Macroeconomics Exam Review 193

Macroeconomics Exam Review 193 - 3.268 Let ( , 1 ) and ( ,...

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Unformatted text preview: 3.268 Let ( , 1 ) and ( , 2 ) be balanced games. By the Bondareva-Shapley theorem, they have nonempty cores. Let x 1 core( , 1 ) and x 2 core( , 2 ). That is, ( x 1 ) 1 ( ) for every ( x 2 ) 2 ( ) for every Adding, we have ( x 1 ) + ( x 2 ) = ( x 1 + x 2 ) 1 ( ) + 2 ( ) for every which implies that x 1 + x 2 belongs to core( , 1 + 2 ). Therefore ( , 1 + 2 ) is balanced. Similarly, if x core( , ), then x belongs to core( , ) for every + . That is ( , ) is balanced for every + . 3.269 1. Assume otherwise. That is assume there exists some y . Taking the first components, this implies that e = e for some ( 0 : ). Let = {...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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