NeumannMorgenstern

The Neumann Morgenstern utility theorem, also known as the expected utility theorem, is a foundational concept in decision theory that describes how rational individuals should make choices under uncertainty. Developed by John von Neumann and Oskar Morgenstern, it posits that if an individual's preferences satisfy a set of axioms, then their choices can be represented by maximizing the expected value of a utility function. This utility function assigns numerical values to outcomes, reflecting the desirability of each outcome. The axioms typically include completeness (all outcomes can be compared), transitivity (if outcome A is preferred to B, and B to C, then A is preferred to C), continuity, and independence (preferences over gambles should not be affected by the addition of a common, equally likely outcome to each gamble).

The theorem is significant because it provides a mathematical framework for understanding and predicting behavior in situations involving risk. It allows for the quantification of preferences and the calculation of optimal decisions by comparing the expected utility of different options. This has broad applications in economics, finance, game theory, and various other fields where decisions with uncertain outcomes need to be analyzed. The expected utility hypothesis has been widely applied, though empirical research has also identified deviations from its predictions, leading to the development of alternative theories of decision-making under risk.