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PracticeQuestionsIW10

# PracticeQuestionsIW10 - Econ 145 Practice Questions I...

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Econ 145: Practice Questions I Ichiro Obara February 5, 2010 1. Consider a room assignment problem with 4 students and 4 rooms { h 1 , . . . , h 4 } . Room h i is initially assigned to student i. Suppose that the preferences of the students are as follows h 2 Â 1 h 4 Â 1 h 1 Â 1 h 3 h 2 Â 2 h 1 Â 2 h 3 Â 2 h 4 h 1 Â 3 h 3 Â 3 h 4 Â 3 h 2 h 3 Â 4 h 4 Â 4 h 1 Â 4 h 2 where Â i is student i ’s (strict) preference over the rooms. Answer following questions. (a) Is the initial allocation e cient? Explain why. (b) Find all e cient allocations. Explain how you found all the e - cient allocations. (c) In general, the set of e cient allocations is larger than the core allocation (given a certain initial assignment). Can you fi nd an example of room assignment problem (with four students and four rooms) such that these two sets coincide? If so, fi nd one. If not, explain why. 2. Consider a room assignment problem with 3 students and 3 rooms { h 1 , ..., h 3 } . Room h i is initially assigned to student i. Answer the following questions.

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• Spring '08
• Serra
• G protein coupled receptors, World War I submarines of the United Kingdom, room assignment problem, W-optimal stable matching

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PracticeQuestionsIW10 - Econ 145 Practice Questions I...

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