A Resolution of St. Petersburg Paradox

TL;DR

This paper offers a rigorous mathematical resolution to the longstanding St. Petersburg paradox using a probabilistic approach, clarifying its implications for decision theory and utility functions.

Contribution

It introduces a novel probabilistic method to resolve the original paradox, addressing limitations of previous variants and providing a clearer understanding of utility and risk aversion.

Findings

Resolves the original St. Petersburg paradox mathematically.

Clarifies the role of utility functions in decision theory.

Addresses limitations of previous variant-based resolutions.

Abstract

The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to resolve it have considered some variants of the original set-up, but the original paradox has remained unresolved, while the proposed variants have introduced new complications and problems. Here a rigorous mathematical resolution of the St. Petersburg paradox is suggested based on a probabilistic approach to decision theory.