Skip to main content



Batman and Game Theory

Christopher Nolan’s acclaimed Batman movie “The Dark Knight” is a phenomenal superhero movie filled with suspense, action, and perhaps most surprisingly, numerous applications of game theory. Let us take a closer look at some of these scenarios.

The opening scene of the movie itself is a game, that deals with the issue of fair division. We have a scenario with a group of robbers heisting a bank. Here, the goal of each “player” is to maximize his profit, which is done by killing other “players” so as to reduce the division of the total amount. Each player provides a unique asset to the team (such as being the one who can disable the alarm or blow open the vault) which initially gives him negotiating power; however, as soon as a member has played out his role, he loses both his negotiating power and value as far as the others are concerned, making him expendable. The dominant strategy here is obviously to eliminate every other player before he eliminates you. As the first article explains, this scenario is really a nuanced version of the popular game known as “The Pirate Puzzle”, in which pirates must split up pieces of gold among themselves.

The scene with the two ferries presents another popular game scenario: the Prisoner’s Dilemma. Each boat is given the choice to blow up the other, and if both boats are still standing after 30 minutes, they both get blown up. Setting up the payoff matrix, we clearly see that the dominant strategy is to blow up the other boat. However in the movie, neither boat chooses to blow up the other (luckily they both end up being saved by Batman). This is because there are other factors that can contribute to the peoples’ choice, such as guilt or morality. The message here is that while game models work on paper, they are far more complex and unlikely to play out as they should in real life due to the multitude of other factors that come into play in peoples’ decisions. The third article explores this in detail.

Another interesting game takes place during the scene where the Joker is negotiating with the mob, asking them for half of their shares in return for eliminating Batman. This scenario again raises the issue of fair division, but as the second article points out, with an interesting twist: the introduction of the concept of diminishing returns. Indeed, while the mobsters might not be thrilled of giving away half of their shares to the Joker, they risk losing more in the long run with every passing day yielding less and less (and eventually yielding nothing) due to the city getting cleaned up by Batman. This scenario is essentially a “shrinking pie game meets ultimatum game”, which the second article explains in detail.

Other game theory scenes include Batman choosing to jump off the roof to save Rachel rather than going after the Joker during the party, Batman being faced with the decision to either save Rachel or Dent, and the list goes on and on. As we can see, there is much more to this movie than meets the eye, and it is interesting to see how Nolan has successfully managed to create a movie with suspense and action scenes that are almost entirely based on game theory models.

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

http://mindyourdecisions.com/blog/2011/03/25/negotiating-with-the-mob-game-theory-in-the-dark-knight-part-2/

http://www.quantitativepeace.com/blog/2008/07/the-dark-knight.html

Comments

Leave a Reply

Blogging Calendar

October 2011
M T W T F S S
 12
3456789
10111213141516
17181920212223
24252627282930
31  

Archives