Original Research

Solving Daniel Bernoulli’s St Petersburg paradox: The paradox which is not and never was

Robert W. Vivian
South African Journal of Economic and Management Sciences | Vol 6, No 2 | a3317 | DOI: https://doi.org/10.4102/sajems.v6i2.3317 | © 2019 Robert W. Vivian | This work is licensed under CC Attribution 4.0
Submitted: 31 July 2019 | Published: 30 June 2003

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Robert W. Vivian, School of Economic and Business Sciences, University of the Witwatersrand, South Africa

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Abstract

It has been accepted for over 270 years that the expected monetary value (EMV) of the St Petersburg game is infinite. Accepting this leads to a paradox; no reasonable person is prepared to pay the predicted large sum to play the game but will only pay, comparatively speaking, a very moderate amount. This paradox was ‘solved’ using cardinal utility. This article demonstrates that the EMV of the St Petersburg game is a function of the number of games played and is infinite only when an infinite number of games is played. Generally, the EMV is a very moderate amount, even when a large number of games is played. It is of the same order as people are prepared to offer to play the game. There is thus no paradox. Cardinal utility is not required to explain the behaviour of the reasonable person offering to play the game.

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Crossref Citations

1. The median-based resolution of the St. Petersburg paradox
Takuya Okabe, Momoka Nii, Jin Yoshimura
Physics Letters A  vol: 383  issue: 26  first page: 125838  year: 2019  
doi: 10.1016/j.physleta.2019.125838