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# stable - his or her lowest-ranked preference Problem 4...

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Stable Marriage Problem Problem 1: Determining all stable matchings Enumerate all the stable matchings for the four men and four women with the following preference lists. m 1 : w 3 > w 1 > w 4 > w 2 m 2 : w 3 > w 2 > w 4 > w 1 m 3 : w 4 > w 3 > w 2 > w 1 m 4 : w 2 > w 4 > w 1 > w 3 w 1 : m 2 > m 4 > m 1 > m 3 w 2 : m 2 > m 1 > m 3 > m 4 w 3 : m 4 > m 3 > m 1 > m 2 w 4 : m 1 > m 4 > m 2 > m 3 Problem 2: No one is happy Determine a list of preferences for four men and four women where no one obtains his or her ﬁrst choice in any stable matching. Problem 3: Some 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
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Unformatted text preview: 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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