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The St. Petersburg Paradox at 300

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  • Christian Seidl

Abstract

Nicolas Bernoulli’s discovery in 1713 that games of hazard may have infinite expected value, later called the St. Petersburg Paradox, initiated the development of expected utility in the following three centuries. An account of the origin and the solution concepts proposed for the St. Petersburg Paradox is provided. D’Alembert’s ratio test is used for a uniform treatment of the manifestations of the St. Petersburg Paradox and its solution proposals. It is also shown that a St. Petersburg Paradox can be solved or regained by appropriate transformations of the winnings or their utilities on the one hand or the probabilities on the other. This last feature is novel for the analysis of the St. Petersburg Paradox. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Christian Seidl, 2013. "The St. Petersburg Paradox at 300," Journal of Risk and Uncertainty, Springer, vol. 46(3), pages 247-264, June.
    • Handle: RePEc:kap:jrisku:v:46:y:2013:i:3:p:247-264
    DOI: 10.1007/s11166-013-9165-9
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    Cited by:

    1. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.
    2. 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.
    3. Yukalov, V.I., 2021. "A resolution of St. Petersburg paradox," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. 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.
    5. Daniel Muller & Tshilidzi Marwala, 2019. "Relative Net Utility and the Saint Petersburg Paradox," Papers 1910.09544, arXiv.org, revised May 2020.
    6. 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.
    7. Jean Baccelli, 2016. "L'analyse axiomatique et l'attitude par rapport au risque," Post-Print hal-01462286, HAL.
    8. 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.

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    More about this item

    Keywords

    St. Petersburg Paradox; Expected utility; Games of hazard; Risk attitude; D81; B16;
    All these keywords.

    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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