It is sometimes concluded from the St. Petersburg paradox that von Neumann-Morgenstern utility functions must be bounded. Some axiom systems for expected utility avoid this conclusion and allow for unbounded utility functions. This note goes a step further and constructs an axiom system which may yield a utility function that takes the value plus infinity. Such a utility function is potentially applicable in situations where “blank checks” or “infinite menus” are ranked along with other prospects.
The Utility of Infinite Menus
By Lars Tyge Nielsen
Economics Letters 39 (1992), 43-47
Abstract
It is sometimes concluded from the St. Petersburg paradox that von Neumann-Morgenstern utility functions must be bounded. Some axiom systems for expected utility avoid this conclusion and allow for unbounded utility functions. This note goes a step further and constructs an axiom system which may yield a utility function that takes the value plus infinity. Such a utility function is potentially applicable in situations where “blank checks” or “infinite menus” are ranked along with other prospects.