The time resolution of the St. Petersburg paradox

TL;DR

This paper offers a utility-free resolution to the St. Petersburg paradox by analyzing the time-average performance of the lottery, providing a mathematically equivalent but conceptually distinct approach from traditional utility-based solutions.

Contribution

It introduces a novel time-based approach to resolve the paradox without relying on utility functions, simplifying the conceptual framework.

Findings

Time-average performance matches Bernoulli's utility-based solution

Eliminates the need for arbitrary utility functions

Provides a conceptually different resolution method

Abstract

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.