3. Five pirates, who have very funny names that start with the letters A, B. C, D, and E have captured 100 gold dubloons of booty from their most recent attack. The pirates have an odd method of dividing booty: Pirate E gets to split the 100 dubloons into five piles of any size (a pile can even be as small as ( if E so desires). Then the pirates, in alphabetical order, select the pile that is most appealing from whichever haven't been taken by those earlier in the alphabet than them (so: A picks one of the five piles; B picks one of the remaining four piles, etc.). (a) In the subgame perfect (rollback) equilibrium, how much booty does Pirate B re- ceive? (b) If instead of Pirate E splitting the booty, it was Pirate C (but the selection process was still the same alphabetical one), how would this change the outcome of the game in equilibrium