Qs Matching problem

1. Consider the marriage matching example given in class with three men and three women. (a) Let the preference matrix be as in Table 1. Argue that the matching (w1, w3, W2) Table 1: A preference matrix. W1 W2 W3 m1 1,3 2,2 3,1 m2 3,1 1,3 2,2 m3 2,2 3,1 1,3 is unstable. (The notation means that m] is matched with w1, m2 matched with w3, and m3 with w2.) (b) Let the preference matrix be as in Table 2. Argue that the matching (w1, w2, W3) Table 2: A preference matrix. W1 W2 W3 m1 1,1 2,1 3,1 m2 1,2 2,2 3,2 m3 1,3 2,3 3,3 is stable