Resolution of the St. Petersburg paradox using Von Mises axiom of randomness

TL;DR

This paper offers a novel solution to the St. Petersburg paradox by applying Von Mises' axiom of randomness, emphasizing the role of cognitive strategies and useful information in decision-making.

Contribution

It introduces a new perspective by using the axiom of randomness to analyze strategies, shifting focus from outcomes to cognitive information processing.

Findings

Cognitive strategies can exploit useful information to influence outcomes.

Expected gains tending to infinity are not always linked to non-random strategies.

A hierarchy of decision-making values is proposed, prioritizing cognitive aspects over expected gains.

Abstract

In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive way by exploiting useful information about the system. In order to determine from a mathematical point of view if a strategy is cognitive, we use Von Mises' axiom of randomness. Based on this axiom, the knowledge of useful information consequently generates results that cannot be reproduced randomly. Useful information in this case may be seen as a significant datum for the recipient, for their present or future decision-making process. Finally, by resolving the paradox from this new point of view, we will demonstrate that an expected gain that tends toward infinity is not always a consequence of a cognitive and non-random strategy. Therefore, this result leads us to define a hierarchy of values in decision-making, where the cognitive aspect, whose statistical consequence is a divergence from random behaviour, turns out to be more important than the expected gain.