Game Theory in the Dark Knight
Spoiler Alert: If you have not seen the movie The Dark Knight, then do not read this article.
In the movie The Dark Knight, there is a scene where the Joker holds two ferries hostage. Both ferries are wired with explosives, and each ferry’s occupants hold the detonator for the other boat. The Joker is in possession of a detonator that can detonate both sets of explosives and destroy both ferries. One ferry holds only civilians, while the other is full of prisoners. The Joker gives the boats an ultimatum. If one ferry’s occupants decide to use their detonator to blow up the other ferry, then they will be safe, but if neither ferry uses their detonator, then the Joker will blow them both up after thirty minutes. This gives rise to an interesting game.
The players are the two ferries, ferry A and ferry B. Their strategies are either to detonate, or not detonate. If we assume that the decisions are made simultaneously, then they could theoretically both decide to detonate at the same time thus ensuring their mutual destruction. The four states then would be (D,D), (N,D), (D,N), and (N,N) where N stands for not detonate and D stands for detonate. Unfortunately for the occupants of the ferries, (N,N) will result in their mutual destruction after thirty minutes when the Joker detonates them both. This game as it stands has two Nash equilibria, (N,D) and (D,N). The reason these qualify as Nash equilibria is because if your opponent decides to detonate, then you have no hope and unless you wish to be vindictive, you should choose to not detonate to at least preserve your morality, and if your opponent decides to not detonate, then you should obviously detonate to ensure your own survival. This reasoning only hold if survival matters more to the occupants of the ferries than morality, which we learn isn’t the case. Neither boat ends up detonating, and as they await their pending death, Batman deals with the Joker allowing both boats to survive. As the article describes, this game could be played out a large variety of ways and it all depends on the moral standing of the ferry riders, and how much faith they have in Batman saving them. It is a very interesting look at a fairly simple game.
http://quantitativepeace.com/blog/2008/07/the-dark-knight.html