A Joker and Two Ferries: Game Theory in The Dark Knight

Two Ferries and a Joker: Game Theory in The Dark Knight

So, this is akin to my earlier post about racquetball (not related to constitutional law). But, there is definitely game theory in one of my favorite movies: The Dark Knight. A quick google search of “game theory in the Dark Knight” will show you that I am certainly not the only one who thinks so.

If you haven’t seen the movie, (1) you’re missing out, (2) this might not be as meaningful of a post for you. Regardless, this is a good little post for a weekend. Beware, spoilers abound.

Part 1: A Joker

In addition to being a great character in a great movie, the Joker gives real insight into the use of “strategy” in playing a long complicated game. Footnote 5 of Weingast explains a strategy: “A strategy specifies the action a player will take at every node of the game”. So, “beat the Batman” is not really a strategy. If we outlined a game like the models in Weingast (sovereign constituent transgression game) where all the nodes are specified, we could say a strategy like,

If A plays challenge, play challenge

Then if A plays challenge again, play challenge again

If A plays acquiesce, play acquiesce

If A plays challenge after your acquiesce, play challenge

Etc Etc. So, it needs to be a complete listing of all the moves you will play in every event.

This gets really interesting when you think about infinitely (or just very long) iterated games. For instance in the Axelrod tournament, the computer programs had to be prepared to answer for every situation. A strategy in that setting could be, play cooperate every time, because that accounts for every contingency. Or it could be as complicated as, play cooperate every time, unless opponent plays defect, then play defect for the next 10 times, then switch to cooperate, unless the opponent plays cooperate 3 times in a row during those 10.  Complicated, but comprehensive.

Now, back to the Dark Knight. The Joker and Batman are essentially engaged in a long game. They each have a strategy to play against each other like you would expect. I think the Joker’s “strategy” is interesting:

The Joker: Do I really look like a guy with a plan? You know what I am? I’m a dog chasing cars. I wouldn’t know what to do with one if I caught it. You know, I just… do things. The mob has plans, the cops have plans, Gordon’s got plans. You know, they’re schemers. Schemers trying to control their little worlds. I’m not a schemer. I try to show the schemers how pathetic their attempts to control things really are. So, when I say… Ah, come here…
[takes Dent’s hand into his own]

{Joker hands Two-Face a gun and points it at himself]

The Joker: Introduce a little anarchy. Upset the established order, and everything becomes chaos. I’m an agent of chaos. Oh, and you know the thing about chaos? It’s fair!
[still holding the gun, Two-Face pauses and takes out his coin]

Two-Face: [showing the unscarred side] You live.

The Joker: Mm-hmm.

Two-Face: [flips, showing the scarred side] You die.

The Joker: Mmm, now we’re talking. {Quotes taken from the Dark Knight IMDB page}

Well! Let’s break this down. The Joker is claiming that his strategy is essentially play random at every node. He is particularly happy when he gets Harvey “Two Face” Dent to subscribe to the philosophy of randomness. A coin flip is theoretically perfectly random. It  may or may not be “fair”, but that is a question for philosophers. So, the Joker gets to live because of the “luck” of the coin flip.

Is play random really a strategy though? Yes! Definitely! Sometimes, it is actually a great strategy. Sometimes you can’t actually do better than random. But it really depends on what your opponent’s strategy is. So, who are the Joker’s opponents? Batman, the police commissioner, the mayor, society, etc. They are characterized as schemers and planners. How do you play against a schemer and a planner? With no plan! Pretty smart. But, that is really only level 1 of the Joker’s genius.  See, the Joker does an excellent job of convincing everyone he comes straight from the looney bin. He dresses funny, he has a crazy laugh, he seems to be unpredictable.  Batman et al devise a strategy to play against the strategy of random.

Therein lies the genius of the Joker. Half (all?) of game theory is the interaction with your opponent and what your expectations of their strategy is, and their expectations of your strategy and the expectations of your expectations of their strategy, ad infinitum. The Joker would do well by playing random. The Joker does extremely well by convincing Batman et al. that he is playing random at every turn. The Joker is a genius in thoroughly convincing everyone that he is in fact playing random when he is doing NOTHING of the sort!

The Joker plans his moves 3 or 4 steps ahead of Batman et al. His opponents would be able to form a strategy to win against his plan, but they don’t bother because they think his actions are random! They don’t anticipate that the Joker would want to be caught and put into jail so that he could escape and kill the informant who would testify against the mob. They thought they were springing a trap on the Joker because they were transporting Harvey Dent who they knew would attract the Joker. But, the Joker knew what they were up to. Again, Batman and company did not think that Joker would be thinking one step ahead, so they did not even bother to think about it.

Another “dumb” move by the Gotham government was to put a whole bunch of people on ferries with the expectation that the Joker would not have thought of that. (The people were put on ferries to get out of the city, after the Joker “takes over”) Anyways, this action leads to part two of this post,

Part 2 “Two Ferries”

This is a textbook game theory game. Here’s the set up:

Ferry 1 is full of convicted felons and some guards.

Ferry 2 is full of civilians fleeing the city.

Instead of analyzing the justice of sending convicts out of the city before other civilians, let’s look at the game they play. The Joker has put bombs on both ferries. Each ferry has a detanator. The Joker tells each ferry they have the detantor to the other ferrie’s bomb.

{Now, let’s examine that a bit further. This is just cheap talk. For all we know each ferry has their own detanator. So, let’s not take that as a given}

The Joker then claims that if neither ferry blows up the other ferry, he will blow up both ferries at midnight.

{I recall an identical premise in one of William Poundstone’s books- it was either Labyrinths of Reason or Prisoner’s Dilemma. You were in a room next to a loved one and you both had a deadline like midnight wherein you would both die unless one of you pressed a button that kills the other. Obviously you don’t want to kill a loved one. But, no need for both of you to die. So you should wait until the last-minute to see if your friends kills you. But they should do the same. Anything other than both of you dying is best. But, the point of his story was about recursive logic of when you should press the button (you should wait until the last second, except that they would do that, so you should do it 2 seconds before, but so should they so you should do it three seconds before etc)}

So, then there is a whole inquiry into democratic legitimacy when people are deciding on whether or not they should vote on whether or not to press their trigger. It is interesting because they actually debate on whether or not they should vote. Then they debate on how they should vote. It is very Robert’s Rules of Order/Congress style of thought there.

So, spoiler alert- the convict ferry throws their trigger overboard, and no one on the civilian ferry can bring themselves to blow up the other ferry. So midnight arrives and both ferries are intact. Then Batman swoops in and stops the Joker from blowing both up. A nice happy story about the possibility of cooperation and coordination amongst opponents.

Bottom line? Well, we see that the Joker is a genius by making his opponents believe he is playing a random strategy, when he is doing anything but. With his pretend strategy as “common knowledge” he is free to play several steps ahead and gain an advantage.

With the two ferries, we see some possible light at the end of a dark tunnel where the possibility of cooperation and coordination seems bleak. There were some hints at democratic sensibilities with the “should we vote on whether we should vote” question, but also of course plenty of questions for the moral philsophers.

And, the Dark Knight is also just an amazing movie.

Posted on July 16, 2011, in Uncategorized and tagged , , . Bookmark the permalink. 2 Comments.

1. As you say, the “Ferries” scene is a well known “game theory in movies” exhibit, but I really liked your juxtaposing it with the Joker’s “chaos” remarks to Harvey Dent. As with many game-theory-inspired analyses of literature, however, when something clever or non-obvious happens I always wonder whether the author/filmmaker is a closet game theorist, or has just made a mistake that turns out to be unintentionally meaningful to game theorists.

In this case, the apparent contradiction you point out between “chaos” and the clever Ferries strategy brings up exactly these doubts. Your suggestion is that the author means to show how poorly the good guys understand the Joker. I guess that poor understanding is shared by Batman, but this seems uncharacteristic of the film’s treatment of its hero generally. Would you be inclined to go further in asserting that there are implicit criticisms by the filmmaker of Batman’s crime-fighting (strategic) skills?

2. Christopher Nolan: Closet Game Theorist? I don’t know. Christopher Nolan: awesome director screenwriter? Absolutely. Memento, The Prestige, and Inception were all great movies. Not really a ton of things you would consider strictly “game theoretic” in those movies, but all deal with social phenomenon in some capacity. Memento deals with a man with short term memory loss and his interaction with strangers who can’t really form any credibility with him. The Prestige does have to do with opponents and strategies, but I can’t think of any specific game theory connections. Inception in a way deals with common and mutual knowledge, in that it deals with dreams inside dreams inside of dreams…all kind of stretches though.

So, I doubt Christopher Nolan would consider himself a game theorist, or even say that there is game theory in his movies. He does seem to utilize interesting social situations that we can all more or less relate to. How can you trust anyone when you can’t remember anything anyone has done? What would you do in the ferry situation? His movies get some discussion started on at least some topic related to social sciences. So, I think he has the intention of making a good “thinking” movie, but probably not “find the game theory Easter eggs in my movie!” Also, I feel the same way when someone talks to me about abstract art. They’ll show me a painting of a blue line on a white canvas, or a red box and tell me it explains the plight of the Russian peasant in the post Stalinist Era, or something ridiculous like that. So, I think people can read into things too much some times. I am definitely guilty of that too though, as one of my future posts on the welfare system in Mario Kart will prove.

Anyways, I don’t think that the filmmaker is necessarily “criticizing” Batman. He is showing him in a non-omnipotent light though. Even the Batman cannot save his beloved Rachel when the Joker lies to them (yet another time when no one should have believed that the Joker would tell them the truth about who was in which room). Despite all of his inventions and brute strength Batman cannot stop the Joker-the Joker is playing head games with everyone. The Joker isn’t particularly strong, well connected, or endearing. He just knows what people think about him and uses it to his advantage.

And really, Batman doesn’t even catch him by being smarter than him. He (Batman) uses a really unethical cell phone hacking device to find him (Joker) and then in a sort of “Deus ex machina” manner, just apprehends him. So, Batman is not a perfect hero by any means. Really awesome and cool, but not perfect. But, that actually makes him a better character because people don’t really relate to perfect people that well. They like someone who is better and more able than them, but still not so good that they become unbelievable. I think. Maybe that is why people in the movie the Incredibles didn’t like the Incredibles? A little too perfect maybe? Also makes me think about all the other movies where people are going after the superheroes, like Watchmen.

So, I’m getting tangential, but I’m interested in either the real public’s or the public in the movies’ perception of “the superhero”. I’ve never really seen anything with Superman, but I think everyone loves him. Not everybody is happy with Batman. Everyone seems to hate the Watchmen. Ah! And who can forget the Xmen! There’s an AMCS project here somewhere…

Some random websites’ ranking of top the three superheroes of all time:

Superman, Spider Man, Batman (Kidzworld)