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The Dark Knight- Game Theory

Christopher Nolan’s 2008 film the Dark Knight contains an excellent example of game theory. Near the end of the movie, the Joker rigs two ferries carrying people out of Gotham with explosives, one with convicts, and one with civilians. He also gives a detonator to the crew of each boat, but it detonates the explosives on the other boat. This can be designed as a game with the two ferries A and B as the players with the following rules. If any member of Ship A pushes the detonator, then Ship B is destroyed and all of Ship A is saved and vice versa.  Additionally, if either ship fails to use the detonator to destroy its opponent, then both ships will be destroyed by the Joker. This can be modeled as a game with the payoff of surviving as 1 and the payoff of the ship being destroyed as -1. The only difference is that both ships cannot both detonate since it is assumed that once one ship is blown up they do not have that option anymore.

Ship A

Ship B

Detonate Don’t Detonate
Detonate Not allowed (1, -1)
Don’t Detonate (-1, 1) (-1,-1)

Based on this payoff matrix, both ships would want to detonate the other ship based on payoffs alone, disregarding the moral repercussions. However, this situation makes many assumptions that make this outcome unlikely. First, there are moral consequences of pressing the detonator that may have a large impact on the decision. If one ship blew up the others, no matter what they would be labeled as murderers. Also, either one or both of the ships could potentially be saved, which is a big reason why both ships are not too eager to push the detonator.

In the movie, the convict ferry throws their trigger overboard, and no one on the civilian ferry can bring themselves to blow up the other ferry. So midnight arrives and both ferries are intact. Batman swoops in and stops the Joker from blowing both up. In this situation, the boats both coordinate on not detonating, providing us with a great example of game theory in popular culture.



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