Problem 5: Matching [25 points]. Assume the following preferences for men and women: m1: W2 > Wi > W3 W1: m4 > mi > mz m2: W1 > W3 > W2 > W4 W2: m > mz > m1 m3: W3 > W4 W3: m4 > m3 > m2 m4: W4 > W3 > W1 > W2 W4: MA 1) [4 points] What is the matching produced by men-proposing DA algorithm? 2) [3 points] What is the matching produced by women-proposing DA algorithm? 3) [11 points] Find the set of all stable matchings and show that they form a lattice. 4) [7 points] Show that women-proposing DA is not strategy-proof for this example: find how woman wj can misrepresent her preferences to get a better match