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145hw1W10

# 145hw1W10 - set of allocations is exactly the set of all...

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Econ 145: Problem Set I Ichiro Obara January 14, 2010 January 26, 2010 Student Name: Student ID: Score Problem 1 Problem 2 Total 1

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1. Consider a general room assignment problem with N students and N rooms. Answer the following questions. (a) Suppose that the initial assignment of rooms is already e¢ cient. Show that TTC algorithm leads to the same allocation of rooms, i.e. every student ends up with his or her initially assigned room. 2
(b) For each initial assignment, you obtain one allocation if you apply TTC algorithm. If you apply TTC algorithm to all possible initial assignments, then you obtain the set of allocations. Show that this

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Unformatted text preview: set of allocations is exactly the set of all e¢ cient allocations. 3 2. Consider the following room assignment problem with 4 students and 4 room f h 1 ; :::; h 4 g : Room h i is initially assigned to student i: Suppose that the students have the following preference. h 3 & 1 h 4 & 1 h 1 & 1 h 2 h 4 & 2 h 3 & 2 h 2 & 2 h 1 h 2 & 3 h 1 & 3 h 3 & 3 h 4 h 2 & 4 h 1 & 4 h 4 & 4 h 3 (a) Find all e¢ cient allocations of the rooms. 4 (b) Find all core allocations. 5 (c) Is the core di/erent for a di/erent initial assignment, say, ( h 4 ; h 3 ; h 2 ; h 1 )? 6...
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145hw1W10 - set of allocations is exactly the set of all...

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