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Course: CSE 202, Spring 2012School: UCSD
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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...
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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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