IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/5233.html
   My bibliography  Save this paper

Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was

Author

Listed:
  • Vivian, Robert William

Abstract

It has been accepted for over 270 years that the expected monetary value (EMV)of the St Petersburg game is infinite. Accepting this leads to a paradox; no reasonable person is prepared to pay the predicted large sum to play the game but will only pay, comparatively speaking, a very moderate amount. This paradox was 'solved' using cardinal utility. This article demonstrates that the EMV of the St Petersburg game is a function of the number ofgames played and is infmite only when an infinite number of games is played. Generally, the EMV is a very moderate amount, even when a large number of games is played. It is of the same order as people are prepared to offer to play the game. There is thus no paradox. Cardinal utility is not required to explain the behaviour of the reasonable person offering to play the game.

Suggested Citation

  • Vivian, Robert William, 2003. "Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was," MPRA Paper 5233, University Library of Munich, Germany, revised 2003.
    • Handle: RePEc:pra:mprapa:5233
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/5233/1/MPRA_paper_5233.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Samuelson, Paul A, 1977. "St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described," Journal of Economic Literature, American Economic Association, vol. 15(1), pages 24-55, March.
    2. George J. Stigler, 1950. "The Development of Utility Theory. I," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 307-307.
    3. Shapley, Lloyd S., 1977. "The St. Petersburg paradox: A con games?," Journal of Economic Theory, Elsevier, vol. 14(2), pages 439-442, April.
    4. Matthew Rabin & Richard H. Thaler, 2013. "Anomalies: Risk aversion," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 27, pages 467-480, World Scientific Publishing Co. Pte. Ltd..
    5. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-563, June.
    6. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    7. Brito, D. L., 1975. "Becker's theory of the allocation of time and the St. Petersburg Paradox," Journal of Economic Theory, Elsevier, vol. 10(1), pages 123-126, February.
    8. Epps, Thomas W, 1978. "Financial Risk and the St. Petersburg Paradox: Comment," Journal of Finance, American Finance Association, vol. 33(5), pages 1455-1456, December.
    9. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
    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. Benjamin Y. Hayden & Michael L. Platt, 2009. "The mean, the median, and the St. Petersburg paradox," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 4(4), pages 256-272, June.
    2. Vivian, Robert William, 2006. "Considering the Pasadena "Paradox"," MPRA Paper 5232, University Library of Munich, Germany, revised Jun 2006.
    3. Vivian, Robert William, 2008. "Considering the Harmonic Sequence "Paradox"," MPRA Paper 21216, University Library of Munich, Germany.
    4. repec:cup:judgdm:v:4:y:2009:i:4:p:256-272 is not listed 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. Christian Seidl, 2013. "The St. Petersburg Paradox at 300," Journal of Risk and Uncertainty, Springer, vol. 46(3), pages 247-264, June.
    2. Helga Fehr-Duda & Thomas Epper, 2012. "Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 567-593, July.
    3. Herzfeld, Thomas & Jongeneel, Roel, 2012. "Why do farmers behave as they do? Understanding compliance with rural, agricultural, and food attribute standards," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 29(1), pages 250-260.
    4. Benjamin Y. Hayden & Michael L. Platt, 2009. "The mean, the median, and the St. Petersburg paradox," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 4(4), pages 256-272, June.
    5. Bruno S. Frey & Matthias Benz, 2004. "From Imperialism to Inspiration: A Survey of Economics and Psychology," Chapters, in: John B. Davis & Alain Marciano & Jochen Runde (ed.), The Elgar Companion To Economics and Philosophy, chapter 4, Edward Elgar Publishing.
    6. James C. Cox & Eike B. Kroll & Marcel Lichters & Vjollca Sadiraj & Bodo Vogt, 2019. "The St. Petersburg paradox despite risk-seeking preferences: an experimental study," Business Research, Springer;German Academic Association for Business Research, vol. 12(1), pages 27-44, April.
    7. William Harbaugh & Kate Krause & Lise Vesterlund, 2002. "Risk Attitudes of Children and Adults: Choices Over Small and Large Probability Gains and Losses," Experimental Economics, Springer;Economic Science Association, vol. 5(1), pages 53-84, June.
    8. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    9. Bronshtein, E. & Fatkhiev, O., 2018. "A Note on St. Petersburg Paradox," Journal of the New Economic Association, New Economic Association, vol. 38(2), pages 48-53.
    10. Carlos Laciana & Elke Weber, 2008. "Correcting expected utility for comparisons between alternative outcomes: A unified parameterization of regret and disappointment," Journal of Risk and Uncertainty, Springer, vol. 36(1), pages 1-17, February.
    11. repec:cup:judgdm:v:4:y:2009:i:4:p:256-272 is not listed on IDEAS
    12. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    13. Horst Zank, 2010. "Consistent probability attitudes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 167-185, August.
    14. Eike B. Kroll & Bodo Vogt, 2009. "The St. Petersburg Paradox despite risk-seeking preferences: An experimental study," FEMM Working Papers 09004, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    15. Tuthill, Jonathan W. & Frechette, Darren L., 2002. "Non-Expected Utility Theories: Weighted Expected, Rank Dependent, And Cumulative Prospect Theory Utility," 2002 Conference, April 22-23, 2002, St. Louis, Missouri 19073, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    16. Dagsvik, John K., 2015. "Stochastic models for risky choices: A comparison of different axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 81-88.
    17. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    18. Chua, Jess H. & Chrisman, James J. & De Massis, Alfredo & Wang, Hao, 2018. "Reflections on family firm goals and the assessment of performance," Journal of Family Business Strategy, Elsevier, vol. 9(2), pages 107-113.
    19. Luís Santos-Pinto & Adrian Bruhin & José Mata & Thomas Åstebro, 2015. "Detecting heterogeneous risk attitudes with mixed gambles," Theory and Decision, Springer, vol. 79(4), pages 573-600, December.
    20. Kemal Ozbek, 2024. "Expected utility, independence, and continuity," Theory and Decision, Springer, vol. 97(1), pages 1-22, August.
    21. Bikhchandani, Sushil & Segal, Uzi, 2014. "Transitive regret over statistically independent lotteries," Journal of Economic Theory, Elsevier, vol. 152(C), pages 237-248.

    More about this item

    Keywords

    St Petersburg paradox; St Petersburg game; expected utility; decision theory;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:pra:mprapa:5233. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.