Game Theory in The Dark Knight
When people think about The Dark Knight, two things come to mind: The Joker and Batman. The Joker, who is the antagonist of the film, terrorizes Gotham city. On the other hand, Batman represents hope for Gotham. Fighting evil never seems challenging for Batman, but he struggles to take down the Joker for almost all of the movie. The conflict between these characters can best be defined as a fight of good vs evil or chaos vs order. Christopher Nolan, who directed this film, utilizes game theory to highlight the principle of good vs evil in the end of the movie. While the example of game theory does not revolve around the Joker and Batman, it is still rooted in good vs evil.
In the end of The Dark Knight, the Joker plants bombs on two ships. One ship has civilians (good), and the other has prisoners (evil). Thus, the ships represent a battle of good vs evil. Game theory applies to this scene because the Joker gives both ships two options: Cooperate or Detonate. One could say both ships should cooperate with one another so they do not blow each other up; however, the Joker tells them they will both be blown up if one does not detonate the other. This is a perfect example of the first game we learned this year: The Prisoner’s Dilemma. Below is the payoff matrix for the Joker’s “social experiment.”
In the matrix above, zeros represent death and ones portray survival. If both ships cooperate, they both die because the Joker will blow them up. The same payoff results if both choose to detonate. The catch with both detonating is that they would have to detonate simultaneously because no dead person can operate a detonator. From an economic theory perspective, both should choose to detonate because they have a payoff of 1 if they do and 0 if they do not (assuming they do not press the detonator at the exact same time). This means that detonating is the dominant strategy for both ships. Whichever ship detonates first has a payoff of one, and the other has a payoff of zero because the latter chose to cooperate. An economist assumes one of the ships will be blown up; nevertheless, the prisoners and civilians of Gotham go against economic theory and decide to take the risk of not playing their dominant strategies.
Because both ships chose not to detonate, they both should have exploded. However, this does not happen because Batman stops the Joker from using his detonator. Symbolically, good trumps evil. In the good ship vs bad ship debate, one might say that the civilians should blow up the prisoners because they are bad for society. One man seems willing to blow up the prisoners, yet his morality gets the best of him. On the other hand, no prisoners want to blow up the civilians. Nobody on either ship had enough evil within them to blow up a boat. Empathy is the key to this game. The people on both ships most likely deviated from rational behavior because they feared the lasting effects of their actions. Some would probably live with PTSD or never forgive themselves for killing others, even if it meant saving themself. This game may have had a much different outcome if the Joker said nobody gets off the boats until one explodes, assuming somebody would have been pushed to their breaking point after hours and possibly days of starvation.
Though the prisoners vs civilians game had a clear dominant strategy for both parties, empathy trumped economic theory. In order to understand why this game had the payoffs that it did, one must study some aspect of behavioral economics. Deviating from rational behavior is not uncommon, but standard game theory revolves around playing what is best for one’s own good. Though detonation was best, neither ship chose to detonate. When studying game theory, it is important to remember that humans are not always rational. Whether its civilians or prisoners, people’s morals can dominate their dominant strategy.
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