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

Philosophies

Marcondes, Diego¹ 

关键词: St. Petersburg paradox;    entrance fees;    Bayesian analysis;   

DOI  :  10.3390/philosophies2020011

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

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 isθ( 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 isθ( 1 / 2 < θ < 1 ) the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takesθas 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 whichθis uniformly distributed in ( 1 / 2 , 1 ), for in this case there is a paradox.

【 授权许可】

CC BY