St Petersburg paradox and cardinal utility function

Abstract

The St Petersburg paradox could be used as an extreme demonstration of the utility function cardinalisation in case of stochastic utility. In this article we reassume the von Neumann and Mongernstern explanation to this paradox based on the risk aversion expressed by the strict concavity of the expected utility function. We suggest the utility function derived from the Pareto distribution of the probability of downfall of the subject in danger. Our cardinal utility function is based on the economically reasonable economic assumption. In contrast to the other often used cardinal utility functions it does not need the specification of its parameters ad hoc. Other advantage of our utility function is its explanation of the difference in decision making of different "players" in the St Petersburg casino, based on their wealth (including the explanation of the situational risk seeking behaviour of players under the boundary of survival).

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