, V.I. & Lambert-Mogiliansky, A., 2018. "Targeting in quantum persuasion problem," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 142-149.
    2. Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2017. "Preparing a (quantum) belief system," Working Papers halshs-01542068, HAL.
    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 & François Dubois, 2015. "Transparency in Public Life. A Quantum Cognition Perspective," PSE Working Papers halshs-01064980, HAL.
    5. Ariane Lambert-Mogiliansky & Adrian Calmettes, 2019. ""Phishing For (quantum-like) Phools" Theory and experimental evidence," PSE Working Papers halshs-02146862, HAL.
    6. V. I. Danilov & A. Lambert-Mogiliansky & V. Vergopoulos, 2018. "Dynamic consistency of expected utility under non-classical (quantum) uncertainty," Theory and Decision, Springer, vol. 84(4), pages 645-670, June.
    7. Hammond, Peter J., "undated". "Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space," Economic Research Papers 270755, University of Warwick - Department of Economics.
    8. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    9. 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.
    10. 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.
    11. 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.
    12. Ariane Lambert-Mogiliansky & Jerome Busemeyer, 2012. "Quantum Type Indeterminacy in Dynamic Decision-Making: Self-Control through Identity Management," Games, MDPI, vol. 3(2), pages 1-22, May.
    13. Ismaël Rafaï & Sébastien Duchêne & Eric Guerci & Irina Basieva & Andrei Khrennikov, 2022. "The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus," Theory and Decision, Springer, vol. 92(2), pages 387-406, March.
    14. 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.
    15. Ariane Lambert-Mogiliansky & François Dubois, 2015. "Our (represented) World: A Quantum-Like Object," Working Papers halshs-01152332, HAL.
    16. Haven, Emmanuel & Khrennikova, Polina, 2018. "A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 186-197.

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