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Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox

Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, Brazil
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These authors contributed equally to this work.
Academic Editors: Julio Stern, Walter Carnielli and Juliana Bueno-Soler
Philosophies 2017, 2(2), 11; https://doi.org/10.3390/philosophies2020011
Received: 16 February 2017 / Revised: 2 May 2017 / Accepted: 4 May 2017 / Published: 10 May 2017
(This article belongs to the Special Issue Logic, Inference, Probability and Paradox)
In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ ( 0 < θ < 1 / 2 ) . The deduction of those fees is the main result of Section 2. We then propose a Bayesian approach to the problem. When the probability of heads is θ ( 1 / 2 < θ < 1 ) the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in ( 1 / 2 , 1 ) the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in ( 1 / 2 , 1 ) , for in this case there is a paradox. View Full-Text
Keywords: St. Petersburg paradox; entrance fees; Bayesian analysis St. Petersburg paradox; entrance fees; Bayesian analysis
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Marcondes, D.; Peixoto, C.; Souza, K.; Wechsler, S. Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox. Philosophies 2017, 2, 11.

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