From St. Petersburg to Monte Carlo: A Resolution Rediscovered and Affirmed
18 Pages Posted: 1 Nov 2017 Last revised: 11 Mar 2021
Date Written: October 1, 2017
The St. Petersburg paradox has served as an intriguing pedagogical device since it was described by Nicolas Bernoulli and Daniel Bernoulli in the 1700s. Many explanations of the paradox have been offered, most involving either theories of individual behavior or the practical difficulties of playing the game. We do not revisit any of the conventional explanations. Rather, we endeavor to demonstrate that the premise underlying the paradox – that the St. Petersburg game’s expected value is infinite – is mistaken. The analysis focuses on how the probability distribution of the game’s duration determines and limits the expected value. We do not claim precedence on so fundamental a resolution of the paradox. Our analysis is guided by the approach first described by the mathematician William Feller in 1945. We conduct a massive array of computer simulations within the framework suggested by Feller’s approach. The simulation results allow for an empirical evaluation of his coherent resolution.
Keywords: St. Petersburg Paradox, Feller’s Resolution, empirical analysis of simulation results
JEL Classification: C70, C63, B16, 91A60
Suggested Citation: Suggested Citation