Joker’s Failed Social Experiment: Game Theory in The Dark Knight

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After going through Game Theory and Nash Equilibrium in multiple courses during my MBA course, the one “game” that kept coming to mind was the one set up by the Joker for two distinct population samples from the city of Gotham in the movie, The Dark Knight.

Context

Here’s the setup:

In case the video is taken down, there’s a short description at a Batman Wiki link here.

The citizens were on one boat, and the criminals were on the other. However, the Joker revealed that there are two bombs on each boat and each boat has a detonator to the other. He gave them an ultimatum: if neither the citizens nor the criminals blow the other up by midnight, the Joker will blow up both ships.

To simplify the setup, I am going to use -1 for a negative result (death), +1 for a positive result (life) for the players.

Game Theory Grid

The joker expected that the result {Kill, Kill} would be chosen by the people on the two boats, i.e. both the criminals and the civilians on the two boats would use the detonator killing each other in the process. However, the result that was observed corresponded with the {Don’t Kill, Don’t Kill} choice, i.e. neither player used the detonator available to them, despite the Joker’s warning.

The Joker assumed that the game was as simple as defined by the grid presented above. At first glance, it does seem that simple. So why did his experiment fail? Because the game wasn’t that simple.

Movie Logic

The movie explained the outcome by presenting that both population samples considered death (a noble death?) to be a better alternative than killing others to save their own lives.

A second argument could be that the game turned into a repeated sequential game. Ever second that passed without one player choosing the kill the other, signalled to the other player that “Kill” was not the strategy of choice for either player.

Real Life

In real life, we have seen such a game played out on the time span of years and decades. We know this game as the “Cold War”. This game, just like the one Joker had designed, was in fact one of Mutually Assured Destruction (MAD). Neither player wanted to trigger an action as the other player would have had enough time to respond “in kind” leading to an assured loss for both the players. It can be argued that the players in the movie would have also had time to act in a similar fashion had the explosion not caused an immediate loss of life.

Another factor that Joker probably never considered was whether the players believed his instructions to be accurate, given the information they had about him. Considering his reputation for being manipulative, it was possible that either detonators would have triggered the explosion on both ships. This hypothesis wasn’t explicitly represented in the movie, but would certainly have been a legitimate argument had it been put forward by the people on the boats.

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