You want to divide students into pairs who will share a 2-bedroom apartment for the coming year (one-sided matching). Your interest is in "stable roommates," i.e. such that there is no blocking pair: no two students would rather room with each other than their current assigned roommates. 1. Suppose there is one 2-bedroom apartment and three students with preferences: A: CAB
You want to divide students into pairs who will share a 2-bedroom apartment for the coming year (one-sided matching). Your interest is in "stable roommates," i.e. such that there is no blocking pair: no two students would rather room with each other than their current assigned roommates. 1. Suppose there is one 2-bedroom apartment and three students with preferences: A: CAB
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 6PA
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Please answer both parts of Question 4.
![QUESTION 4
You want to divide students into pairs who will share a 2-bedroom apartment for the coming
year (one-sided matching). Your interest is in "stable roommates," i.e. such that there is
no blocking pair: no two students would rather room with each other than their current
assigned roommates.
1. Suppose there is one 2-bedroom apartment and three students with preferences:
A: CAB
B: ABC
C: Bc A
How do these preferences show that there do not exist any stable roomates?
2. You might worry that the problem is the odd number of students. Argue that in the
following setting with 4 students, there is a stable match:
A: DACAB
B: AB DBC
C: B➤c Ac D
D: CD B>DA](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F817c8572-7700-4c39-925d-bcc16b158f3c%2F16e88d73-b11a-4464-b02f-1fe3ec860625%2Fkiyeryp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 4
You want to divide students into pairs who will share a 2-bedroom apartment for the coming
year (one-sided matching). Your interest is in "stable roommates," i.e. such that there is
no blocking pair: no two students would rather room with each other than their current
assigned roommates.
1. Suppose there is one 2-bedroom apartment and three students with preferences:
A: CAB
B: ABC
C: Bc A
How do these preferences show that there do not exist any stable roomates?
2. You might worry that the problem is the odd number of students. Argue that in the
following setting with 4 students, there is a stable match:
A: DACAB
B: AB DBC
C: B➤c Ac D
D: CD B>DA
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