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Solving Daniel Bernoulli's St Petersburg Paradox: The Paradox which is not and never was

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  • Vivian, Robert William

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 ofgames played and is infmite 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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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5233.

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Date of creation: 2003
Date of revision: 2003
Publication status: Published in South African Journal of Economic & Management Sciences NS6.2(2003): pp. 331-345
Handle: RePEc:pra:mprapa:5233

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Keywords: St Petersburg paradox; St Petersburg game; expected utility; decision theory;

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References

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  1. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-54, Summer.
  2. 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.
  3. Epps, Thomas W, 1978. "Financial Risk and the St. Petersburg Paradox: Comment," Journal of Finance, American Finance Association, vol. 33(5), pages 1455-56, December.
  4. 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.
  5. Matthew Rabin & Richard H. Thaler, 2001. "Anomalies: Risk Aversion," Journal of Economic Perspectives, American Economic Association, vol. 15(1), pages 219-232, Winter.
  6. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
  7. Shapley, Lloyd S., 1977. "The St. Petersburg paradox: A con games?," Journal of Economic Theory, Elsevier, vol. 14(2), pages 439-442, April.
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Cited by:
  1. Vivian, Robert William, 2008. "Considering the Harmonic Sequence "Paradox"," MPRA Paper 21216, University Library of Munich, Germany.
  2. Benjamin Y. Hayden & Michael L. Platt, 2009. "The mean, the median, and the St. Petersburg paradox," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 4(4), pages 256-272, June.
  3. Vivian, Robert William, 2006. "Considering the Pasadena "Paradox"," MPRA Paper 5232, University Library of Munich, Germany, revised Jun 2006.

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