3. There are 10 men and 10 women. Let's index the men from 1 to 10 and let's index the women from 1 to 10. A man (woman) with index i has skill level i. If a man with skill level i marries a woman with skill level j then they earn a joint income of i * j. For example, if man 5 marries woman 10 they earn a joint income of 50. These 10 men and women engage in a matching game: every woman announces her preferred husband. All women make their announcements simultaneously. If two or more women choose the same husband only the more skilled woman gets to choose - all the other women are "mismatched" and get 0. Find the pure-strategy Nash equilibrium of this matching game. Show that it is uni