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Theorem

Mixture-Space Theorem

Game Theory

The mixture-space theorem, proved by Israel Nathan Herstein and John Milnor in 1953, is a utility-representation theorem in microeconomic and decision theory showing that a preference relation defined over a general mixture space, one satisfying axioms of completeness, independence and mixture continuity, can be represented by a utility function that is linear with respect to the space's mixture structure. Herstein and Milnor's paper both introduced the formal definition of a mixture space and proved the theorem for it, generalizing both the von Neumann-Morgenstern expected-utility theorem and the standard utility-representation theorems used for ordinary consumer preferences.

Facts
Statement
A utility-representation theorem for preferences defined over general mixture spaces. 1
Proof Year
1953 1
Classification
Statement Form
Existence Theorem 1
Connections

Has Statement Form

Existence Theorem, Concepts

In Branch

Game Theory, Branches of Mathematics
Source Mixture-space theorem - Wikipedia

Proved By

John Milnor, Mathematicians
Source Mixture-space theorem - Wikipedia
Sources
1. Mixture-space theorem - Wikipedia
  • Intro, first sentence
    utility-representation theorem for preferences defined over general mixture spaces.
  • Intro, third sentence
    It was first proven by Israel Nathan Herstein and John Milnor in 1953
  • Lead section
    It was first proven by Israel Nathan Herstein and John Milnor in 1953, together with the introduction of the definition of a mixture space.
  • In Branch: Game Theory, Lead
    In microeconomic theory and decision theory, the Mixture-space theorem is a utility-representation theorem for preferences defined over general mixture spaces.
  • Proved By: John Milnor, Lead
    It was first proven by Israel Nathan Herstein and John Milnor in 1953, together with the introduction of the definition of a mixture space.
  • In Group: Decision Theory and Utility, Lead paragraph
    In microeconomic theory and decision theory, the Mixture-space theorem is a utility-representation theorem for preferences defined over general mixture spaces.
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