On the St. Petersburg paradox
type: Item
instance of: scholarly article
title: On the St. Petersburg paradox
zbMATH Open document ID: 0762.01007
DOI: 10.1007/BF00329984
author: Jacques Dutka
published in: Archive for History of Exact Sciences
publication date: 1993-02-09T00:00:00Z
review text: The originator of the St. Petersburg paradox was \textit{Niklaus (1) Bernoulli} (1687-1759). He sent several game problems to \textit{P. R. de Montmort} (esp. no. 4 and 5 with infinite expectation but in which the experienced gambler would risk at most twenty ducats). He received an unsatisfactory solution by the Swiss mathematician \textit{Gabriel Cramer} (1704-1752) and later in 1731 the solution by \textit{Daniel (1) Bernoulli} (1700-1782), which has been published in Commentarii Akad. Sci. Petropolis 5, 175-192 (1738). Therefore \textit{d'Alembert} coined the expression `St. Petersburg Paradox'. A historical exposition of its genesis is given and a sketch of some of the attempts at its solution is worthwhile since in the modern era it has attracted the attention not only of the probabilists, statisticians and game theorists, but also economists. The early development of probability theory is also sketched, e.g. \textit{G. Cardano} (1539), \textit{Guido Grandi} (1671-1742), \textit{Blaise Pascal} (1623-1662) with his famous wager in the Pensées (a forerunner of decision theory), \textit{Ch. Huygens} (1629-1695) with his five problems, \textit{Gottfried W. Leibniz} (1646-1716) with his degree of certainty. Some earlier and new reviews of the problem are mentioned as \textit{E. Czuber} (1882), \textit{Paul A. Samuelson} (1977), and \textit{Gérard Jorland} (1987), the latter one contains several errors. In 1985 \textit{A. Martin-Löf} obtained a limit theorem for the total gain in a series of St. Petersburg games. A computer simulation relevant to the paradox is being added. 48 references.
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60-03
zbMATH DE Number: 110342
zbMATH Keywords: St. Petersburg paradox
zbMATH Keywords: infinite expectation
zbMATH Keywords: moral expectation
zbMATH Keywords: utility
zbMATH Keywords: history of probability
zbMATH Keywords: Daniel Bernoulli
Wikidata QID: Q29541967
MaRDI profile type: Publication
cites work: Q5797010
cites work: Q5727620
cites work: Q5831977
cites work: Q5818455
cites work: Q5538132
cites work: Huygens' foundations of probability
cites work: Q4068666
cites work: Q4754553
cites work: A limit theorem which clarifies the ‘Petersburg Paradox'
cites work: Q3933679
cites work: Pascal and the Invention of Probability Theory
cites work: Q4403141
cites work: The St. Petersburg paradox: A con game?
cites work: Early history of the theory of probability
cites work: Theory of games and economic behavior.
full work available at URL: https://doi.org/10.1007/bf00329984
OpenAlex ID: W2041710248
Recommended article: On the St. Petersburg Paradox
Recommended article: A resolution of St. Petersburg paradox
Recommended article: Q4838517
Recommended article: The St. Petersburg paradox: an experimental solution
description: scientific article; zbMATH DE number 110342