Rubinstein2005-page35

Rubinstein2005-page35 - A preFerence relation % on X is...

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October 21, 2005 12:18 master Sheet number 33 Page number 17 Utility 17 Figure 2.1 Two defnitions oF continuity oF preFerences. is that iF a is preFerred to b , then “small” deviations From a or From b will not reverse the ordering. Defnition C1: A preFerence relation % on X is continuous iF whenever a Â b (namely, it is not true that b % a ), there are neighborhoods (balls) B a and B b around a and b , respectively, such that For all x B a and y B b , x Â y (namely, it is not true that y % x ). (See fg. 2.1.) Defnition C2:
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Unformatted text preview: A preFerence relation % on X is continuous iF the graph oF % (that is, the set { ( x , y ) | x % y } X X ) is a closed set (with the product topology); that is, iF { ( a n , b n ) } is a sequence oF pairs oF elements in X satisFying a n % b n For all n and a n a and b n b , then a % b . (See fg. 2.1.) Claim: The preFerence relation % on X satisfes C1 iF and only iF it satisfes C2....
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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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