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Toward a Resolution of the St.Petersburg Paradox

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  • Mamoru Kaneko

    (Emeritus Professor, Waseda University and University of Tsukuba)

Abstract

We study the St.Petersburg paradox from the viewpoint of bounded intelligence. Following Llyod Shapley, we reformulate its coin-tossing gamble introducing a finite budget of the banker, while this is as a resolution in the narrow sense as long as the standard expected reward criterion is adopted. It is still impossible for both banker and people to participate and to generate positive profits. We introduce cognitive bounds to people to modify the expected reward criterion and show that many people are incomparable to between participation and not. This is a rationalistic though people have cognitive bounds, and we take one more step of going to semi-rationalistic behavioral-probability for incomparable alternatives. This shows that some people show positive probabilities of participation in the coin-tossing with a fee producing positive profits for the banker. The last part is formulated as a monopoly market and its activeness is shown by the Mote Carlo simulation method.

Suggested Citation

  • Mamoru Kaneko, 2020. "Toward a Resolution of the St.Petersburg Paradox," Working Papers 2014, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2014
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    Keywords

    St.Petersburg Paradox; Shapley's Modification; Expected Utility Theory with Probability Grids; Cognitive Bounds; Bounded Intelligence; Incomparability; behavioralprobability; Monte Carlo Method;
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