Proof — Von Neumann–Morgenstern expected utility theorem
Statement
If preferences over lotteries satisfy completeness, transitivity, continuity, and the independence axiom, they can be represented by a unique (up to affine transformation) expected utility function. Rational choice under uncertainty is equivalent to maximizing expected utility. This axiomatization underpins decision theory, economics, and game theory.
Formula
Expected utility representation
Equation
U(L) = Σ pᵢ u(xᵢ)
Source
von Neumann & Morgenstern, Theory of Games and Economic Behavior, 1944.
Domains
mathematics, economics, game-theory
People
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- Theorem: Von Neumann–Morgenstern expected utility theorem
- Proof: Von Neumann–Morgenstern expected utility theorem