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The Petersburg Paradox: Menger revisited

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  • 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.

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  • 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
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    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.
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