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Batman: The Dominant Strategy

link: http://www.denofgeek.com/us/movies/batman/253726/the-dark-knight-the-joker-and-game-theory

Game Theory, as we have learned, is prevalent not just in economics or bargaining but also in board games and media. The Dark Knight is a perfect example of how game theory is included in films. The Dark Knight received widespread praise not only because of the outstanding acting and the great action shots, but also for its character development of the Joker. The Joker is one of the superhero universe’s most feared villains not because of his physical abilities but because of his cleverness and his trickery.

In The Dark Knight, the Joker, true to his name, created many horrific yet interesting “games” of life and death that his victims had to play in. The epic opening scene is a game that involves six bank criminals robbing a bank. Each robber is trying to maximize his payout, and kills his accomplice to keep the shares for themselves until the Joker is the lone survivor:

https://www.youtube.com/watch?v=Yqvbv-SB4bg

Another example of game theory in The Dark Knight is the interrogation scene. In this scene, Batman must decide to save his love interest, Rachel Dawes, or the politician, Harvey Dent. In Batman’s perspective, the value of saving Rachel is higher than the value of saving Harvey, but he fails to consider whether the Joker is lying about their respective locations, and Rachel dies as a result:

https://www.youtube.com/watch?v=ys7nYaHvZos

Perhaps the most terrifying and applicable game in The Dark Knight is the ferry scene. In this scene, two ferries, one packed with civilians and one packed with prisoners, are given a detonator to blow up the other’s ship. If one ferry blows up the other’s ship, only that ship’s passengers will die. However, if no one blows the other’s ship up, then both ships’ passengers will die:

https://www.youtube.com/watch?v=K4GAQtGtd_0

This is a classic example of the Prisoner’s Dilemma, except the stakes are much higher. According to Nash, the equilibrium would be to “confess,” or for one ship to blow up another, and the civilians actually choose this strategy. However, due to the emotional burden of killing thousands of people, neither ship blows up the other. Fortunately, Batman saves both ships in time and subdues the Joker, making Batman the hidden dominant strategy.

The ferry scene raises some important questions about Game Theory and Nash’s Equilibrium. Nash’s Equilibrium assumes that either each decision is unbiased or bias is incorporated in the payoffs. However, can humans really play a game without emotion, and how can we accurately measure our emotional bias numerically? Furthermore, some civilians raised an interesting point that the criminals “already had their chance.” This raises the question: should we consider the other players’ previous actions, and if we do, how can we accurately measure how much those previous actions affect the game?

 

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