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The St. Petersburg paradox: An experimental solution

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  • Da Silva, Sergio
  • Matsushita, Raul

Abstract

The St. Petersburg paradox refers to a gamble of infinite expected value, where people are likely to spend only a small entrance fee for it. There is a huge volume of literature that mostly concentrates on the psychophysics of the game; experiments are scant. Here, rather than focusing on the psychophysics, we offer an experimental, “physical” solution as if robots played the game. After examining the time series formed by one billion plays, we: confirm that there is no characteristic scale for this game; explicitly formulate the implied power law; and identify the type of α-stable distribution associated with the game. We find an α=1 and, thus, the underlying distribution of the game is a Cauchy flight, as hinted by Paul Samuelson.

Suggested Citation

  • Da Silva, Sergio & Matsushita, Raul, 2016. "The St. Petersburg paradox: An experimental solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 66-74.
    • Handle: RePEc:eee:phsmap:v:445:y:2016:i:c:p:66-74
    DOI: 10.1016/j.physa.2015.10.045
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. repec:cup:judgdm:v:4:y:2009:i:4:p:256-272 is not listed on IDEAS
    4. David Durand, 1957. "Growth Stocks And The Petersburg Paradox," Journal of Finance, American Finance Association, vol. 12(3), pages 348-363, September.
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    More about this item

    Keywords

    St. Petersburg paradox; α-stable distributions; Cauchy flight; Power laws;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

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