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145hw2W10

# 145hw2W10 - 3 2 Matching Answer the following questions...

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Econ 145: Problem Set II Ichiro Obara Due February 9, 2010 Student Name: Student ID: Score Problem 1 Problem 2 Total 1

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1. Kidney Exchange Suppose that there are 5 patient-donor pairs ((1 , d 1 ) , ..., (5 , d 5 )) . Let k i be the kidney of donor i. Each patient has the following “pref- erence” over { k 0 , ..., k 5 } ( k 0 is the option to be given some priority in the waiting list). k 5 1 k 2 1 k 3 1 k 0 1 k 1 1 k 4 k 1 2 k 5 2 k 4 2 k 0 2 k 2 2 k 3 k 4 3 k 1 3 k 0 3 k 2 3 k 5 3 k 3 k 1 4 k 4 4 k 2 4 k 3 4 k 0 4 k 5 k 4 5 k 2 5 k 3 5 k 5 5 k 0 5 k 1 (a) Apply TTCC (Top-Trading-Cycle-and-Chain) algorithm. What is the final allocation? 2
(b) Whose kidney will be assigned to patients in the waiting list?

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Unformatted text preview: 3 2. Matching Answer the following questions regarding matching. (a) Show that every stable matching is eﬃcient. 4 (b) Find an example of matching that is eﬃcient, but not stable. 5 (c) Suppose that all men’s preferences are identical and all women’s preferences are identical. Explain how the set of all stable match-ings look like. 6...
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145hw2W10 - 3 2 Matching Answer the following questions...

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