The Petersburg Paradox: Menger revisited
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.
|Date of creation:||2012|
|Contact details of provider:|| Postal: D-24098 Kiel,Wilhelm-Seelig-Platz 1|
Phone: 0431-880 3282
Fax: 0431-880 3150
Web page: http://www.vwl.uni-kiel.de/en
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, Oxford University Press, vol. 88(1), pages 136-138.
When requesting a correction, please mention this item's handle: RePEc:zbw:cauewp:201204. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics)
If references are entirely missing, you can add them using this form.