Time resolution of the St. Petersburg paradox: a rebuttal

Abstract

eters (2011) claims to provide a resolution of the three century old St Petersburg paradox by using time averages and thereby avoiding the use of utility theory completely. Peters also claims to have found an error in Menger (1934, 1967) who established the vulnerability of any unbounded utility function to the St Petersburg paradox. This paper argues that both these claims in Peters (2011) are incorrect. The time average argument can be circumvented by using a single random number (between zero and one) to represent the entire infinite sequence of coin tosses, or alternatively by applying a time reversal to the coin tossing. Menger’s proof can be reinstated by comparing the utility of playing the Super St Petersburg game to the utility of an arbitrarily large sure payoff.