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The Petersburg Paradox at 300

Author

Listed:
  • Seidl, Christian
Abstract
In 1713 Nicolas Bernoulli sent to de Montmort several mathematical problems, the fifth of which was at odds with the then prevailing belief that the advantage of games of hazard follows from their expected value. In spite of the infinite expected value of this game, no gambler would venture a major stake in this game. In this year, de Montmort published this problem in his Essay d'analyse sur les jeux de hazard. By dint of this book the problem became known to the mathematics profession and elicited solution proposals by Gabriel Cramer, Daniel Bernoulli (after whom it became known as the Petersburg Paradox), and Georges de Buffon. Karl Menger was the first to discover that bounded utility is a necessary and sufficient condition to warrant a finite expected value of the Petersburg Paradox. It was, in particular, Menger's article which provided an important cue for the development of expected utility by von Neumann and Morgenstern. The present paper gives a concise account of the origin of the Petersburg Paradox and its solution proposals. In its third section, it provides a rigorous analysis of the Petersburg Paradox from the uniform methodological vantage point of d'Alembert's ratio text. Moreover, it is shown that appropriate mappings of the winnings or of the probabilities can solve or regain a Petersburg Paradox, where the use of probabilities seems to have been overlooked by the profession.

Suggested Citation

  • Seidl, Christian, 2012. "The Petersburg Paradox at 300," Economics Working Papers 2012-10, Christian-Albrechts-University of Kiel, Department of Economics.
    • Handle: RePEc:zbw:cauewp:201210
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    References listed on IDEAS

    as
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    Cited by:

    1. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    2. Ulrich Schmidt & Christian Seidl, 2014. "Reconsidering the common ratio effect: the roles of compound independence, reduction, and coalescing," Theory and Decision, Springer, vol. 77(3), pages 323-339, October.
    3. 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.
    4. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.
    5. Yukalov, V.I., 2021. "A resolution of St. Petersburg paradox," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    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. Daniel Muller & Tshilidzi Marwala, 2019. "Relative Net Utility and the Saint Petersburg Paradox," Papers 1910.09544, arXiv.org, revised May 2020.
    8. Jean Baccelli, 2016. "L'analyse axiomatique et l'attitude par rapport au risque," Post-Print hal-01462286, HAL.

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    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical

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