Two-Sided Markets (2018)
Prepared by:
Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York
email:
malkevitch@york.cuny.edu
web page:
http://www.york.cuny.edu/~malk/
Two-sided markets:
Eight hospitals (upper table) and 8 medical students (second table) have ranked each other as indicated in the tables below. For example, Hospital 5 (names in first column) has ranked Medical Student 2, second, while Medical Student 4 has ranked Hospital 2 fourth.
Hospital rank medical students (Column 1, hospital names)
|
1
|
5
|
7
|
1
|
2
|
6
|
8
|
4
|
3
|
|
2
|
2
|
3
|
7
|
5
|
4
|
1
|
8
|
6
|
|
3
|
8
|
5
|
1
|
4
|
6
|
2
|
3
|
7
|
|
4
|
3
|
2
|
7
|
4
|
1
|
6
|
8
|
5
|
|
5
|
7
|
2
|
5
|
1
|
3
|
6
|
8
|
4
|
|
6
|
1
|
6
|
7
|
5
|
8
|
4
|
2
|
3
|
|
7
|
2
|
5
|
7
|
6
|
3
|
4
|
8
|
1
|
|
8
|
3
|
8
|
4
|
5
|
7
|
2
|
6
|
1
|
Students rank hospitals (Column 1, student names)
|
1
|
5
|
3
|
7
|
6
|
1
|
2
|
8
|
4
|
|
2
|
8
|
6
|
3
|
5
|
7
|
2
|
1
|
4
|
|
3
|
1
|
5
|
6
|
2
|
4
|
8
|
7
|
3
|
|
4
|
8
|
7
|
3
|
2
|
4
|
1
|
5
|
6
|
|
5
|
6
|
4
|
7
|
3
|
8
|
1
|
2
|
5
|
|
6
|
2
|
8
|
5
|
3
|
4
|
6
|
7
|
1
|
|
7
|
7
|
5
|
2
|
1
|
8
|
6
|
4
|
3
|
|
8
|
7
|
4
|
1
|
5
|
2
|
3
|
6
|
8
|
What is a reasonable way to pair the medical students to the hospitals?
In the United States a system based on the ideas developed for solving this problem by the mathematicians David Gale and Lloyd Shapley are correctly used to match medical school students needing a hospital to do their residency with hospitals needing medical students for residency positions. Alvin Roth, who has a doctorate degree in Operations Research helped with others in designing the system currently in use.