Two-Sided Markets Example (2018)

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York


web page:

The theory behind this example is related to one of the most cited research papers in mathematics (by David Gale and Lloyd Shapley) and resulted in a Nobel Memorial Prize in Economics for Shapley and Alvin Roth (Gale was dead by the time the prize was given). This circle of ideas is used for pairing medical school graduates with hospitals and for school choice.

4 men rank 4 women without ties

1 st 2nd 3rd 4th
m1 w1 w2 w3 w4
m2 w2 w1 w4 w3
m3 w1 w4 w2 w3
m4 w2 w3 w4 w1

4 women rank 4 men without ties

1st 2nd 3rd 4th
w1 m4 m3 m2 m1
w2 m4 m3 m1 m2
w3 m2 m1 m4 m3
w4 m4 m2 m3 m1

What are reasonable ways for the men and woman to be paired?

Here we are assuming people don't have the option of NOT being paired.