The Pirate Problem
Five pirates (who used to be hedge fund managers before they gave up their life of sin and took up an honest profession) attack and board a ship. While plundering the boat, they uncover a chest filled with 100 identical, indivisible gold coins. Before parting ways, the pirates must decide how to divide the treasure.
They commit to the following proposal scheme:
The pirates rank themselves #1 – #5, by ascending seniority. The most junior pirate, #1, goes first. He proposes a split of the treasure. The split could go any way; there are no rules aside from indivisibility of coins. (We can notate his proposal as follows: [20 – 20 – 20 – 20 – 20], or [45 – 30 – 24 – 1 – 0], for example).
Once Pirate #1 submits his proposal, all pirates vote. If a majority, or at least a tie, of the pirates vote in favour, the pirates split the treasure according to the proposal and go their separate ways. Alternately, if a clear majority votes against the proposal, Pirate #1 is thrown overboard to the sharks, and Pirate #2 presents a proposal of his own. And if that proposal fails, it goes to pirate #3, and so on.
Recall that these pirates used to run hedge funds, so they are all very smart (in this domain, anyway) and think rigorously through each proposal. Obviously, they all care more about maximizing their own treasure than about their fellow pirates. But they also abide by pirate code: if a proposal passes voting, they will honour it.
You are the most junior pirate, and you get to make the first proposal. How much treasure can you get?