1. (Two-Sided Matching) Consider a matching market with four men and three women, who have preferences as follows: m1: w1 > w2 > w3 w1: m2 > m3 > m1 > m4 m2: w3 > w2 > w1 w2: m4 > m2 > m3 > m1 m3: w3 > w1 > w2 w3: m4 > m2 > m1 > m3 m4: w1 > w3 > w2 a. Use the DA algorithm to find the man-optimal stable matching. b. Are there other stable matchings? If so, what are they? c. Is the man-optimal stable matching Pareto efficient for the men? d. Under the man-proposing DA, could m1 misreport his preferences in a way that would leave no man worse off than under truth-telling and strictly improve the outcome for at least one man? How about m2, m3 or m4?

I need help understanding stability and efficiency.