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

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Entrance Fee

**Theorem**

**1.**

## 3. Bayesian Approach

**Lemma**

**1.**

**Lemma**

**2.**

**Theorem**

**2.**

## 4. Uniformly Distributed $\mathbf{\theta}$

**Theorem**

**3.**

## Author Contributions

## Conflicts of Interest

## Appendix A

**Proof 1**

**(Theorem 1).**

**Proof 2**

**(Lemma 1).**

**Proof 3**

**(Lemma 2).**

**Proof 4**

**(Theorem 2).**

**Proof 5**

**(Theorem 3).**

## References

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**Figure 1.**Entrance fees for different values of n and for $\theta \in \{0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45\}$. Each figure presents the graph of ${e}_{n}$ as a function of n, for selected values of $\theta $, that are the values on top of each graph. The x-axis presents the values of n and y-axis the values of ${e}_{n}$, for each considered $\theta $.

**Table 1.**The maximum value c someone with total wealth w must be willing to pay to play a trial of the St. Petersburg game according to the logarithm utility function, for different values of w.

Total Wealth $\left(\mathit{w}\right)$ | Maximum Value $\left(\mathit{c}\right)$ | Total Wealth $\left(\mathit{w}\right)$ | Maximum Value $\left(\mathit{c}\right)$ |
---|---|---|---|

2 | 3.35 | 500 | 9.99 |

4 | 4 | 1000 | 10.96 |

20 | 5.77 | 10,000 | 14.24 |

50 | 6.90 | 100,000 | 17.56 |

100 | 7.80 | 500,000 | 19.88 |

200 | 8.73 | 1,000,000 | 20.88 |

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## Share and Cite

**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.
https://doi.org/10.3390/philosophies2020011

**AMA Style**

Marcondes D, Peixoto C, Souza K, Wechsler S. Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox. *Philosophies*. 2017; 2(2):11.
https://doi.org/10.3390/philosophies2020011

**Chicago/Turabian Style**

Marcondes, Diego, Cláudia Peixoto, Kdson Souza, and Sergio Wechsler. 2017. "Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox" *Philosophies* 2, no. 2: 11.
https://doi.org/10.3390/philosophies2020011