Consider the following House Allocation Problem with 6 agents and houses a, b, c, d, e, f.

Agents' preferences:

1 2 3 4 5 6

d f f b b f

b e a a d a

f d b c c d

e b e d f b

a a d e a c

c c c f e e

a) Determine the matching obtained by the Serial Dictatorship with =(1,2,3,4,5,6).

b) Prove that the matching obtained in a) is Pareto efficient.

c) Would the Serial Dictatorship matching obtained with =(6,3,5,4,1,2) also be Pareto efficient? How about the matching (e, a, f, b, d, c)?

d) Prove that a Serial Dictatorship is nonbossy