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
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Julio Stern, Walter Carnielli and Juliana Bueno-Soler
Received: 16 February 2017 / Revised: 2 May 2017 / Accepted: 4 May 2017 / Published: 10 May 2017
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
. 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
the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes
as a random variable assuming values in
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
is uniformly distributed in
, for in this case there is a paradox.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Marcondes, D.; Peixoto, C.; Souza, K.; Wechsler, S. Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox. Philosophies 2017, 2, 11.
Marcondes D, Peixoto C, Souza K, Wechsler S. Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox. Philosophies. 2017; 2(2):11.
Marcondes, Diego; Peixoto, Cláudia; Souza, Kdson; Wechsler, Sergio. 2017. "Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox." Philosophies 2, no. 2: 11.
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