145hw3W10answer

145hw3W10answer - Econ 145: Problem Set III Suggested...

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Suggested Answer March 9, 2010 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? Answer: By applying worker-proposing DAA, we have Thus, we have the matching ( f 1 ,w 1 ,w 3 ) , ( f 2 ,w 2 ,w 4 ) (b) How would you define firm-proposing deferred acceptance algorithm? Describe an algorithm and apply it to the above problem to derive a matching. Answer: Based on the Lecture Note of Many-to-One Matching (p.23-24), we define firm-proposing DAA as follows. (1) Split firms with capacity q to q small firms with one capacity. Each of these q small firm has the exactly the same preference over workers as original firms. (2) Create workers’ artificial rankings among small firms from the same firm. (3) Apply the DAA. We apply firm-proposing DAA to above modified preference. Call splitted small firms as f 1 A , f 1 B , f 2 A and f 2 B . Also artificially assume that all workers prefer f 1 A to f 1 B and f 2 A to f 2 B . Thus, we have ( f 1 ,w 1 ,w 4 ) , ( f 2 ,w 2 ,w 3 ). 1
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This note was uploaded on 04/25/2010 for the course ECON 145 taught by Professor Obara during the Winter '10 term at UCLA.

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145hw3W10answer - Econ 145: Problem Set III Suggested...

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