Matching/TwoSided Markets (2017)
Prepared by:
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk/
A teacher has equal numbers of boys (men) and girls (women) in her class and wants to set up study groups consisting of a boy and a girl. The boys are asked which girls they would like to have as a study group partner and the girls are asked the same question. The "rankings" of the men for the women and women for the men appear below. Thus Man 3 ranks Girl 5 second, and Girl 4 in 5th place. Woman 1 likes Man 3 second best. Ties in the rankings are not allowed.
What pairing(s) of boys and girls are such that no girl/boy pair would be happier with each other than the "mate" in the pair to which they are assigned? Such a pairing is called "stable."
How might one measure, if there are many stable pairings, when one pairing is better than another?
Can one reasonably assume that the rankings the boys and girls produce are "honest?"
Can you think of situations in "traditional" K12 curriculum where teaching this kind of problem would support the traditional content?
Men:
m_{1}

2

3

1

5

4

m_{2}

1

3

2

5

4

m_{3}

1

5

2

3

4

m_{4}

4

3

1

2

5

m_{5}

5

4

3

2

1

Women:
w_{1}

2

3

1

5

4

w_{2}

1

3

2

4

5

w_{3}

2

4

1

3

5

w_{4}

3

4

1

2

5

w_{5}

5

3

4

1

2
