Marriage Model
1. Assume that there are three Ws and three Ms. Specify the preferences of each agent so that the DAA generates the same match when the Ms propose as when the Ws propose.
2. W={A, B, C} and M={X, Y, Z} with the preferences as specified in Table:
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A
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B
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C
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X
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Y
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Z
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Y
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Z
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X
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A
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B
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A
|
|
X
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X
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Z
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B
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A
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C
|
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Z
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Y
|
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C
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B
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a) Check whether the matching π={(A,Y), (B,Z), (C,X)} is stable. Explain your answer.
b) Check whether the matching π={(A,Y), (B,Z), (C,X)} is efficient. Explain your answer.
c) Find a stable matching π' determined by the DAA when the Ms propose (Show the process). Is the matching π' efficient? Explain.
d) Find a case where a W misrepresents so that she gets better off by altering the outcome from π'. Write her reported preference ordering in that case.
e) Find a stable matching π'' determined by the DAA when the Ws propose (Show the process). Is the matching π'' efficient? Explain.
f) Find a case where a M misrepresents so that he gets better off by altering the outcome from π''. Write his reported preference ordering in that case.