IDEAS home Printed from https://ideas.repec.org/a/nea/journl/y2016i32p12-29.html
   My bibliography  Save this article

Utility Theory of General Lotteries

Author

Listed:
  • Danilov, V.

    (Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia)

Abstract

Generalizing the notions of roulette lotteries, horse lotteries, and quantum lotteries, we introduce maximally general notion of lottery. It uses the theory of ordered vector spaces. Under appropriate conditions on preference relation between lotteries (generalizing the conditions considered by von Neumann, Savage, Aumann and Anscombe) we give a formula for the utility of lotteries. Its ingredients are a utility function of prizes and a belief functional giving probability of events. Inthe second part of paper we discuss the issue about updating of beliefs under receiving additional information. We give a formula for the updated belief (which generates Bayes rule and von Neumann-Luders projection postulate), suppose that the ordered vector space is the real part of C*-algebra.

Suggested Citation

  • Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    • Handle: RePEc:nea:journl:y:2016:i:32:p:12-29
    as

    Download full text from publisher

    File URL: http://www.econorus.org/repec/journl/2016-32-12-29r.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    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. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    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. Bleichrodt, Han & Eichberger, Jürgen & Grant, Simon & Kelsey, David & Li, Chen, 2021. "Testing dynamic consistency and consequentialism under ambiguity," European Economic Review, Elsevier, vol. 134(C).
    6. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
    7. Ozgur Evren, 2024. "Second-Order Representations: A Bayesian Approach," Working Papers w0291, New Economic School (NES).
    8. 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.
    9. Han Bleichrodt & Jurgen Eichberger & Simon Grant & David Kelsey & Chen Li, 2018. "A Test of Dynamic Consistency and Consequentialism in the Presence of Ambiguity," Discussion Papers 1803, University of Exeter, Department of Economics.
    10. Nobuo Koida, 2012. "Nest-monotonic two-stage acts and exponential probability capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 99-124, May.
    11. 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.
    12. Yaron Azrieli & Christopher P. Chambers & Paul J. Healy, 2020. "Incentives in experiments with objective lotteries," Experimental Economics, Springer;Economic Science Association, vol. 23(1), pages 1-29, March.
    13. 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.
    14. 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.
    15. 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.
    16. Nathalie Etchart-Vincent, 2002. "Adequate Moods for non-EU Decision Making in a Sequential Framework," Post-Print halshs-00004830, HAL.
    17. 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.
    18. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    19. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    20. Brian Hill, 2009. "Confidence and ambiguity," Working Papers hal-00489870, HAL.

    More about this item

    Keywords

    utility function; probability; measurement; ordered vector space; updating; C *-algebra;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

    Statistics

    Access and download statistics

    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:nea:journl:y:2016:i:32:p:12-29. 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: Alexey Tcharykov (email available below). General contact details of provider: https://edirc.repec.org/data/nearuea.html .

    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.