Lect16_Slides

Lect16_Slides - Under the iterative procedure, it must have...

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Important Announcement Monday is a holiday, no class on Wednesday either! So this is it. I hope you enjoyed the course! I will hold a review session the night before the final. Date: Sunday, June 5. Time and location will be announced on the class web site. Expect 7 or 8 pm.
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Matching A matching is a mapping from one set of items to another set of items. Items can be people, firms, schools etc. Match can be one to one or many to one. Most common matching problem is marriage! Question: Does there exist a stable matching Given n men and n women, where each person has ranked all members of the opposite sex with a unique number between 1 and n in order of preference, can we match he men and women together in such a way that no two people of opposite sex who would both rather have each other than their current partners.
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Gale Shapley Algorithm Produces Stable Match Suppose there are two people, say orange circle and purple square that would prefer to break their existing matches and join together.
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Unformatted text preview: Under the iterative procedure, it must have been the case that at some point orange circle lined up in front of purple square and was turned away. However, this is a contradiction, since it implies purple square must have at one point had a match she preferred to orange circle, but ended up with a less preferred match. Under the iterative procedure the matches retained by squares can only improve. Most Preferred Match When circles propose to squares, the resulting stable match is the most preferred stable match of the circles. Likewise, when squares propose to circles, the resulting stable match is the most preferred stable match of the squares. Matches of interns to hospitals use this procedure. In the past, interns and hospitals were asked to submit their rankings and the "Hospitals Propose" version of the iterative procedure was used. This was recently changed....
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This note was uploaded on 12/26/2011 for the course ECON 171 taught by Professor Charness,g during the Fall '08 term at UCSB.

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Lect16_Slides - Under the iterative procedure, it must have...

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