different firms, {A, 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. (That is, they are part of the rules of the 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,0), where 0 indicates not getting any internship, is 5 if X A 4 if X B 3 if X C v,(X) = 2 if X D 1 if X E 0 if X 0. So the game proceeds: Simultaneously, each student chooses which internship to apply for, then cach firm that receives at least one application selects exactly one student for its internship.

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
Section: Chapter Questions
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3. 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. (That is, they are part of the rules of the game.)
The students all rank the firms in alphabetical order, so each student i's payoff from getting the
internship with firm X e (A, B,C, D, E,0), where 0 indicates not getting any internship, is
5 if X A
4 if X B
3 if X C
v(X) =
2 if X D
1 if X E
0 if X 0.
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 Ea dominated strategy in the game?
Transcribed Image Text:3. 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. (That is, they are part of the rules of the game.) The students all rank the firms in alphabetical order, so each student i's payoff from getting the internship with firm X e (A, B,C, D, E,0), where 0 indicates not getting any internship, is 5 if X A 4 if X B 3 if X C v(X) = 2 if X D 1 if X E 0 if X 0. 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 Ea dominated strategy in the game?
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