The Pirate Game in The Dark Knight
For those who still have not seen The Dark Knight yet, go do that now. Otherwise lets get started:
The film opens up with a literal bang, when two men in a clown masks break through a window to zip-line across onto the building across the street. Their target? The controller for the silent alarm of the bank down below. Meanwhile, a truck filled with more armed clowns approach the bank from below. Now here’s where it gets interesting. From the conversation in the car, we learn that these 5 men were gathered to rob a bank for the Joker, and each get a share of the loot afterwards; however it’s clear that there is some friction because the Joker will be getting a share without doing any of the work. This is where the game begins. Up on the roof we see one clown disable the silent alarm, and then quickly be shot in the back by his fellow thief, hey one less share right? The shooter makes his way downstairs to open the safe, making conversation with another clown. The second clown questions where the alarm clown went and is greeted with the truth: “Boss told me when the guy was done, I should take him out. One less share, right?” The vault clown is returned in favor with a bullet to his back, as the safe swings open. Everyone see where this is going? Ultimately it boiled down to the Joker actually being among the distrustful thieves, and the him walking away with all of the loot. Pretty great plan right?
At this point the relevance to class should be obvious: game theory. I’m not going to fill this post with a poster and graphs full of the statistics and calculations of the game being played but I can give a simple overview. This game is called the Pirate Game, in the study of game theory. It is essentially a multiplayer extension of the Prisoner’s Dilemma: cooperate and everyone wins, but attempt to betray each other and everyone loses. The original pirate game plays out like this with three players:
There are three pirates, we’ll call them A, B, and C. They follow a strict seniority tradition in which A > B > C. Now there is a 100 gold coins to be split and they’re deciding how do be fair so they propose a democracy. The eldest proposes a split and everyone votes to agree or disagree, majority rules. If the vote is rejected, the proposer of the plan is thrown overboard and we repeat. If there is a tie, then the proposer gets a casting vote. If we believe that the players are completely rational then the following occurs. If only B and C were playing, B would automatically win since he has the casting vote and can overrule C. A uses this information to his advantage because if he paid C just one gold coin, that is already more than C could have possibly earned otherwise: thus the solution is A-99, B-0, C-1.
We learn from this game that we can pay off “weaker” players by providing a small incentive (like player C) and the a leader can exploit the greed of other players to win. The robbery scene plays out similarly, where the original proposer (the Joker), subtly holds the most power. He plays on the distrust of each thief, proposing they kill each person once their usefulness has expired. The Joker “pays off” each player with an extra share of the pot, but in the end there’s a twist, he breaks the rules and just kills the last member anyways. Typical Joker, am I right?
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