IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v84y2018i4d10.1007_s11238-018-9659-7.html
   My bibliography  Save this article

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

Author

Listed:
  • V. I. Danilov

    (Russian Academy of Sciences)

  • A. Lambert-Mogiliansky

    (Paris School of Economics)

  • V. Vergopoulos

    (Université Paris 1 Panthéon-Sorbonne and Paris School of Economics)

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

  • 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.
    • Handle: RePEc:kap:theord:v:84:y:2018:i:4:d:10.1007_s11238-018-9659-7
    DOI: 10.1007/s11238-018-9659-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-018-9659-7
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-018-9659-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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.
    5. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    2. Danilov, V.I. & Lambert-Mogiliansky, A., 2018. "Targeting in quantum persuasion problem," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 142-149.
    3. Ariane Lambert-Mogiliansky & Adrian Calmettes, 2019. ""Phishing For (quantum-like) Phools" Theory and experimental evidence," PSE Working Papers halshs-02146862, HAL.
    4. Vladimir Ivanovitch Danilov & Ariane Lambert-Mogiliansky, 2017. "Preparing a (quantum) belief system," PSE Working Papers halshs-01542068, HAL.
    5. Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    6. Minardi, Stefania & Savochkin, Andrei, 2019. "Subjective contingencies and limited Bayesian updating," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1-45.
    7. Takashi Hayashi, 2012. "Expanding state space and extension of beliefs," Theory and Decision, Springer, vol. 73(4), pages 591-604, October.
    8. Esponda, Ignacio & Vespa, Emanuel, 2023. "Contingent Thinking and the Sure-Thing Principle: Revisiting Classic Anomalies in the Laboratory#," University of California at San Diego, Economics Working Paper Series qt32j4d5z2, Department of Economics, UC San Diego.
    9. Joseph E. Stiglitz, 2017. "The overselling of globalization," Business Economics, Palgrave Macmillan;National Association for Business Economics, vol. 52(3), pages 129-137, July.
    10. John Y. Campbell, 2016. "Restoring Rational Choice: The Challenge of Consumer Financial Regulation," American Economic Review, American Economic Association, vol. 106(5), pages 1-30, May.
    11. Joshua Schwartzstein & Adi Sunderam, 2021. "Using Models to Persuade," American Economic Review, American Economic Association, vol. 111(1), pages 276-323, January.
    12. Jacquemet, N. & Luchini, S. & Malézieux, A. & Shogren, J.F., 2020. "Who’ll stop lying under oath? Empirical evidence from tax evasion games," European Economic Review, Elsevier, vol. 124(C).
    13. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    14. 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.
    15. Robert Kast & André Lapied, 2010. "Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty," Theory and Decision, Springer, vol. 69(1), pages 27-53, July.
    16. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    17. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    18. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    19. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray," Theory and Decision, Springer, vol. 71(1), pages 1-10, July.
    20. Gérard Mondello, 2022. "Information Source's Reliability," GREDEG Working Papers 2022-21, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France, revised Oct 2022.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:84:y:2018:i:4:d:10.1007_s11238-018-9659-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.