Game Theory and the Prisoner's Dilemma in Batman

Though anyone whose seen the Dark Knight immediately calls to mind the ferry scene when talking about the theme of game theory, the theme is actually pretty extensive throughout the film.

Game Theory
First off, game theory is a mathematically-based tool of decision making which analyzes different strategies in competitive situations in order to maximize outcome. There is a multitude of examples of game theory in politics and economics, but one of the most prominent one is Anthony Downs' model of how political candidates will often become more moderate in order to appeal to the majority of voters.

Political candidates must move their ideologies closer to the center in order to appeal to the most voters

In the opening scene of Batman: the Dark Knight, we are shown a bank robbery in which each robber is trying to maximize the profit he receives from the robbery. Each robber has a job and one he has accomplished his task, he is no longer of any value to the rest of the robbers. So, he is shot by the robber ahead of him.

The Joker, much like the politicians in the Downsian model of voting, anticipates people's actions and plans accordingly. By using game theory, the Joker accurately predicts that all the players (robbers) will act in self-interest. The robbers all play the game for money, but they are too focused on maximizing their own profit that they fail to see that they will likely be shot by the person ahead of them, just as they were shot. In the end, the winner of the game is the player who simply pauses to apply logic to it.

Prisoner's Dilemma
The prisoner's dilemma is a type of game theory which shows why two individuals (states, countries, etc.) may not cooperate, even if it is in their own best interest to do so.

The prisoner's dilemma as applied to actual prisoners

The most common application of the prisoner's dilemma in politics is in regards to the Cold War. In the Cold War arms race version of the prisoner's dilemma, the Soviet Union and United States would have both benefited the most by not building nuclear weapons at all (or disarming), because they would have saved not only money and resources, but also the fear citizens in both countries experienced as a result of the arms race. Both countries also would have benefited if they built (and used) more nuclear weapons. They would only benefit, though, if the other country stopped building nuclear weapons. Lastly, if both countries built and used nuclear weapons it would have resulted in mutually assured destruction. Even if both countries just built nuclear weapons without using them, the result would be a world that is constantly on the brink of nuclear destruction. The main points being, that no one really wins in the latter option and neither of the countries knew what the other was doing/would do at any given time!

In the Dark Knight, the Joker sets up a prisoner's dilemma by telling two ferries, one filled with criminals and the other with everyday citizens, that they must blow the other ferry up within 30 minutes, otherwise both the ferries get blown up.

In a very nihilist effort to, once again, show that everyone is self-interested and selfish at their core, the Joker sets up this genius experiment. Though the Joker failed in proving his point because of third party (Batman) interference, he was correct in calculating that there was a very high probability of at least one person, in the midst of all the chaos, to act in self-interest and blow up the other ferry.

A simplified version of the ferry scene in chart form, excludes the possibility of Batman saving both ships 

Fair Division and the Ultimatum Game

Fair division is another type of game theory, and the concept is pretty simple; each player in the game receives a fair share of whatever is being divided.

The ultimatum game is a twist on fair division in which two players (or groups) interact in order to decide how to split an amount of money.As Stephen J. Dubner, author of Freakonomics explains,

"The first player proposes how to divide the sum between themselves, and the second player can either accept or reject this proposal. If the second player rejects, neither player receives anything. If the second player accepts, the money is split according to the proposal. The game is played only once, and anonymously, so that reciprocation is not an issue."

Oftentimes the first player proposes a 50-50 split, but other times the first player offers 70-30 or 60-40, so on and so forth.Obviously it is in the best interests of the second player to take even 1% over nothing, but sometimes the second player will take nothing just out  pride or the disgust of getting anything less than 50%.

An example of the ultimatum game in politics comes from the Obama Administration's bailout proposal. Although many voters who were against the proposal were aware of the potential trickle down impact it could have on them, they remained adamantly against it. Though these voters arguably had more to gain from supporting the proposal, they were so disgusted at the implications of the amount of government involvement in business that they chose the route which resulted in a smaller payoff.  

...Just because this is the only time i'll be able to use this video for school-related purposes

Christopher Nolan ties in the game theory aspects of fair division and the ultimatum game in the scene where the Joker negotiates with the mob.
In the scene, the Joker offers to kill Batman for half of their shares in the mob money which the mob cannot get access to on its own.Though the mob's immediate reaction is disgust at the Joker's belief that he could take so much of the money, they quickly realize that they are dealing with an ultimatum game; if they decline the Joker's offer, it is very likely that they will get absolutely nothing because they can't locate their money.There is no negotiating, as the ultimatum game is played only once, so the mob ultimately (no pun intended) take the offer.

The Joker plays the ultimatum game with the mob