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### stable

Course: CSE 202, Spring 2012
School: UCSD
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Word Count: 189

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Marriage Stable Problem Problem 1: Determining all stable matchings Enumerate all the stable matchings for the four men and four women with the following preference lists. m1 m2 m3 m4 :w3 :w3 :w4 :w2 &gt; w1 &gt; w2 &gt; w3 &gt; w4 w1 w2 w3 w4 :m2 :m2 :m4 :m1 &gt; w4 &gt; w4 &gt; w2 &gt; w1 &gt; m4 &gt; m1 &gt; m3 &gt; m4 &gt; w2 &gt; w1 &gt; w1...

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Marriage Stable Problem Problem 1: Determining all stable matchings Enumerate all the stable matchings for the four men and four women with the following preference lists. m1 m2 m3 m4 :w3 :w3 :w4 :w2 > w1 > w2 > w3 > w4 w1 w2 w3 w4 :m2 :m2 :m4 :m1 > w4 > w4 > w2 > w1 > m4 > m1 > m3 > m4 > w2 > w1 > w1 > w3 > m1 > m3 > m1 > m2 > m3 > m4 > m2 > m3 Problem 2: No one is happy Determine a list of preferences for four men and four women where no one obtains his or her rst choice in any stable matching. Problem Some 3: one gets the last choice Determine a list of preferences for four men and four women such that in every stable matching one person receives his or her lowest-ranked preference. Problem 4: Unique stable matching Suppose that all men have identical preference lists in an instance of the stable marriage problem. Show that there exists exactly one stable matching. Problem 5: More than one stable matching Suppose that more than one woman receives her lowest-ranked choice when the men propose. Prove that there exist at least two stable matchings between the men and the women. 1
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