Please read and familiarize yourself with Chapter 15.1 (Course Allocation) and 15.3 (The Harvard Business School Method) of the core book available to download on Moodle. 1. Consider a setting with 4 students ($1, ..., 84), each needing to be assigned to 2 courses, and 4 courses (C1, ..., C4), each with capacity 2. Preferences of the students are strict and responsive and given by: PSI P$2 P$3 Ps SA C3 C2 C1 C₁ C2 C3 C2 C2 CA C1 C3 C3 C4 C1 C4 C4 Compute the matching that results from using the Harvard Draft Method such that students are assigned a number equal to their index (student s₁ is assigned number 1, student s2 is assigned number 2, etc.), when students submit their true prefer- ences. Given the numbers assigned to each student, can any student benefit from misrepresenting their preferences? 2. Consider the same setting as in question 1, but the numbers assigned to each stu- dent are uniformly random. Can any student benefit from misrepresenting their pref- erences? If so, which ones can do so?
Please read and familiarize yourself with Chapter 15.1 (Course Allocation) and 15.3 (The Harvard Business School Method) of the core book available to download on Moodle. 1. Consider a setting with 4 students ($1, ..., 84), each needing to be assigned to 2 courses, and 4 courses (C1, ..., C4), each with capacity 2. Preferences of the students are strict and responsive and given by: PSI P$2 P$3 Ps SA C3 C2 C1 C₁ C2 C3 C2 C2 CA C1 C3 C3 C4 C1 C4 C4 Compute the matching that results from using the Harvard Draft Method such that students are assigned a number equal to their index (student s₁ is assigned number 1, student s2 is assigned number 2, etc.), when students submit their true prefer- ences. Given the numbers assigned to each student, can any student benefit from misrepresenting their preferences? 2. Consider the same setting as in question 1, but the numbers assigned to each stu- dent are uniformly random. Can any student benefit from misrepresenting their pref- erences? If so, which ones can do so?
Chapter2: Productions Possibilities, Opportunity Costs, And Economic Growth
Section: Chapter Questions
Problem 3SQ
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Question
Answer question 2 only.
Transcribed Image Text:Please read and familiarize yourself with Chapter 15.1 (Course Allocation) and 15.3
(The Harvard Business School Method) of the core book available to download on Moodle.
1. Consider a setting with 4 students ($1, ..., 84), each needing to be assigned to 2
courses, and 4 courses (C1, ..., C4), each with capacity 2. Preferences of the students
are strict and responsive and given by:
PSI
P$2
P$3
Ps
SA
C3
C2
C1
C₁
C2
C3
C2
C2
CA
C1
C3
C3
C4 C1
C4
C4
Compute the matching that results from using the Harvard Draft Method such that
students are assigned a number equal to their index (student s₁ is assigned number
1, student s2 is assigned number 2, etc.), when students submit their true prefer-
ences. Given the numbers assigned to each student, can any student benefit from
misrepresenting their preferences?
2. Consider the same setting as in question 1, but the numbers assigned to each stu-
dent are uniformly random. Can any student benefit from misrepresenting their pref-
erences? If so, which ones can do so?
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