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Dynamic consistency of expected utility under non-classical (quantum) uncertainty

Author

Listed:
  • Vladimir Ivanovitch Danilov

    (CEMI - Central Institute of Economics and Mathematics of the RAS)

  • Ariane Lambert-Mogiliansky

    (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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

  • Vassili Vergopoulos

    (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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Quantum cognition in decision making is a recent and rapidly growing field. In this paper, we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework, we formulate axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neumann–Lüders postulate applied to beliefs. A dynamically consistent quantum-like agent may violate dynamic recursive consistency, however. This feature suggests interesting applications in behavioral economics as we illustrate in an example of persuasion.

Suggested Citation

  • Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky & Vassili Vergopoulos, 2018. "Dynamic consistency of expected utility under non-classical (quantum) uncertainty," Post-Print halshs-01885415, HAL.
    • Handle: RePEc:hal:journl:halshs-01885415
    DOI: 10.1007/s11238-018-9659-7
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    References listed on IDEAS

    as
    1. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    2. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
    3. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    4. George A. Akerlof & Robert J. Shiller, 2015. "Phishing for Phools: The Economics of Manipulation and Deception," Economics Books, Princeton University Press, edition 1, number 10534.
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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. Ariane Lambert-Mogiliansky & Adrian Calmettes, 2019. ""Phishing For (quantum-like) Phools" Theory and experimental evidence," PSE Working Papers halshs-02146862, HAL.
    4. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    5. Khrennikova, Polina & Patra, Sudip, 2019. "Asset trading under non-classical ambiguity and heterogeneous beliefs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 562-577.

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