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The St. Petersburg Paradox at 300

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  • Christian Seidl

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    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

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    Bibliographic Info

    Article provided by Springer in its journal Journal of Risk and Uncertainty.

    Volume (Year): 46 (2013)
    Issue (Month): 3 (June)
    Pages: 247-264

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    Handle: RePEc:kap:jrisku:v:46:y:2013:i:3:p:247-264

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    Web page: http://www.springerlink.com/link.asp?id=100299

    Related research

    Keywords: St. Petersburg Paradox; Expected utility; Games of hazard; Risk attitude; D81; B16;

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    1. George J. Stigler, 1950. "The Development of Utility Theory. II," Journal of Political Economy, University of Chicago Press, vol. 58, pages 373.
    2. Shapley, Lloyd S., 1977. "Lotteries and menus: A comment on unbounded utilities," Journal of Economic Theory, Elsevier, vol. 14(2), pages 446-453, April.
    3. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    4. 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.
    5. 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.
    6. Bentham, Jeremy, 1781. "An Introduction to the Principles of Morals and Legislation," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number bentham1781.
    7. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    8. Morgenstern, Oskar, 1976. "The Collaboration between Oskar Morgenstern and John von Neumann on the Theory of Games," Journal of Economic Literature, American Economic Association, vol. 14(3), pages 805-16, September.
    9. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    10. Arrow, Kenneth J, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, MIT Press, vol. 88(1), pages 136-38, February.
    11. Shapley, Lloyd S., 1977. "The St. Petersburg paradox: A con games?," Journal of Economic Theory, Elsevier, vol. 14(2), pages 439-442, April.
    12. Tibor Neugebauer, 2010. "Moral Impossibility in the Petersburg Paradox : A Literature Survey and Experimental Evidence," LSF Research Working Paper Series 10-14, Luxembourg School of Finance, University of Luxembourg.
    13. Aumann, Robert J., 1977. "The St. Petersburg paradox: A discussion of some recent comments," Journal of Economic Theory, Elsevier, vol. 14(2), pages 443-445, April.
    14. 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.
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    Cited by:
    1. Gollier, Christian & Hammitt, James & Treich, Nicolas, 2013. "Risk and Choice: A Research Saga," IDEI Working Papers 804, Institut d'Économie Industrielle (IDEI), Toulouse.

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