Question

Three companies were given an opportunity to hire one of the three best graduating students of NYU. Consider below the following preference orderings of the 3 companies (α; δ; and β) and the 3 top students (Harry, Liam, and Zayn), where G is the option of any student to pursue graduate studies (e.g. Zayn would rather do further studies if he doesn’t get to work for δ, etc.).

a LiamZayn Harry | Harry> Zayn, Lian 3 δ | Liam>_ Harry Zayn

a. Find a stable matching profile using a company-proposing deferred-acceptance mechanism (i.e. Gale-Shapely algorithm).
b. Are the students here better o¤ than in a situation where they do not have that option to do graduate studies? Explain and show how option G made a difference in the outcome.
c. Does the presence of option G always lead to an optimal outcome for the students? Explain your answer.

Answer 1