Game Theory in The Dark Knight (Warning Spoilers!)
The Dark Knight: Awesome movie. What makes it so great? Well maybe it’s Christopher Nolan’s blue-black imagery and talent for suspense. Or perhaps it’s Christian Bale’s ability to incapacitate Gotham City’s entire SWAT team while nursing the world’s worst sore throat. Who knows for sure? But I think (and I’m sure many people would agree) what made the movie for me was Heath Ledger as the devilishly clever and manipulative “Joker”, pulling the strings on movies’ plot-lines. What is so great about the joker is his ability to manipulate the outcome of so many situations (and of course his deeply disturbing sense of humor). Why is the joker so good at what he did? He knows a little bit of game theory.
The Joker sets up the games in the film–this allows him to create the choices and the payoffs. His style is to present the players with games that always offer a dominant strategy but also a Nash Equilibrium that leaves the players worse off than if they had cooperated. This article from mindyourdecisions.com deals with the robbery in the opening scene.
In this scene the Joker organizes a bank robbery. He tells each of the robbers to kill one other robber in order to increase their share of the money. The robbers are presented with two choices: to kill or not to kill. The dominant strategy is obviously (at least if you’re a sociopath) to kill the other robber to increase your return on the job. But in the end all the robbers kill each other and the Joker is the only winner in the game.
What’s interesting to note is that the Joker believes that people are generally self-interested. Game theory works so well with his schemes because self-interest is a basic assumption of game theory. The “Ferry Scene” is a case where game theory fails the Joker, because the players are not strictly self-interested. Here’s the Game:
Two ferries are loaded with bombs. Each ferry has the detonation key to the other ferry. If neither of the ferries has pushed the big red button by midnight, both explode. Otherwise the ferry that remains gets to safety. Here the dominant strategy is to push the button, so the Joker assumes the ferries will annihilate each other. He doesn’t, however, count on both ferries having the ethical strength to take the passive strategy. This is why batman has enough time to find the Joker before he can detonate the ferries.
The Dark Knight is filled with games as it plays with human self-interest and philanthropy. Think about it the next time you see it! And for all you movie buffs, the final scene of The Good, the Bad and the Ugly also has a great game. Enjoy!