A suppose that every students preference is the same

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following questions. (a) Suppose that every student’s preference is the same . Explain why every allocation is e cient in this case. 1
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(b) Suppose that the students have the following preference. h 2 Â 1 h 1 Â 1 h 3 h 3 Â 2 h 2 Â 2 h 1 h 3 Â 3 h 1 Â 3 h 2 Find all core allocations. (c) Suppose that there is an additional room h 4 which does not be- long to anyone initially. The preference of the students is given by h 4 Â 1 h 2 Â 1 h 1 Â 1 h 3 h 3 Â 2 h 2 Â 2 h 4 Â 1 h 2 h 4 Â 3 h 3 Â 3 h 1 Â 3 h 2 Explain why the standard TTC algorithm gets stuck in this case. (d) How would you modify the TTC algorithm to allocate these four rooms to the three students? Make sure that your algorithm does not generate any ine cient allocation. Your proposal should not be speci fi c to this particular problem: it should be applicable to general cases where there are more rooms than students. 3. Consider a matching problem with 4 men and 4 women. Suppose that men and women have the following preferences (we assume that every man and every woman is acceptable).
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