The Game theoretical take on the decisions of the two boats in The Dark Knight
In the Dark Knight, the Joker (antagonist) takes over two ships: one carrying passengers on their way out of the city harbour and one carrying criminals. He then reveals he has placed detonators on both ships, and the remote to set off the detonator for a given ship is in the opposite ship. The passengers have two choices: either blow up the other ship, or leave themselves to the mercy of others who get saved if they blow up the other ship. Additionally, if neither ship blows up the other, the Joker blows both up.
The strategy matrix will be represented with the strategies of the two following entities: Ship 1 and Ship 2. Both ships have identical choices: either blow up the other ship (B) or don’t (N). Essentially, what the joker set out to prove was that humans are inherently selfish and cannot sacrifice for others.
| B | N | |
| B | D,D | L,D |
| N | D,L | D,D |
The payoffs are expressed as D and L where D is death and L is life. It also follows that L>D and is the preferred alternative. As we can see, in the above strategy matrix, there are two Nash equilibrium, (B,N) and (N,B). This shows that either ship would want to blow the other up as soon as possible, so that they may live: the logical choice. This is what the Joker set out to prove.
Obviously, in the movie, people are good and not rational to a fault; they do not blow each other up and Batman saves the day. From a game theory perspective, however, the Joker should have won and shown the world that humans are rational before moral.
Relevant Link: https://www.youtube.com/watch?v=JMq059SAQXM&feature=share