Consider five students, {1,2,3,4,5}, applying for five summer internship positions with five different firms, {A, B, C, D, E}. Each student applies for exactly one internship. The firms all rank the students in numerical order: each firm selects at most one student, and will always select a lower-numbered student over a higher-numbered student if more than one student applies for its internship. Since the firms always select in this way, we do not view them as strategic participants in this game. The students all rank the firms in alphabetical order, so each student i's payoff from getting the internship with firm X ∈ {A, B, C, D, E, }, where indicates not getting any internship, is

vi(X)= 5 if X=A
4 if X=B
3 if X=C
2 if X=D
1 if X=E
0 if X= ∅

So the game proceeds: Simultaneously, each student chooses which internship to apply for, then each firm that receives at least one application selects exactly one student for its internship.

a. For Student 1, which pure strategies are strictly dominated?
b. For Student 2, is applying for internship E a dominated strategy in the game?