The Dark Knight, The Joker, and Game Theory

How crazy was Heath Ledger as Joker in The Dark Knight? We look at what game theory can tell us about the villain and his motivations.

This article comes from Den of Geek UK.

“You wanna know how I got these scars?” Heath Ledger’s Joker asks in The Dark Knight. It’s a rhetorical question the Clown Prince of Crime utters twice in the film, followed by two very different stories – one involving his alcoholic father, the other concerning his ex-wife and a razor blade.

These stories are the perfect illustration of the character’s ambiguity, as written by Jonathan and Christopher Nolan. One story could be true, the other false. Or they both might be true; the Joker’s scars may have become as ghoulish as they are because of these two separate incidents. Or maybe neither is true; it’s all part of the trickster’s slippery persona.

Like John Doe in David Fincher’s Seven, the Joker seems to bubble up in Gotham City like a phantom from its collective unconscious – a walking embodiment of its social malaise. Bruce Wayne’s loyal friend Alfred suggests that the Joker’s a character who “just wants to watch the world burn.” The Joker compares himself to a dog chasing a car; he wouldn’t know what to do if he actually caught up with it. Yet in another scene, the Joker pointedly denies the suggestion that he’s insane.

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“No, I’m not,” he tells smooth gangster Gambol (Michael Jai White). “I’m not.”

So just what is the nature of the Joker’s madness, as portrayed in The Dark Knight? What is it that motivates him to become a self-described “Agent of chaos”? One thing’s for sure, the Joker is far from your typical supervillain…

The Prisoner’s Dilemma

If you’ve seen the Oscar-winning film A Beautiful Mind, you’ll be familiar with the American mathematician John Nash. He contributed hugely to the model of game theory in the 1950s, when the cold war was at its height.

Game theory, described very simply, is the study of underlying strategies in human interaction. Through analyzing two people playing Tic-Tac-Toe, for example, you could come up with a mathematical formula which shows all the different possible moves that each player could make, and from this conclude which approach is most likely to score you a victory. In fact, lots of mathematicians have already done this for us.

There’s a thought experiment which is often used to illustrate how game theory works, called “The Prisoner’s Dilemma.” Adam Curtis once described it in his BBC film, The Trap.

“The Prisoner’s Dilemma” goes like this. A jewel thief is attempting to sell a stolen diamond for a million dollars. A gangster is keen to buy it, so the jewel thief and the gangster make a deal over the phone: rather than meet face to face, they’ll leave the gem and the money in separate locations for the other to collect.

Now, the jewel thief has no way of knowing whether the gangster will tell the truth about the location of the money, and the gangster doesn’t know that the jewel thief will be honest about where he’ll leave the diamond, either.

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Game theory suggests that, from the jewel thief’s point of view, it’s tactically better to lie than to tell the truth. In the worst possible sequence of events, the gangster will have also lied about the location of the money, which means that, if the jewel thief also lies, he’ll still get to keep the diamond. In the best-case scenario, the gangster will have told the truth and the jewel thief will therefore get to walk home with the diamond and the cash.

read more: 10 Times the Joker Almost Nailed Batman

With the very real threat of nuclear armageddon looming in the 1950s, game theory was eagerly taken up by American scientists as a means of predicting enemy behavior. By viewing the cold war as a game of Tic-Tac-Toe between west and east, game theory could create a model of both sides’ strategies and their likely outcomes.

Here’s Professor Philip Mirowski, an economic and political philosopher, explaining how this works in The Trap:

“This is a type of war that had never been fought before. And as we all know, the outcome would have been so devastating that it’s impossible to consider all of its consequences. [Scientists] still wanted to say there was a rational way to approach such a virtual war, and game theory could offer that to them. That you could incorporate your enemy into your own thinking; that you could mathematically understand what your enemy was going to do to the point where you and your enemy would play the exact same sub-strategies.”

This means of using strategy to achieve equilibrium would soon proliferate far beyond the nuclear bunkers of the cold war thanks to the Nobel Prize-winning theories of John Nash. In his own words, Nash often described human interaction as being like a poker game; both sides are modulating their behavior to get what they want out of the other person – even if they’re not conscious of doing so.

If everyone in the game is working for their own self-interest, Nash argued, then they’d ultimately find stability – a state where everyone gets what they want without falling out. Or, in cold war terms, everyone can carry on about their daily business without being blown up by a nuclear warhead.

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The Nash equilibrium, as it’s widely called, has been applied to all kinds of sciences, from economics to football matches. We can also see this strategic theory in the Joker’s way of thinking – and, indeed, some math and philosophy scholars noted the parallels not long after The Dark Knight’s release. Let’s have a look at a few examples of the Joker’s behavior and how they apply to the basics of game theory.

The Bank Robbery

It’s The Dark Knights memorable opening scene: five robbers in clown masks embark on an elaborate bank heist, rappelling onto the roof from a nearby building, cutting the power and pairing off to storm various parts of the building. As they do so, they talk about a weird guy in make-up who put them on the job. And then something unexpected happens. One by one, they turn on each other – each mentioning something to the effect that, with fewer members of the gang left, the more money there is to go around.

By the time the Joker has torn off his mask to reveal an even more ghoulish face beneath, the villain’s accomplices are all dead – each tricked into offing the other once they’ve fulfilled their part in the Joker’s plan. It’s a superb opening scene, recalling the famous heist from Michael Mann’s 1995 thriller Heat while also giving us an early insight into the way this particular incarnation of the Joker thinks and schemes.

read more: Why The Dark Knight is Still The Best Superhero Movie

The Joker’s bank heist hinges on the assumption that the robbers working with him are violent, amoral and driven only by greed; when offered enough money, they’re willing to turn on each other for a share of it. Had any of the robbers proven the Joker wrong and refused to kill their partners in crime, it’s likely that the plan would have fallen apart quite quickly. But of course, the robbers don’t disappoint, thus delivering the Clown Prince of Crime the outcome he’d been expecting all along.

As this YouTube video explains, the Joker’s orchestration of the opening heist has much in common with the Pirate Game, a thought experiment akin to the Prisoner’s Dilemma mentioned above. In brief, the game sees five pirates, each more senior than the last, trying to decide the best way to dish out 100 gold coins. If the most senior pirate wants to keep the lion’s share of the coins, he has to appeal to the other pirates’ desire to stay alive and maybe make a little bit of money. The Pirate Game’s best outcome, from the senior pirate’s point of view, sees him walk off with 98 coins, two of his cohorts dead and the other two left behind with one measly gold coin each.

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In the case of the heist in The Dark Knight, the Joker is, of course, the senior pirate. But because he’s the Joker, he finds a way of playing the game where he gets all the money and all of his compatriots wind up face down with a bullet in their backs.

The Games People Play

Just about every move the Joker makes in The Dark Knight has a similar strategic underpinning.

Take the sequence where the Joker negotiates with Gotham’s most vicious gangsters over killing Batman, and how much it should cost. The Joker says he wants half of the gangsters’ money, which understandably causes a ripple of anger in the room. The Joker counters by saying that, with Batman on the loose in Gotham, the gangsters will lose money because they won’t be able to run their business anymore (“Soon, little Gambol here won’t be able to get a nickel for his grandma”).

In a brilliantly detailed article, Presh Talwalkar explains that the Joker is playing a variation on the Shrinking Pie Game in this scene. The scenario is this: two kids are arguing over how to split up an ice cream pie, which is rapidly melting because it’s a hot, sunny day. One kid gives the other a simple ultimatum: we either stand here arguing over the pie until it melts, or we agree to divide it in two now and we both get to enjoy it.

The Joker plays the same game with the gangsters: make this deal now before it’s too late.

Again and again, the Joker sets other characters against each other, making them unwitting (or unwilling) participants in a game. There’s the scene where the Joker throws a broken pool cue at the feet of a pair of hoodlums and tells them to “try out” – essentially fight each other to the death – for a place in his gang. Or there’s the sequence where the Joker forces Batman to ‘choose’ between Rachel and Harvey Dent, since they’re both about to be blown up at exactly the same moment (the Joker being the Joker, this choice is soon revealed to be nothing of the sort).

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read more: The Actors Who Have Played The Joker

All Joker’s interactions with other characters are about manipulation, largely working on the assumption that they’ll give one thing up in exchange for something else which will help them or somebody close to them. Cops are corrupted into giving up vital information because they have loved ones in Gotham’s hospital. The mob give Joker a fortune in exchange for Batman’s death. Citizens try to kill an accountant because the Joker threatens to destroy a hospital.

For a maniac in clown makeup, the Joker sure likes to strategize. But maybe that’s because the Joker is far less crazy than he’d have Batman believe.

The Madness of the Joker

See how the Joker prickles, just slightly, at Gambol’s suggestion that he’s crazy? Do you see the flicker of an expression in Heath Ledger’s performance which suggests something like, “You don’t have a clue who or what I am?”

This tiny moment is perhaps the key to understanding the Joker’s true nature.

The Joker’s genius is in making his actions seem irrational when they’re anything but. Because why would a sane person do something as hare-brained as rob a mob-controlled bank? What kind of sick person would blow up a hospital? Through his bizarre appearance and actions, the Joker successfully obfuscates his true way of thinking.

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read more: The Many Deaths of the Joker

Far from a crazed nihilist, the Joker is cunning in ways that Batman or his ally Commissioner Gordon fail to grasp. When Batman succeeds in arresting the Joker roughly midway through the film, he hasn’t reckoned on the possibility that the Joker had planned on being caught all along. By failing to recognize that the Joker’s moves are profoundly strategic, Gotham’s powers of good wind up underestimating him over and over again.

The Joker says to Harvey Dent, “I don’t have a plan,” yet this clearly isn’t true. He says he believes in chance, yet the Joker’s games of chance are always rigged in his favor.

Everything the Joker does in The Dark Knight is informed by a particularly dark reading of game theory – that humans are entirely ruled by self-interest. It echoes the philosophical thinking of the homo economicus, or economic man, as introduced in the 19th century by such writers as John Stuart Mill or Adam Smith. Here’s a quote from the latter:

“It is not from the benevolence of the butcher, the brewer or the baker that we expect our dinner, but from their regard to their own interest.”

The Joker takes this to his own conclusion: that altruism doesn’t exist, and that human beings are so self-interested that they’ll kill each other if they have to. As the villain tells Batman, “Their morals, their code – it’s a bad joke. You’ll see. I’ll show you – when the chips are down, these civilized people, they’ll eat each other. See, I’m not a monster. I’m just ahead of the curve.”

Origins and Motivations

The Dark Knight keeps the Joker’s precise origins shrouded in mystery, and even his motivations appear to change over time. We see the Joker rob a bank and negotiate with the mob for even more money, yet he later burns it. Then we’re led to assume that he wants to kill Batman, but then he reveals that this was never his intent. Engaging Batman in an unending game of psychological cat-and-mouse, it seems, is the Joker’s sole interest.

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read more: Joker Movie Review

There’s a theory that the Joker’s an ex-soldier, because how else do you explain his weapons training, his expertise with explosives? Whatever the villain’s past was before he decided to don his suit and makeup, the Dark Knight trilogy gently implies that Batman may have inadvertently created the Joker himself. At the end of Batman Begins, we see Gordon warn the Dark Knight about escalation:

“We start carrying semi-automatics, they buy automatics. We start wearing kevlar, they buy armor piercing rounds. You’re wearing a mask. Jumping off rooftops…”

Gordon then recounts the crimes of a new felon with “a taste of the theatrical” – thus drawing the link between Batman’s activities and the rise of the Joker. Inspired by Batman’s approach to upholding the law, the Joker’s inspired to unleash his own form of chaos.  

The Joker is not motivated by money or power for its own sake, but by his own games.

The Two Boats

The Joker’s bleak view of human nature is ultimately proved false in his final game. Two boat-loads of passengers are given until midnight to press a button, detonating the explosives in the other ship’s hold before the Joker blows up both boats himself.

From a strategic point of view, the scenario seems perfectly simple: one boat’s full of criminals, the other full of ordinary civilians. Why shouldn’t the civilians blow up the criminals in order to save themselves? Who would miss them? The same could be said from the criminals’ perspective: we’re shunned by society anyway. Why not blow up a bunch of strangers in order to save ourselves?

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Yet the Joker failed to factor in such human instincts as conscience and distrust in his strategic model. Blowing up the other boat may be the logical thing to do, but what about the psychological fallout afterwards? Could you live with yourself if you’d sacrificed dozens of lives to save your own? As it turns out, the passengers of both boats came to the conclusion that they could not. Maybe the Joker isn’t quite as far ahead of the curve as he thought he was.

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Much has been written about The Dark Knight being a Batman movie for the War on Terror era. Batman, the thinking goes, is an allegory of the US defending itself from terrorist threats, and the Joker represents the outside forces of chaos which threaten it. Yet it’s arguable that The Dark Knight is more complex than a battle between the US on the side of Good and the Joker on the side of Evil.

The Joker uses terror tactics and cunning to manipulate the people of Gotham in a repeated attempt to prove that reality conforms to his own worldview. Yet in the film’s final act, the Joker’s plans are thwarted by the blind spot in his thinking: the people on the boat refuse to kill each other. Batman risks his own life to save Gordon’s son from Harvey Dent, before literally taking the fall for Dent’s crimes.

If there’s a ray of sunshine to be found in The Dark Knight, it’s the assertion that altruism and selflessness really do exist. Among the many themes Christopher Nolan’s film touches on, maybe one of them is the importance of generosity and empathy. With so many of us living among strangers in cities, fearful of terrorism or what the economic climate might do to us next, it’s surely more important than ever to hold on to those human traits – to bear in mind that we’re not the greedy, selfish machines that the Joker believes us to be.