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PracticeQuestionsIW10

# PracticeQuestionsIW10 - Econ 145 Practice Questions I...

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Econ 145: Practice Questions I Ichiro Obara January 31, 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 f nd an example of room assignment problem (with four students and four rooms) such that these two sets coincide? If so, f nd one. If not, explain why.

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PracticeQuestionsIW10 - Econ 145 Practice Questions I...

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