11/20/2009

Batman's Game Theory in The Dark Knight

I found a really cool article that relates Game Theory, in the story line of Charles Roven's Batman, The Dark Knight. The opening scene is a group of thieves robbing a bank. Now game theory is, a set of ideas and principles that guides strategic thinking. (Png, Lahman) -in which success in making strategic choices depends on the choice of others. (Wikipedia) When the bank heist is going on, the goal of each player is to maximize profits. To do this one player eliminates the other in order to increase individual profit margin. Each player has to wait until a specific task is complete before he can eliminate another player. The game theory choice is to eliminate a player first or to be eliminated. The dominant strategy takes place in the elimination of each player until the joker is the only one that makes a profit!

Another game theory in this movie is when 2 separate boats are faced with the choice of blowing up the other boat, getting blown up itself, or waiting and both boats getting blown up. Neither boat choses to ignite the bomb and so both boats end up surviving. Equilibrium is a state of balance, Nash Equilibrium is when 2 players know each others equilibrium strategy, or the point of their maximum potential. The Nash Equilibrium in this case is that each boat knows what its choices are and its strategic strategy the Nash Equilibrium takes place when neither boat can exceed it's potential by changing it's strategy. Of coarse Batman saves the day and the game theory ends successful for both parties.


5 comments:

Erin said...

This was an excellent article that truly drives home the point of game theory. In economics we generally focus on game theory as profit maximization, but the article states examples that include more than just money. When people's lives are at stake more is on the line than just the gain or loss of profit. In the example of the two boats in dark night both boats had the opportunity to completely ensure their survival by killing everyone on the other boat, or everyone on both boats would die at a certain time if nobody chose to push the button. I think this is a good example to help a person understand game theory, but probably isn't a very likely instance. A third party usually doesn't have the power to create a situation where everyone ultimately loses.

Kyle said...

I think the article you chose was great. One item that it pointed out that I found interesting was that game theory is limited in what it can do. In the example of the ships, there were many other factors such as moral beliefs that persuaded the passengers to not detonate the bombs. Although game theory is very useful in many situations, it is important to remember that it is based on assumptions, many of which are not completely captured in our economic models.

Deric said...

I agree that this is a good model to demonstrate the concept of game theory. One thing that I find to be a common theme in the movie, the post, and the comments is that even if you plan well, there are so many factors in game theory, and life in general, that can not be calculated. So no matter how well you understand game theory or how well you plan, somthing can always go wrong and leave you on the short side of the stick. That is why its called a "game theory" and not "calculated fact" I guess.

Dr. Tufte said...

-1 on Kaylee for a spelling error.

LOL: game theoretical situations are a common motif in movies, because they work to create tension (and sometimes uncertainty).

Kyle: the other factors you mention can and should be included in the payoffs to the players.

Deric's right too: game theory is what we use for all the situations that aren't cut and dried.

Batman Games said...

Interesting theory, but not easy to follow unless you are familiar with the maths game theory.