A logical analysis of a 259-year-old paradox sometimes employed to attack the use of expected monetary values in decision theory or game theory. In the "Petersburg game," first propounded by Nicolas Bernoulli in 1713, a person who is indifferent to risk is asked to pay a large entrance fee to a gambling game in which he will receive an uncertain payoff of infinite expected value. From the nature of the game, however, it is apparent that no rational person would accept this offer. This paper specifies a sufficient reason: that no rational person would believe the payoff. Hence, the Petersburg game does not expose any logical or mathematical absurdity in a risk-neutral utility for money. Moreover, the empirically absurd conclusion that it leads to rests on an additional, easily overlooked assumption about the credulity of the gambler — an assumption that is itself empirically absurd.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
Permission is given to duplicate this electronic document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes. Unauthorized posting of RAND PDFs to a non-RAND Web site is prohibited. RAND PDFs are protected under copyright law. For information on reprint and linking permissions, please visit the RAND Permissions page.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.