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

Batman as an Allegory of the Bush Administration

A common political analysis of Batman by movie critics and movie-goers alike is that The Dark Knight was written as a parallel to the Bush Administration's war on terror.

Much like our society at any point in history, Gotham is laden with criminals and businessmen motivated by a seemingly insatiable greed for money. Then the Joker is introduced. A man who commits evils for the sake of anarchy, and has no desire for material rewards.

The Joker also films a murder of a Batman imitator and threatens to continue this cycle or murder until he gets what he wants. The Joker's evil for the sake of evil mentality, along with his filmed murder of Gotham city citizen creates a very convincing parallel between Osama Bin Laden, as well as the filmed beheading of American journalist Daniel Pearl. Moreover, much like Gotham city officials at first, the Bush Administration at first refused to, then attempted to negotiate with terrorists. Eventually, however, both the officials of Gotham and the Bush Administration gave into using un-democratic means of dealing with the grave threats they faced after negotiation attempts failed.

The only person who has the power to defeat the Joker is Batman, a man who operates outside the law. Commissioner Gordon calls upon and works with Batman because he recognizes that sometimes the only way to protect a democracy is to use un-American measures. Even Harvey Dent, the moral center of Gotham, becomes convinced by the end of the film that terrorism cannot be fought within the boundaries of the law.

In the midst of the Guantanamo Bay reports during Bush's presidency, Americans split into three distinguishable groups. These groups were comprised of those who thought that the torture was inexcusable and the officials in charge should be put on trial for war crimes, those who thought torture was sometimes a necessary means to an end as long as Americans have government transparency in regards to it, and those who agreed torture was sometimes a necessary means to an end but wanted only to secretly acknowledge the use of such unlawful means.

American Innocence: Maintaining the Bliss of Ignorance
The citizens of Gotham city seem to be completely content and, until the end, thankful for the existence of Batman. They know that he uses illegitimate means to protect them, yet they choose to turn a blind eye because it works out in their favor. Batman tracking all phone communications, a complete legal violation of privacy, is never revealed to the public and is thus, portrayed by Christopher Nolan as a necessary means to fighting evil that the citizens don't need to know about.

Batman Begins, but Batman-related wisdom nonetheless

Although this works for the city of Gotham, its parallel in real life is extremely controversial, as gross violations of privacy, even for the sake of doing good, present an easily-corruptible slippery slope if put into the wrong hands. Moreover, with the lack of government transparency, American citizens would not know if the information was in the wrong hands.

The citizens of Gotham can be compared to the aforementioned third category of American citizens in wake of the torture reports of Guantanamo Bay. Much like the American citizens who agreed torture was sometimes necessary when fighting terrorism and were okay with it as long as they didn't have to know about it, the citizens of Gotham accept that sometimes unlawful means are necessary to fight evil but want to remain innocent and blissful with no in-depth knowledge of the acts being committed.

Gotham City

A Failed Liberal Democracy

In Batman: The Dark Knight, we are essentially told by Christopher Nolan that liberal democracy, while being the backbone of America and good in theory, does not work in practice. In other words, the liberal democracy being ineffective when it comes to protecting the people in it is a prevalent theme in Batman the Dark Knight. The state of Gotham at the beginning of the film is a city running rampant with crime. When Harvey Dent, the idealistic conservative hard-on-crime District Attorney, decides to put thousands of Gotham's criminals behind bars in an act of retribution and incapacitation (both conservative-leaning goals), he sets off a horrible chain of events. 

The mob's efforts to get back at Dent for sending so many criminals to jail and at Batman for constantly foiling their plans are deficient, so they accept the help of the Joker, an existential enemy of Gotham city and Batman. The Joker's only motivators seem to be showing that even the best people will act out of self-interest and, plainly, evil for the sake of evil. 

The city's police have no power over the Joker, the city has exhausted all political policy options, and even Harvey Dent, Gotham's personification of hope, has no power to stop this massive threat to the city. And so the city officials turn to Batman. 

The city of Gotham is portrayed as a place crawling with crime that liberal democracy cannot possibly control. Even the glimpse of hope offered by Harvey Dent is trampled over by more crisis for the city. Many of the policemen and government officials are corrupt or easily corruptible.  Officer Anna Ramirez, for example, turns in Harvey Dent because of a threat from mob boss Sal Maroni.

The Joker explains people and corruption

The  one person who can save Gotham is Batman. It is surprising that in a democracy, the only person that can protect a whole city is a man who operates entirely outside of all democratic allowances. Batman uses his own judgement and is his own judge and jury.

Batman using his own judgement. A normal person would get charged with assault and battery but in Gotham, it's okay as long as it's in the name of justice. Or if you're a billionaire playboy with cool weapons.

In fact, he even goes so far as to invade on the privacy of about 30 million people for the sole purpose of defeating one threat. Whether this is Christopher Nolan's way of commenting on Bush's Patriot Act or not, it is a completely un-democratic means to a noble end. The sonar device is so ethically questionable, in fact, that Lucius Fox insists on resigning when the goal of the privacy invasion is reached.

Lucius Fox resigns

Everything Batman does to safeguard Gotham is an exception to the rule of law that everyone else has to follow. He does not follow the laws of democracy, yet is seen as the hero and the only person who can keep the Gotham safe. This whole idea is so obviously right-wing that some may go as far as to say it is fascist, in the George Orwell-ian Conservative sense. Yet we view Batman as a hero, a protector of our civil liberties. And, thus, we make exceptions for everything he does, even though any other normal citizen who did the same things would be considered a dangerous criminal who would elicit a response similar to this from us everyday citizens: