2. (20 pts) a. Run Gale-Shapley Algorithm and show your steps using the preference lists tables below. Are there any unstable pairs in the final match? b. Modify Gale-Shapley Algorithm such that women will propose instead of men. Show the final match. c. Compare and discuss the matches produced above in terms of men- optimality/women-pessimality and women-optimality/men-pessimality. men's preference list 3rd women's preference list 2nd 3rd 2nd 5th 1st 5th Victor Bertha Amy Diane Erika Clare Amy Zeus Victor Wyatt Yancey Xavier Erika Amy Diane Bertha Clare Bertha Victor Zeus Yancey Xavier Wyatt Wyatt Xavier Bertha Erika Clare Diane Amy Clare Wyatt Xavier Yancey Zeus Victor Yancey Amy Diane Bertha Clare Erika Diane Victor Zeus Yancey Xavier Wyatt Zeus Bertha Diane Amy Erika Clare Erika Xavier Wyatt Zeus Yancey Victor