IDEAS home Printed from https://ideas.repec.org/p/zbw/cauewp/201204.html
   My bibliography  Save this paper

The Petersburg Paradox: Menger revisited

Author

Listed:
  • Seidl, Christian

Abstract

The Petersburg Paradox and its solutions are formulated in a uniform arrangement centered around d'Alembert's ratio test. All its aspects are captured using three mappings, a mapping from the natural numbers to the space of the winnings, a utility function defined on the space of the winnings, and a transformation of the utilities of the winnings. The main attempts at a solution of the Petersburg Paradox are labeled according to their most fervent proponents, viz. Bernoulli and Cramer, Buffon, and Menger. This paper also investigates the role of the probabilities for the Petersburg Paradox: they may well be used to solve a Petersburg Paradox, or to re-gain it by means of appropriate transformations. Thus, the probabilities are also instrumental for the Petersburg Paradox. The Petersburg Paradox can only be avoided for bounded utility functions. Its various solution proposals are but disguised attempts of filling in the missing behavioral justification for the boundedness of utility functions. This paper also corrects several misconceptions which have crept in the respective literature.

Suggested Citation

  • Seidl, Christian, 2012. "The Petersburg Paradox: Menger revisited," Economics Working Papers 2012-04, Christian-Albrechts-University of Kiel, Department of Economics.
    • Handle: RePEc:zbw:cauewp:201204
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/56036/1/688564992.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 136-138.
    3. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    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. Christian Seidl, 2013. "The St. Petersburg Paradox at 300," Journal of Risk and Uncertainty, Springer, vol. 46(3), pages 247-264, June.
    2. Marie Pfiffelmann, 2011. "Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting," Theory and Decision, Springer, vol. 71(3), pages 325-341, September.
    3. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    4. Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 71-83.
    5. Kim Kaivanto & Eike Kroll, 2014. "Alternation bias and reduction in St. Petersburg gambles," Working Papers 65600286, Lancaster University Management School, Economics Department.
    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. Salvatore Greco & Fabio Rindone, 2014. "The bipolar Choquet integral representation," Theory and Decision, Springer, vol. 77(1), pages 1-29, June.
    8. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    9. Pavlo Blavatskyy, 2024. "A puzzle of roulette gambling," Journal of Risk and Uncertainty, Springer, vol. 69(2), pages 219-234, October.
    10. Rieger, Marc Oliver, 2012. "Optimal financial investments for non-concave utility functions," Economics Letters, Elsevier, vol. 114(3), pages 239-240.
    11. Ganna Pogrebna & Pavlo Blavatskyy, 2009. "Coordination, focal points and voting in strategic situations: a natural experiment," IEW - Working Papers 403, Institute for Empirical Research in Economics - University of Zurich.
    12. Ido Erev & Ira Glozman & Ralph Hertwig, 2008. "What impacts the impact of rare events," Journal of Risk and Uncertainty, Springer, vol. 36(2), pages 153-177, April.
    13. Pavlo R. Blavatskyy, 2016. "Risk preferences of Australian academics: where retirement funds are invested tells the story," Theory and Decision, Springer, vol. 80(3), pages 411-426, March.
    14. Pavlo R. Blavatskyy, 2016. "A monotone model of intertemporal choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 785-812, October.
    15. Enrico Giorgi & Thorsten Hens, 2006. "Making prospect theory fit for finance," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 20(3), pages 339-360, September.
    16. Marie Pfiffelmann, 2007. "How to solve the St Petersburg Paradox in Rank-Dependent Models ?," Working Papers of LaRGE Research Center 2007-08, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    17. Rieger, Marc Oliver & Wang, Mei, 2004. "Cumulative prospect theory and the St.Petersburg paradox," Papers 04-28, Sonderforschungsbreich 504.
    18. David Peel & David Law, 2007. "Betting on odds on Favorites as an Optimal Choice in Cumulative Prospect Theory," Economics Bulletin, AccessEcon, vol. 4(26), pages 1-10.
    19. Llamazares, Bonifacio, 2018. "An analysis of the generalized TODIM method," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1041-1049.
    20. Ghazi, Soroush & Schneider, Mark, 2024. "Market value of rarity: A theory of fair value and evidence from rare baseball cards," Journal of Economic Behavior & Organization, Elsevier, vol. 219(C), pages 318-339.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:zbw:cauewp:201204. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/vakiede.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.