Slides12-2010

# Slides12-2010 - Outline Result A:A Result A:B Result A:C...

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Unformatted text preview: Outline Result A:A Result A:B Result A:C Von Neumann-Morgenstern - Proof I: Lecture XII Charles B. Moss September 17, 2010 Charles B. Moss Von Neumann-Morgenstern Outline Result A:A Result A:B Result A:C Result A:A Result A:B Result A:C Charles B. Moss Von Neumann-Morgenstern Outline Result A:A Result A:B Result A:C Result A:A I A:A If u ≺ v then α < β implies (1 − α ) u + α v ≺ (1 − β ) u + β v (1) I The direction of the assertion is that if u ≺ v and α < β , then the preference ordering must follow. I To demonstrate this we start with axiom 3:B:a given 0 ≤ α ≤ 1 u ≺ v ⇒ u ≺ α u + (1 − α ) v ⇒ u ≺ (1 − β ) + β v (2) Charles B. Moss Von Neumann-Morgenstern Outline Result A:A Result A:B Result A:C I Continued I Intuitively, this axiom states that if u is the inferior bundle, then any bundle constructed with any combination of v must be preferred to u . I bf Axiom 3:B:b reverses this axiom by saying that if u is the preferred bundle then it must also be preferred to a bundle containing any amount of v ....
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Slides12-2010 - Outline Result A:A Result A:B Result A:C...

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