Rubinstein2005-page62

Rubinstein2005-page62 - October 21, 2005 12:18 44 master...

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October 21, 2005 12:18 master Sheet number 60 Page number 44 44 Lecture Four Figure 4.2 Two defnitions oF convexity. Convexity 2: The relation % satisfes convexity 2 iF For all y , the set AsGood ( y ) = { z X | z % y } is convex. (Recall that a set A is convex iF For all a , b A and For all λ ∈[ 0, 1 ] , λ a + ( 1 λ) b A .) This captures the intuition that iF both z 1 and z 2 are better than y , then the average oF z 1 and z 2 is defnitely better than y . Claim: A preFerence % satisfes convexity 1 iF and only iF it satisfes convex- ity 2. Proof: Assume that % satisfes convexity 1 and let
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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