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Thursday, August 21, 2008

Game theory in The Dark Knight. Fun article analyzing the Joker's opening heist in the context of the pirate game, an interesting situation with a nicely counter-intuitive result:

Three pirates (A, B, and C) arrive from a lucrative voyage with 100 pieces of gold. They will split up the money according to an ancient code dependent on their leadership rules. The pirates are organized with a strict leadership structure—pirate A is stronger than pirate B who is stronger than pirate C.

The voting process is a series of proposals with a lethal twist. Here are the rules:

1. The strongest pirate offers a split of the gold. An example would be: “0 to me, 10 to B, and 90 to C.”
2. All of the pirates, including the proposer, vote on whether to accept the split. The proposer holds the casting vote in the case of a tie.
3. If the pirates agree to the split, it happens.
4. Otherwise, the pirate who proposed the plan gets thrown overboard from the ship and perishes.
5. The next strongest pirate takes over and then offers a split of the money. The process is repeated until a proposal is accepted.

Pirates care first and foremost about living, then about getting gold. How does the game play out?
If everyone acts maximally rationally, A comes away with 99 of the 100 coins, which is pretty fantastically unexpected.