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Von Neumann-Morgenstern Utility Theorem
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What is an expected utility function according to Von Neumann-Morgenstern?
An expected utility function according to Von Neumann-Morgenstern is a real-valued function that assigns to each possible gamble or risky choice an expected utility, reflecting the desirability of outcomes weighted by their probabilities.
What is the Von Neumann-Morgenstern Utility Theorem?
The Von Neumann-Morgenstern Utility Theorem is a foundational theorem in expected utility theory that establishes a mathematical model of individual preferences over risky choices. It explains how individuals can order their preferences consistently in a way that can be represented by a utility function.
What does it mean for preferences to be rational in the context of the Von Neumann-Morgenstern theorem?
In the context of the Von Neumann-Morgenstern theorem, rationality means that an individual's preferences are complete and transitive, allowing for consistent decision making under uncertainty.
How does the theorem relate to the concept of 'risk aversion'?
The theorem allows for the derivation of a utility function that reflects an individual's level of risk aversion. The curvature of the utility function indicates the degree of risk aversion, with concavity suggesting risk aversion and convexity indicating risk preference.
What are the axioms of the Von Neumann-Morgenstern Utility Theorem?
The axioms of the Von Neumann-Morgenstern Utility Theorem are completeness, transitivity, continuity, and independence. These axioms provide the basis for constructing a utility function representing an individual's preference over uncertain outcomes.
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