145hw1 - h 4 needs to be renovated. Hence there will be a...

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Econ 145: Problem Set I Ichiro Obara January 15, 2009 January 27, 2009 1. Consider the following room assignment problem. There are 4 students and 4 room { h 1 , ..., h 4 } . Room h i is initially assigned to student i. Suppose that the students have the following preference. h 3 Â 1 h 4 Â 1 h 1 Â 1 h 2 h 4 Â 2 h 3 Â 2 h 2 Â 2 h 1 h 2 Â 3 h 1 Â 3 h 3 Â 3 h 4 h 2 Â 4 h 1 Â 4 h 4 Â 4 h 3 (a) Find all e cient allocations of the rooms. (b) Find all core allocations. (c) Is the core di f erent for a di f erent initial assignment, say, ( h 4 ,h 3 ,h 2 ,h 1 )? (d) Suppose that only 3 rooms are available for the next year be- cause
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Unformatted text preview: h 4 needs to be renovated. Hence there will be a student who is not assigned any room (now a typical allocation looks like ( h 3 , h 2 , , h 1 ), where means no room is assigned). Every student prefers any room to no room. For example, student 1s preference is h 3 1 h 1 1 h 2 1 . Find all e cient allocations and all core allocations in this case (given that h 1 , h 2 and h 3 are assigned to student 1, 2, and 3 initially). 1...
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