7 pirates are trying to share 100 recently plundered gold coins. Pirate shar- ing rules are complicated, and involve seniority and voting. The pirates are ordered by seniority so that the captain (player 1) goes first, followed by the first-mate (player 2), through to the lowly cabin-boy (player 7). The rules of the vote are that the most senior pirate currently aboard ship proposes a split of the coins among the other pirates (coins can not be cut in half or divided further). Everyone votes, and so long as a majority (a fraction equal to or greater than one half) vote “Aye!” then that share is enacted and the gold is split. If more than a half vote “nay” then the 1 pirate who proposed the share is thrown overboard, and the next-most- senior pirate proposes a split among those remaining. Pirates are assumed to be a mercenary lot. Their worst outcome is being thrown overboard, but long as they’re alive they enjoy two things: i) Gold coins and ii) seeing their friends thrown overboard. However, they value gold disproportionately and would not trade a single coin for the enjoyment of seeing all their friends thrown overboard. (a) What is the sub-game perfect outcome of this game? (b) What is the sub-game perfect outcome for a ship with 100 pirates aboard? Suppose instead that a strict majority were required to pass a split (so if a half or more vote ‘nay’ then the proposer is thrown overboard). What is the sub-game perfect outcome for 7 pirates now?