Sources:

http://en.wikipedia.org/wiki/Pirate_game

http://mindyourdecisions.com/blog/2008/08/19/game-theory-in-the-dark-knight-a-critical-review-of-the-opening-scene-spoilers

In class, we have discussed game theory in terms of examples, such as “The Prisoner’s Dilemma.” With this, we have discussed strategies for each of the players in the game and the existence of dominant strategies. Another common example used when discussing game theory is “The Pirate Puzzle.” We can use similar techniques as we have used in class in order to determine the strategies involved in this puzzle. This example can also be related to the bargaining theories and auctions we have seen in class.

The Pirate Puzzle involves 3 players in its simplest version (“pirates”): A, B, and C. Each of these pirates have different amounts of power and are ranked strongest, next strongest, and weakest, respectively. The objective is for the pirates to a chest of gold that they have just acquired. A, being the strongest pirate, gets to suggest a split of the money first and then all 3 pirates get to vote on whether to accept/reject the proposal. If there is a tie, the pirate who proposed the split gets to decide. If the pirates agree to a split, then they do so, otherwise the pirate who made the proposal is thrown overboard and the next strongest pirate, B, gets to make the next proposal. We can assume that each of the pirates are intelligent and look ahead to the possible outcomes and reason backwards to determine their strategy. Looking at the puzzle in this way, you can see that having A thrown overboard will be extremely detrimental to C because B will have the deciding vote to except his own proposal, which will inevitable 100% of the gold for himself and nothing to C, because C has absolutely no power. Aware of this, it will be in C’s interest to fight to keep A on board by agreeing to any A proposal offering C more than 0%. Knowing this, A will make a proposal to give B nothing and give C 1% while keeping 99% for himself. C will accept this because it is better than nothing, so this will, in fact, be the actual split, and it is clear that the “strongest” pirate, A, has a lot of power. Players in this game determine their worth from their voting power and some players can be bought off. The “strongest” player, or the leader, wins by “exploiting conflict among the weaker players. This game can be extended to playing with many more players as well.

An example of this pirate puzzle can be found in the opening scene of the recent film, The Dark Knight. In this scene, a robbery takes place. This robbery has been orchestrated by the Joker and originally involves five robbers. Originally, these robbers predict that they will be splitting the money five ways, however the Joker has actually told each to kill one of the others once they have completed their task. In the end, the Joker ends up with all of the money. The Joker, as the “strongest” player, offers each of the weaker players a better option than a five-way split by telling them to kill one of the other robbers, so they are inclined to do so, in favor of a better split. Little do each of them know, however, that each of the other robbers (“players”) are getting this same opportunity from the Joker, to receive a better profit. The Joker plays off of the conflict between the robbers and, “being the “strongest pirate,” was able to sequentially bribe the weaker robbers one by one”.