Question: 1. (20 points) Consider a marriage problem (M, W, P) for which there are two sta- ble matchings, u and u'. Suppose all (some) men

1. (20 points) Consider a marriage problem (M, W, P) for which there are two sta- ble matchings, u and u'. Suppose all (some) men prefer their partners under / over their partners under u' weakly (strictly). Prove that all (and some) women prefer their partners under u' over their partners under / weakly (strictly). 2. (20 points) Consider the following marriage problem with three men and two women: P(m1) : W2 > W1; P(m2) : W2; P (m 3) : W1 > W2; P(w1) : mi > m3. P(w2) : m3 > m2 > m1; Find men optimal and women optimal matching

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