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145hw3W10

# 145hw3W10 - Econ 145 Problem Set III Ichiro Obara Due...

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Econ 145: Problem Set III Ichiro Obara Due February 23, 2010 Student Name: Student ID: Score Problem 1 Problem 2 Total 1

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1. Many-to-One Matching Suppose that there are 4 workers w 1 , ..., w 4 and 2 firms f 1 , f 2 with capacity q 1 = q 2 = 2. Their preferences are as follows. w 1 f 1 w 4 f 1 w 3 f 1 w 2 , f 2 w 1 f 1 , f 2 w 2 f 1 w 2 f 2 w 3 f 2 w 4 f 2 w 1 , f 1 w 3 f 2 , f 2 w 4 f 1 (a) Apply Worker-proposing deferred acceptance algorithm. Which matching would result? 2
(b) How would you define Firm-proposing deferred acceptance algo- rithm? Describe an algorithm and apply it to the above problem to derive a matching. 3

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2. School Choice Mechanism Consider a school choice with 4 students s 1 , ..., s 4 and 2 schools p 1 , p 2 . p 1 can accept only one student and p 2 can accept two students.

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