Game Theory and The Dark Knight

I suspect that many of you got a chance to see The Dark Knight movie this weekend.

Just as an aside, I will say that I thought that the movie was sweet. Definitely the best Batman movie, maybe one of the best superhero movies ever made. Heath Ledger is terrifyingly good throughout. Aaron Eckhart and Christian Bale give excellent performances as well, and Maggie Gyllenhaal is a hell of lot better than Katie Holmes.

Anyway, there is a scene in the movie that got me thinking about game theory, and that is what I want to talk about. Beware, if you haven't seen the film, this discussion includes some big spoilers.

In the final battle the Joker has rigged two ferries carrying people out of Manhattan Gotham to explode. One ferry carries mostly civilians with a substantial National Guard presence. The other ferry contains large numbers of prison inmates and some guards. The Joker has rigged both to explode, and he has given the crew on each boat the detonators -- only they have the detonator for the other boat. He announces the rules of the game to the crew and passengers of each vessel.

  • 1) Each of them have the power to blow up the other boat and then their boat will live.
  • 2) If they get to midnight with know no exploded boats, the Joker will detonate both.
  • 3) Any attempt to leave or defuse the bombs will result in the destruction of both boats.
  • Now there is probably some horrible twist that the Joker had in mind that would subvert these rules. Maybe each detonator was actually for their own boat. For the purposes of this discussion, however, we will assume that the rules are actually as the Joker describes them.

    Clearly, the Joker's intention with this scheme was to have one of the boats blow up the other. The boat filled with civilians might feel entirely justified in blowing up a boat filled with felons to save themselves. They have committed no crimes, there are children aboard, etc. The boat filled with criminals could easily overpower the guards and blow up the boat of civilians to save themselves.

    The tricky part for the actors on both boats is to try and guess what the other party is likely to do. The longer you wait, the more likely the scheme will be foiled and both will be saved. On the other hand, the longer you wait the more likely the other boat will decide to kill you.

    The whole thing strikes me as an interesting application of game theory to decision making. Because the people on the boats have no way of communicating with one another, they have to judge their best course of action based on what they think the other people will do.

    Whenever you have a game theory problem, it is best to draw a payoff matrix. A payoff matrix lists each of the actor's options and the resulting payoff depending on how each actor performs. The interesting part is that the payoffs are contingent on the responses of both players.

    To illustrate a point, I want to divide the payoffs matrices into two types: the simple case and the complex case. The simple case doesn't include any of the complications that are certainly present in the film. It is shown below.

    solid windowtext .5pt;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-insideh:
    .75pt solid windowtext;mso-border-insidev:.75pt solid windowtext'>



    style='mso-bidi-font-weight:normal'>Prisoner Boat




    style='font-size:10.0pt;font-family:Arial;color:#3366FF'>Press button

    style='font-size:10.0pt;font-family:Arial;color:#3366FF'>Don't press button



    style='font-size:10.0pt;font-family:Arial;color:red'>Press button

    style='font-size:10.0pt;font-family:Arial'>Not Allowed

    style='font-size:10.0pt;font-family:Arial;color:red'>-- style='font-size:10.0pt;font-family:Arial'>\Dead style='color:red'>

    style='font-size:10.0pt;font-family:Arial;color:red'>Don't press button

    style='font-size:10.0pt;font-family:Arial;color:red'>Dead style='font-size:10.0pt;font-family:Arial'>\-- style='color:red'>

    style='font-size:10.0pt;font-family:Arial;color:red'>Dead style='font-size:10.0pt;font-family:Arial'>\Dead

    The simple payoff matrix assumes that there are no consequences -- social or otherwise -- to one boat deciding to blow up the other. Further, it assumes that the probability of rescue before midnight is zero. If no one presses a button, they are both dead. The option of both pressing the button is not allowed because presumably the blown up boat would not have that option.

    You can figure out pretty quickly how the situation described in the simple matrix will end: both sets of passengers would be running to push the button. That is the best option from the point of view of both boats. (You would be running fast too because a reasonable player would also assume that the other boat knew exactly what you knew.)

    However, the situation is much more complicated than the simple payoff matrix suggests because of the two assumptions we had to make. Below is a matrix that includes these complexities.

    solid windowtext .5pt;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-insideh:
    .75pt solid windowtext;mso-border-insidev:.75pt solid windowtext'>



    style='mso-bidi-font-weight:normal'>Prisoner Boat




    style='font-size:10.0pt;font-family:Arial;color:#3366FF'>Press button

    style='font-size:10.0pt;font-family:Arial;color:#3366FF'>Don't press button



    style='font-size:10.0pt;font-family:Arial;color:red'>Press button

    style='font-size:10.0pt;font-family:Arial'>Not Allowed

    style='font-size:10.0pt;font-family:Arial;color:red'>Murderers style='font-size:10.0pt;font-family:Arial'>\Dead style='color:red'>

    style='font-size:10.0pt;font-family:Arial;color:red'>Don't press button

    style='font-size:10.0pt;font-family:Arial;color:red'>Dead style='font-size:10.0pt;font-family:Arial'>\Murderers style='color:red'>

    style='font-size:10.0pt;font-family:Arial;color:red'>Dead style='font-size:10.0pt;font-family:Arial'>\Dead
    (Possibility of Rescued\ style='color:#3366FF'>Rescued)

    The assumptions in the simple payoff matrix are wrong. For one, there would very likely be consequences to blowing up the other boat. For the civilian boat, there is the social stigma of being murderers -- even if it is murder of felons. There may well be legal repercussions. For the prisoner boat, the social stigma may be less (they are already in prison), but the legal consequences are probably greater. Thus, in pressing the button, both actors face a non-zero penalty. You could say that the penalty is trivial compared to being dead, but it is still there.

    Second, this being a superhero movie there is a non-trivial probability that the people on both boats will be saved before midnight. (You wonder whether the characters know that they are in a movie and account for this in estimating their probability of rescue.) The non-trivial possibility that both boats could live is a strong temptation to wait and not push the button.

    The presence of these two complexities explains why this situation doesn't immediately degenerate into explosion.

    It also poses interesting personal questions too: how would you respond? How would you rate the size of the relative payoffs? What is the probability from your point of view of the other ship blowing you up? What is the probability -- given your limited knowledge -- of being saved? The interesting part of game theory problems (at least for me) is that people vary in their estimation of probabilities of other people's actions and vary in their weighting of the different payoffs. This variation makes profit-maximizing play even more difficult to engineer.

    For my part, I found the actual result in the film to be a little surprising. I mean, come on, a guy on the prisoner ship throws the bomb detonator out the window. Really? Maybe I'm cynical, but that strains credulity. It may have been important to the message of the film -- Gothamites are willing to stand up for right and prove that the Joker's cynicism was unfounded -- but it hardly seemed like realistic behavior.

    Anyway, I don't remember the last time I saw such a cunning use of game theory for suspense value in a movie. I am curious to hear what people thought of that situation. (Further, I am hardly an expert in the subject, so if I have committed some substantive error please let me know.)

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I found it more incredulous that the prisoner wasn't immediately attacked for his action. It's certainly not out of the realm of possibility that the man either expected the Joker to kill them all anyway or just decided he was not going to let other people die. It certainly fits the theme of the movie and while it does go against typical crowd behavior, let alone among hardened criminals, there are plenty of noteworthy incidents of similar altruism in life and death situations. I just can't imagine the guy wouldn't immediately become the outlet for all the fear the prisoners and their guards were feeling.

I did love the Joker's twisted use of people's morality and actions to try and make them do what they hated to such as forcing Batman to make a choice while secretly giving him false information or switching the clowns and hostages in the skyscraper scene. It's the first comic movie in memory I can think of where the villain's schemes were cunning rather than just convoluted or stupid. Even as much as I liked Batman Begins, the microwave macguffin turned what could have been a believable terror attack scenario into a clearly fictional struggle.

Great film, and you bring up one of my favorite scenes and issues of it.

Assuming that I trusted the Joker to be honest with the game situation (something that I would not readily grant) I would argue in favor of pushing the button. If accused of being a murder I would then argue against the more complex matrix. Why assume that if you press the button you are a murderer? We could agree that whomever presses the button is responsible for the death of some set of individuals, but killing is not identical to murder. Murder implies some moral or legal guilt, that they did the wrong thing. There are many situations where an individual is responsible for the death of another, but is not considered a murderer, e.g., extreme cases of self-defense.

Why not characterize the Joker scenario more like that of self-defense. I can imagine trying to tell a jury, "We were scared for our lives. We only knew that someone on the other boat had a means to kill us. We didn't know if they were rational or trusting that we would not push the button. Being threatened with the possibility of a horrible death we decided that we had to defend ourselves against possible harm."

In that case it very well may be justified to push a button, even if such an action results in the death of many people. At least, I hope the jury will think so.

why so incredulous? nobody ever specified what the crime that Tiny Lister's character had committed was, it may not have been murder. There is also the possibility that someone may be in prison and actually sorry he is there.

If he's right, it could certainly be helpful the next time he has a parole hearing.

besides, he was the biggest guy there.

The guy who threw the detanator out the window for whatever reason (i.e morality, a low sense of self worth compared to the civilians on the ferry) preferred not to blow up the other ship. The only way he could assure this outcome given the company he was in (a group of people with little respect for socially exceptable rules of behavior) was to throw the detonator out the window. This way, no one could overtake the guards and press it. It was a rational and strategic choice given his preferences.

... a guy on the prisoner ship throws the bomb detonator out the window.

In Gotham City?!? He must have been from out of town.

By Pierce R. Butler (not verified) on 21 Jul 2008 #permalink

A couple of thoughts. I'm not sure what US (or NYC) law states but under English law duress is no defence to murder. This might make someone think twice before they in particular were the one to trigger the bomb.

Also, the same thought about the Joker lying occurred to me during the film and I do not think it can be lightly set aside. The people on the boats would realise that anyone psychotic enough to set such bombs would hardly baulk at being duplicitous in their statements about how the bombs could be triggered. The people on the boats have zero information as to whether the Joker is telling the truth or lying. Pulling the trigger to check he is telling the truth hardly seems to be worth the risk of killing yourself and several hundred people to me.

michael #1 seems to be describing the factors weighing into a very similar philosophical problem - the trolley problem. is actively killing someone to save five others as justifiable than indirectly killing someone to save the five? if you are fully aware of the outcome of each action - in this case, not pressing the button will probably result in the death of everyone on your own boat, while pressing the button results in the death of everyone on the other boat - the joker introduces a really interesting twist by making you "value" the lives of one boat over those of the other.

great post.

"2) If they get to midnight with know exploded boats, the Joker will detonate both."

If this sentence didn't make you wince, may the spelling/grammar police come and take you away. Shame, since the rest of the article was immediately prejudiced in my mind because of it.

By Oblivious (not verified) on 22 Jul 2008 #permalink

Too much thinking makes my head hurt, i will simply apply occam's razor. It doesn't matter to me which boat im on, given the chance to save my hide, i will blow the others to bits.

By Random Person (not verified) on 22 Jul 2008 #permalink

The thought that crossed my mind when the prisoner threw the detonator out the window was NOT that he was trying to save the civilians, but that he wanted to make sure he was killed himself. Maybe he was suicidal and not altruistic...

So let me get this straight: in a movie where a guy with superhuman strength, intelligence, wealth, and wisdom dresses up as a bat and seemingly can pass through walls (remember the interrogation scene?), and who is never discovered despite being one of the few men with the means to get all the hardware required to be the Batman (not to mention not covering his face completely), the thing that strikes you as unrealistic is the mercy of a hardened criminal?

C'mon! It's fantasy, let's not be so picky.

I enjoyed the post, though.

By Mack the Knife (not verified) on 22 Jul 2008 #permalink

The people in both boats did the right thing. They refused to participate in a contrived moral delima that forced them to act with brutality. Also there is every reason to suspect that the Joker had either done a double cross (trigger blows up the attacker's ship) or that he intended to blow up the survivors no matter what the outcome. Given that, the true moral choice is passive resistance.

You realize that Gotham City isn't exactly New York, thus they weren't in Manhattan, and that the place used in the shot wasn't New York either but Chicago right?

By Captain Obvious (not verified) on 22 Jul 2008 #permalink

Manhattan? Do you know who Batman even is? Regardless it was filmed in Chicago so this isn't NYC at all.

By mlvassallo (not verified) on 22 Jul 2008 #permalink

A couple of things about the prisoner who threw the detonator out the window. First don't allow false assumptions about prisoners to cloud your thinking. Even the Arkham prisoners, the worst of the worst, are not animals regardless of drama. Second, prisoners have families too, and this is reflected in a code that they live by in leaving each others families alone. Elijah Anderson in "Code of the Street" gives a good view into the realities of familial relations. Finally, there is among prison populations a certain level of anarchism is response to authority figures. A role that the joker took on by enforcing his rules upon the prisoner population and thereby creating a scenario where the prisoners would look for a third way. Prisoner populations have a tendency to choose other than safe/sane routes in response to authority. Bruce Western discusses some of the issues in his latest book on how prisoner populations view the authority figures and why they respond to particular stimuli in other than rational ways.

In Gotham City?!? He must have been from out of town.

Dude? He the president of the frickin future! Didn't you watch The Fifth Element?

Saving people is his job. 24-7.

Pierce Butler's comment cracks me UP!

I haven't seen the movie but I've read a little (seriously, a tiny little) about game theory so this all sounds fascinating.

My instinct, personally, is to completely distrust Joker (Do we have the criminals detonator or our own? Is he really waiting until midnight? Is he blowing both ships anyway?) for one thing. And I want to say I would not be able to blow up another ship. I'd hunker down and wait for The Batman and just hope none of us get blown up.

But then if one of my children was on my ship? Now I'm not so sure. Batman! HURRY!!

Great post!

I'd guess that most everyone would choose to view this in terms of the "simple case" matrix: The only substantial option to live is to blow the other boat up. The only other way to live is if Batman rescues them, which even in Gotham is not a very probable thing. So you have to balance out two probabilities: the chance that the joker is lying versus the chance that batman will save us. I'd put the probability of joker lying very LOW since this is precisely the kind of devious thing he would do, given the evidence the people have at that point. I would put the chance of batman saving us very LOW also, since its a practical impossibility given the care with which the joker has set up the game. Of course the story is no fun if people make the rational choice, and that's what makes batman a super hero: he does the impossible.

By I wanna live (not verified) on 22 Jul 2008 #permalink

Wouldnt the button have short circuited in the water and blown up the other boat? Also, if you can believe theres a billionaire dressed up like a bat that fights crime without using guns, but technology that isnt even invented yet, then why cant you believe someone would throw a button out of a window?

I thought it was obvious in the movie, that Tiny Lister's character was in cahoots with the Joker.

It was another one of The Joker's tricks, the detonator was actually attached to YOUR OWN boat. The joker was counting on the civillians doing the "right" thing and blowing up the prisoners. But being the Joker, the joke is, they would be blowing themselves up.

Tiny's character knew/realized that if the guards on their ship pressed the button then they would blow themselves up. The prisoner threw away the detonantor confidentally knowing the "good citizens" of Gotham would soon press their detonanator as the clock got closer to midnight, blowing themselves up, inadverntly saving the convicts.

Was I the only one who thought that?!

I thought it was obvious....

( a similiar plot twist happens when Joker gives the address of Racheal Dawes and Harvey Dent, and gives Batman time to save one. But the Joker purposefully switches the addresses to pull a "joke" on Batman)

Since this is Pure Pedantry, I should point out that you find something incredible if you are incredulous. Things can't believe or disbelieve so they can be incredible but not incredulous. Good day.

If the prisoner who threw the detonator out the window had been scape-goated for his action and possibly killed, it would have given nice foreshadowing to the relationship between the batman and the citizens of Gotham at the end of the movie.

As I see it, pushing the button would be a premeditated act of mass murder. It would be hard for the defense to argue it as an act of self-defense since the architect of the "experiment", the Joker, a sociopath and terrorist, would be considered an untrustworthy source on which to base a decision.

Two != too

Gotta love how this asshole spoiled the ending for thousand of people and wrote a shit article. GJ ASS HAT!

I always suspected that the devices on either ship would blow up both ships or the ship that pressed the trigger. I find it funny how it is mentioned time and again that the "joker has no rules" and yet the good guys always expect things to be as they seem.

I don't think that the people on the boats had a real plan, just resigned themselves to death rather than take the risk of killing everyone on both boats...

By sirjoebob (not verified) on 22 Jul 2008 #permalink

Anyone think that the Joker had each boat rigged to blow itself up and not the other boat?

The Joker thrives on watching purity become tainted. From the swat teams prepping to kill the innocent clowns to 2face becoming a murderer.

Personally it would've been great to see the 'citizen' boat go up in smoke because you would've seen those people commiting suicide from their own greed.

There's the real game, to me it wasn't about odds and who will act first, it was about greed and self-sustain. The real hint to this was the boat captain saying 'we're still here'

The irony is that this setup is called the 'Prisoner's Dilemma', at least in sociology. Each actor gets the opportunity to 'cooperate' or 'defect', and the payoff matrix is put together depending on which kind of game you want the actors to be playing.

The stress in the PD comes from the difference between payoffs across decisions (well, that's true of all the arrangements of payoffs, but). The PD payoff matrix is considered Pareto non-optimal, because each actor choosing what's best for them leads to a situation where neither actor really gets what they wanted.

In DK, obviously nobody wants to be a murderer, and nobody wants to die. There don't have to be positive payoffs in order for it to be a PD matrix; what counts is that the RELATIVE values are maintained. It's not a strict PD matrix, because the Joker's putting a penalty on double-cooperation (he'll blow them both up if neither blows up the other), and that technically kills the matrix values. There's no strategic way to win, because ultimately your negative payoff (getting blown up) sits totally in the hands of someone else (either the other boat or the Joker). The 'rescue from the situation' mitigations really don't apply, because if the Joker's believable enough to carry off the 'if anyone abandons ship, I blow it up', there's no reason to think the passengers on either ship believe they're getting out of there by any other means. It'd be like saying "Instead of pulling over for this cop, I'm going to keep driving and hope he has a heart attack before he catches me or reports my license. Go go go!".

While it wasn't a perfect PD, it was very effective dramatically, because I think you can count out possible Joker-collusion (the convict who throws out the detonator). Cinematically, there's no indication this guy knows the situation's a lie; what he's saying is "I'll take my chances with the other people or the Joker, but I'm not going to kill anyone." Before their detonator's thrown out, the tension is 'which boat will?'; after, it's 'will the run-of-the-mill citizens do something a boatload of convicts didn't?'. Assuming either a further, totally not-hinted-at twist (collusion) or a drama-weakening, unused modification of the game (each detonator's to the ship it's on) lessens the scene with no real reason for doing so. While it would've been in character for the Joker to rig the boats to blow themselves, it's BETTER if they don't, and I think his directorial choices from the rest of the film say he'd choose for the better option.

By equinox216 (not verified) on 22 Jul 2008 #permalink

"They refused to participate in a contrived moral delima that forced them to act with brutality."

Game theory is the science of contrived moral dilemmas.

It's just as well neither boat had any economists on it otherwise they would really have been in trouble.

By dirigible (not verified) on 22 Jul 2008 #permalink

I thought the point of the prisoner throwing the detonator out of the window was clear from the dialog that preceded him throwing it out. The guy holding the button had never killed anyone before and didn't know what it was like. The prisoner did, and would never do it again. The guy holding the button wasn't qualified to make that decision.

By Joseph Johnston (not verified) on 22 Jul 2008 #permalink

Personally I think the prisoner's reaction is the best safe one and consistent with a street level mentality. If anyone on his boat pushes the button he will be held accountable to some degree. Either it will blow up his boat, likely killing him; or it will blow up the other boat, resulting in some kind of punishment; or it will blow up both boats (what I'd do if I was Joker). A double cross, from the Joker, is a thoroughly obvious conclusion. By taking one detonator out of play, he dumps the choice on the other boat and cuts the number of fingers on buttons roughly in half. Furthermore, the half removed would arguably be the half most prone to getting him killed. Who is he more scared of? Killers, thieves, and gang bangers? Or Ma and Pa Sixpack? While this is not "game theory", or even solid statistical math, it is consistent with a clever street level mindset, with or without the moralistic choices tossed in. In short, it is "common sense".

What this analysis is missing is this simple fact.

The Joker represents a total rejection of the rules--complete anarchy. The fact that he develops this intricate series of "rules" for his game is contrary to that position.

He wants people to reject the rules--and that (to me) was the most interesting portion of the game. This means you have to assume (50/50) that the rules of the game are a lie.

Then you have the following Scenarios.

1. The whole game is a sham and the Joker intends to kill everyone no matter what. Nash Equilibrium for both boats: Do nothing--wait to be saved if possible.

2. The whole game is a sham and no one will die. Maybe a little flag that says "GOTCHA" will pop out. Nash Equilibrium: Do nothing. It doesn't matter if you see the "gotcha" and the alternative is death for one (or both of the boats)

3. The game is real, but the detonates are for your OWN boat. In this case the Joker is punishing the person who thinks the rules matter and rushes to push the button to detonate the other boat. Nash Equilibrium (if both boats distrust the Joker) is to do nothing (because there is an 50/50 chance your committing suicide).

4. The game is real, and the detonators work the way he describes. Nash Equilibrium: Run to push the button.

Now if you play all of these games simultaneously--you will note that 3 out of 4 of the possibilities require you to do nothing at all. There is only one scenario where pushing the button might save you.

That was why the prisoner threw the controller out the window. Being a criminal--he would know not to trust the "rules" of another criminals game. And that the most likely outcome of playing his game is that everyone loses.

Re: Julie

If instead of wanting to ensure that his boat didn't blow up the civilians, that guy could have gone down into the bilge and manually exploded his own boat with a lighter, or maybe a battery.

I love Game Theory but at least put the word "SPOILER ALERT" on the top. You just screw up a good perfectly good movie for everything.

I really do not find it strange at all that the prisoner throws the detonator overboard. I think it is almost a guarantee that at least one prisoner on the boat regretted the actions he made that put him in prison, and resented the others on the boat for even considering killing innocent civilians when he believed they were all criminals anyways. I think he believed that if someone had to die, they were the ones that deserved it most.

C'mon dude, this is on Digg with a typo. Get it together.

I would have gone and poked holes in all the gas cans in the boat. Then all the gas would be gone/gone enough that there may be little to no explosion and probably a manageable fire. But what do I know.

By mad bomber (not verified) on 22 Jul 2008 #permalink

I think it worked because it was one prisoner. The gaurds were willing to have someone push the detonator, and if you look, after he threw it out the window, a couple inmates look varying degrees of disappointed and angry. These are bad men true and we're not sure what they would have done, but it only took one good guy to take the option away from them.

the prisoner who threw out the detonator stood up for his own opinion. that was believable. yes its weird though that no one jumped him after he did what he did. but then again, he was the biggest dude with a lazy eye, who wants to throw the first punch? on the other boat, the civilians not manning up to detonate the prisoners' boat is typical of civilians. unless it's clear and present (and visible) danger, people find it hard to say.. HEY IM GUNNA KILL SOMEONE. what do u guys think?




not only that they deserved it, but I think he also saw it as a chance at redemption, if he was going to die he was going to die making one final, humane decision. I think he also probably factored in the possibility of the detonator blowing up their own boat.

it entered my mind right away, but after i thinking about it, it is an almost absolute certainty that the detonators were for their own boats. almost everything the Joker said in the movie was a lie: the location of Rachel and Harvey, how he got his scars, telling Gotham to avoid bridges then attacking ferry's. he even lied to the bank robbers at the beginning. the only honest threat was blowing up the hospital.

therefore, if the people on the boats had been following the jokers actions, the only logical action would be to wait it out and hope that Batman comes to the rescue.

Why is it a spoiler? The ferry scene wasn't crucial to the plot. It's not like he talked about how Rachel Dawes died.

I think Joesph brings up a valid point.. a possibility, nonetheless..

By Nick Rosnett (not verified) on 22 Jul 2008 #permalink

AP- thanks for your analysis; it was exactly what I was thinking. In fact, you could throw in another scenario that suggests no action- each detonator controls both bombs. Detonation of one is detonation of both. Action: wait

Also, regarding the actions of Tiny- didn't anyone else notice that they seemed to play on the "religious convict" profile? After he threw the detonator out the window, he went back to a group of prisoners, and seemed to join them in prayer. But perhaps that was my own religious background colouring the scene...

I think that the post and much of the commenting miss the tension: it wasn't a tension within a game theoretic framework, it was a tension between morality and the game-theoretic model of rationality. Both sides hesitated to push the button because doing so was wrong. (This speaks to the inadequacy of consequentialist moral theories in general).

I think the Joker's motivation was to try and show that even good people when pushed will do evil things. He rejected any sort of social order, including morality.

Finally, I think the reason the prisoner wasn't attacked when he threw out the detonator was because the guards and (at least many of) the other prisoners were ashamed - ashamed of seriously contemplating the mass murder of innocent people out of bare self-interest. (Also, notice that he after his action, he rejoined what appeared to be a large group of other prisoners who were all bowing their heads together. This group may well have discouraged those who disagreed with his action to stay quiet about it.)

NYC folk only wish Batman Begins and The Dark Knight were filmed there. Sorry, your city will never be as cool as Chicago. :-P

i like Harvey Dent's/two face's reasoning, since there is no solution that will result in a positive (assuming that no help will arrive) why not leave it to unbias probablility- flip a coin, draw a card it makes it easier to justify your decision and its quicker than voting or contemplating on it until 12:00

By Fat Batman (not verified) on 22 Jul 2008 #permalink

Just one note, they were leaving Gotham, not New York.

Eh if the batman movie wasn't constantly applying SHIT Philosophy in a movie where the main charter runs around in (water down)bat costume.

both groups would have blow up each other at the same time and the final battle would have been as entertaining as all the other fights before.

By carrie kelly (not verified) on 22 Jul 2008 #permalink

I think that understanding the Joker never plays by any rules is a HUGE factor in deciding what to do. It negates the morality of the choice. Neither group is worthy or unworthy since you don't know who is going to die at the end of the night. What you do know is if at midnight both ships blow up everyone dies. But by pulling the trigger half the people die.

The joker is twisted enough to let the survivors live with the crushing guilt so I wouldn't put it past him to let one group go. Especially since they have lost all their faith in humanity.

Of course the movie is about Batman so the internal movie logic should always be, "Choose Batman." But otherwise, pull the trigger, let someone live.

I think it's interesting that so many of you think it likely that the joker 'switched' the detonators and that each detonator blows up the ship it's currently on. It's true that the joker doesn't 'play by the rules' and that he's a chaotic individual, but he does have motivations and desires. He puts the hostages in clown suits so that the SWAT team will shoot the wrong people. He gives the wrong addresses for Harvey Dent and Rachel (possibly to breed resentment between the rescuer and rescuee, who is not the rescuers first choice.

So what do you think the Joker wants more? Assume that someone does trigger a detonator. If the detonators blow up both ships, it merely proves that he was right and kills a bunch of people. If the detonators blow up the ships that they're on, you end up with dead murderers and live innocents. But if the Joker was in fact true to his word, then you would end up with a nice big explosion, a bunch of dead innocents, and a boatload of murderers. Possibly a boatload of previously innocent murderers. That sounds more like the Joker's style to me.

If I were on the boat, I would argue thusly:

Look, what happens if we press the button?

If it blows us up, the other boat will blamed for it anyway.
If it blows them up, we can all agree that the other boat pressed their own detonator and it blew them up in a Joker duoble cross.

So the only valid question is: do we think this button will blow us up? Otherwise, you press the button, because there are no repercussions to it.

By kthejoker (not verified) on 22 Jul 2008 #permalink

For what it's worth, the prisoner who threw the detonator overboard went back to his group of buddies and they appeared to be praying or at least meditating waiting for midnight, so maybe he wasn't a murderer or he had been reformed or just didn't want another boatload of innocent people on his conscience. As for why he wasn't attacked - he was a big mean looking dude.

I only had two problems with the logic of the scene. First, they discover the hold of ship is full of explosives and there is a wrapped cardboard box on top. Wouldn't their first thought have been, "Maybe opening the box will set off the bombs?" (it was before the Joker told them the rules). Secondly, the guys holding the detonators stayed right in the middle of the crowd of people during the crisis. If they had been locked in the bridge, it would have taken the mob mentality aspect out of it. I did like that they voted, though - the vote showed that the rational solution would be to blow up the other boat, but the emotional/moral choice was to wait and either die or hope for rescue.

Personally, I would think someone would have tried escaping from the boat unless they had some certainty that the Joker would know if they did.

Great scene in a great movie, though...

I just wanted to say I thought that it was more ridiculous that on a boat full of people who believe they have the moral high ground nobody decided to step up to the plate of taking the trigger and blowing the other boat.

The criminal's actions didn't surprise me at all because sometimes criminals are forced into doing what they do out of love and nothing else. All he said was that he would do what 'should have been done 10 minutes ago' and it was a simple and truthful statement, which I can imagine coming from somebody in the underworld. Sadly civilized people seem less likely to do it because they believe they have the moral high ground.

Personally? I think the prisoner who threw the trigger had the right answer, to me in times of moral dilemma I think the question is what a child would do, and I think it would be a child who would know right away that the trigger needed to be thrown away, morality or not.

Mack the Knife, Batman doesnt have superhuman strength, or superhuman intelligence. He has a detective mind, and the burning desire to obliterate crime... and alot of money

The reason that someone can believe in the concept of Batman, at least as far as the movie goes, and not a convict throwing out the detonator has to do with at least two factors.

Factor one, Batman's universe has rules.

First, Batman can do things that normal people can't do but not things that are impossible. For instance, he uses his cape as a hang glider, he doesn't fly.

Second, the movie consistantly made the crimanials of Gotham out as cold hearted murders.

Factor two, is a preconcived idea about convicts that someone may have.

These rules are part

By Robearbobo (not verified) on 22 Jul 2008 #permalink

The reason that someone can believe in the concept of Batman, at least as far as the movie goes, and not a convict throwing out the detonator has to do with at least two factors.

Factor one, Batman's universe has rules.

First, Batman can do things that normal people can't do but not things that are impossible. For instance, he uses his cape as a hang glider, he doesn't fly.

Second, the movie consistantly made the crimanials of Gotham out as cold hearted murders.

Factor two, is a preconcived idea about convicts that someone may have.

These rules are part

By Robearbobo (not verified) on 22 Jul 2008 #permalink

What if he had in fact given the passengers their own detonator and lied to them saying it was for the other bost.

By ez cheese (not verified) on 22 Jul 2008 #permalink

As for the prisoner who threw the detonator out the window, he did the only rational thing under the circumstances. Do you honestly think that the gotham underworld doesn't know this guy? In his place, knowing the street rep of the joker, my bet would have been that the detonator went to the boat I was on or that both have to be clicked at the same time to disarm the bombs.

Remember that they knew the other boat had children on board, do you have any idea what happens to child molestors or killers in prison? He illustrates the difference between a criminal and a law breaker. He is 'made' as far as the cops and the streets are concerned, the fact that his parole hearing will go very well indeed is beside the point.

In Alan dean fosters "The man who used the universe" the acknowledges that a person can be on both sides of the line of law at the same time. That prisoner has perhaps bought himself a chance to walk that line.

Further, you also have to take into account the signaling inherent in neither boat being immediately blown up. In essence, this is actually an iterated game of PD, and in any given moment the actors have the choice of cooperate or defect. The caveat being that they are aware of the final iteration, and thus the incentive carries back to immediately defect. However, the fact that neither boat did so sends a signal that even 15 minutes of guaranteed life (and a lifetime more of probable life) is incentive enough to continue to cooperate.

First off, I find it completely unrealistic that at no point did they attempt to contact the Joker in reply to clarify the rules. Perhaps there were further stipulations that could have been brought to light; what if we do something really creepy and sadistic that you didn't think of, Joker? Would this be an acceptable compromise? Like REALLY creepy. Like a poop buffet. How about it? Lives are on the line. I could do a LOT of really horrible stuff the Joker might like to save myself.

Also, they should have been like "what is my home city known for?" (1. Batman 2. Falafel) and taken that information into consideration when choosing further steps to be taken. Realizing that they were in such an elaborately designed trap with a myriad of fairly straightforward rescue scenarios built in, one would have to assume that the main character of the story would be directly involved. There's just economy of criminal effort to be considered-- why go to ALL that trouble instead of just blowing up the boats unless you're planning to get beaten up by Batman and suspended upside-down later?

I give this movie a -100 for realism. I don't believe in super-flexible hero armor, flying tank cars or the idea that a single vigilante could chance across (and intervene in) enough crimes to have a statistically significant effect on overall crime. Also, Rachel's face got like TOOOOTALLY different between this one and the last one.

By Lbotronic (not verified) on 22 Jul 2008 #permalink

This is the classic Prisoner's Dilemma. It is also how we elect Congress. The entire US will benefit from continuously changing the politicians. But, their seniority system means that each state gets more if they reelect their own state's politician. Do what's best for your state and the US suffers. Do what's best for the US and your state might suffer. You can only do whats best for everybody if your trust everybody else. The Joker used his bombs onboard the ferries to manipulate the people on the ferries. The Congress uses its seniority system to manipulate the people in each state. Same payoff matrix.

By Barry Smith (not verified) on 22 Jul 2008 #permalink

One thing to consider is that we(as viewers/comic fans) know a whole lot more about Joker than they people on the boats. As far as they know, Joker always keeps his word. He said kill the lawyer or I blow a hospital, and lo and behold, he blew a hospital. He said he would kill three particular people, and managed to get two of them.

Also remember his speech to Harvey in the hospital room, about how people won't panic as long as things are defined and going with the 'plan'.

By Josh West (not verified) on 22 Jul 2008 #permalink

What the prisoner did was completely irrational. It sealed the fate of the prisoners because either they get blown up or both get blown up, no way out of it. The Joker puts special emphasis on being a man of his word, so the rules of the game were, in all likelihood, accurate. The Joker prefers to corrupt people, so he was banking on corrupting the civilians out of their self-interest to consider the prisoners not worthy of living over them and becoming murderers themselves. The Batman factor was just a deus ex machina, and their morality would've led them to both dying.

By Descartes (not verified) on 22 Jul 2008 #permalink

I found this to be the most ludicrous of all scenes in the movie. Sure, game theory is fun and this is a movie, but the scene basically made the world seem that of children. Am I really supposed to believe that a boat full of hardened criminals, some of whom would likely identify with the joker, will simply let this pass?

You can't call this a murder though. This is called self-preservation. If you do not take an action, you will die. And by the way, every time the Joker says he will commit a crime, he commits it, so this is not something where you can think the Joker was testing them and if they passed he would have let them live.

This was probably the most ridiculous scene of all, but it seems everyone loves it. Talk about being small minded.

Self-Defense wouldn't normally apply in this situation. (at least legally speaking) If you point a gun at my head and tell me to shoot someone or you will shoot me, I have two choices.

1. Shoot the innocent party and accept responsibility for that (and possibly live if the 'villain' keeps their bargain)

2. Get shot.

(3rd is to shoot the villain I guess, which is what basically ends up happening in the batman situation... in this circumstance you may or may not be excuses for your use of self-defense, as the situations would vary)

People who kill others are never 'innocent', but sometimes society will deem them to have a socially acceptable defense for doing so.

By JamesFromCanada (not verified) on 22 Jul 2008 #permalink

It's interesting that the civilian boat held a vote first, and then gave the power to one man, who changed his mind, whereas the prisoner boat had the detonator taken by one prisoner, who then sacrificed their choice by throwing it out the window. The prisoners were shown as having more humanity than the civilians. The civilians were shown as base and selfish, while the prisoners were ready to sacrifice for the greater good. Perhaps there is a message of redemption in there. Ultimately I really enjoyed the final outcome... good film.

In the movie, nobody really knows the Joker. As far as they're concerned, the Joker may be lying and they blow themselves up. There are a few possible outcomes in this movie.
1. Each detonator blows both ferries.
2. Pushing the detonator blows you up.
3. Pushing the detonator doesn't do anything and you still get blown up.
4. The detonator blows the other ferry, but the neither ferries want to get their hands dirty because the guard controls the other detonator with the prisoners.

As for why didn't they just jump off the ferry, the Joker said that he was going to blow up the ferry if anybody tried to escape.

Here's a related problem I heard on Car Talk:
Their answer was interesting, but, were I in that situation, I would spend most of my time trying to get through to my fellow inmates, that even if someone has been to the room twice, that doesn't mean we all have been once! Also worrying about their ability to remember and follow instructions to the letter.

I misunderstood that part of the movie when I saw it (I was drunk). I thought that the detenators blew up their own ships. I almost feel that this would have been better because

1) It would better explain the reluctance to push the button.

2)It would have made the moment when the prisoner threw the detonator away more dramatic.

3) The Joker would have been showing how unwilling people are to make the last sacrifice.

By Harlequin (not verified) on 22 Jul 2008 #permalink

Its possible the prisoner who got rid of the detonator had been himself captured by Batman, and therefore had a great deal of respect for his ability to catch criminals such as the Joker.

It seemed to me that the use of the large prisoner who threw the detonator out the window was actually a clever twist playing on the assumptions of the audience. I doubt I was the only one who thought that surely the prisoner was going to use the detonator. To me the fact that this "lowlife" was willing to stand up and deny any right of judgment is quite heartening.

By Jin_chaos (not verified) on 22 Jul 2008 #permalink

seemingly can pass through walls (remember the interrogation scene?)

He was already there.

Ok, way too much analysis and discussion for such a simple point. It was a classic prisoner's dillema with a slight twist in the 2 possible outcomes for mutual moral behavior.

I hate to be the cloud on a sunny day but, the game was flawed. In the beginning the detonators are found and brought to the captains of each boat. After wards, the Joker lays out the rules of the game and severs their radio communication and restores the electrical power (or it is restored by the crew).

But, here is a solution that the script/screenplay left out. Each boat had power restored. And being a seaworthy craft, each boat must have had signal lights. Both sets of crews would have had someone with the knowledge of Morse code. Why didn't the captains signal each other using the lamps?

And if someone already mentioned this, I was too lazy to read everyone's comments.

By Jason Self (not verified) on 22 Jul 2008 #permalink

Manhattan? Gotham is Chicago dude. Gotham always has been Chicago. The movie was filmed in Chicago. Chicago places and street names were used IN the movie. New York gets lame heroes like Spiderman and Superman. Batman has Chicago written all over him.

"In the final battle the Joker has rigged two ferries carrying people out of Manhattan (Gotham) to explode."

That's great.. except the movie is set in Chicago. Notice the prominent Chicago Police Cars throughout the movie...

Couple things:

First, mersmann and Barry Smith above say that this is a Prisoner's Dilemma situation. I believe a previous commenter mentioned this, but I'll reiterate: it is not a Prisoner's Dilemma. Let's just look at the situation as it is according to the Joker's rules. The cooperate option (don't push/don't push) was not a collectively better outcome than any other. The Joker stated he would blow up both boats if this were the outcome. For another, it isn't clear that the (push/push) option is even coherent: when one boat chooses this option, it automatically rules the other boat's being able to avail themselves of it (since they are blown to pieces). The whole force of a Prisoner's Dilemma is that when each party does what is individually rational for them when considered in isolation, the end result is collectively worse than if they had both cooperated.

Second, Rav3n187 says this:

You can't call this a murder though. This is called self-preservation. If you do not take an action, you will die.

This kind of reasoning has extremely implausible implications. One is that if I am dying and in need of an organ transplant, I would be morally justified in killing an innocent person in order to obtain their organ. I suspect that even Rav3n187 would not accept this (almost no one does), and it indicates that something has gone wrong in the quoted bit.

There's a further complication that i see...the boat with the prisoners has guards and police who have to represent the law and have a duty to protect civilians. Thus, there is an additional dialema for the people on that boat...theorectically, they wud be less likely to detonate the boat with the civilians because of their sense of civil duty.
In my view, this gives the boat with the civilians a greater chance of survival....knowing that the police guards on the other boat may oppose any notion of pressing the detonator.

anyone agree or se where im coming from?

Fantastic article! I am a college student currently taking Microeconomics and I learned about game theory just yesterday. Thanks for sharing this really great example!

Rose, Gotham is a nickname for New York from the 19th century. They filmed in Chicago, but Batman has always been a commentary on the dark soul of NYC.

By Jason Weaver (not verified) on 26 Jul 2008 #permalink

I actually found the prisoner's solution to the dilemma very realistic, when you take into account that it was that individual's interests that decided the outcome, not the entire boat.
And when it comes down to his interests, it makes sense. He was the biggest, and probably the leader of the prisoners. If they overtook the guards and pressed the button, any legal consequences would likely affect him even if he didn't take part. That results in the second worst outcome (next to death).
And if they didn't riot, and the guards pushed the button, they would likely blame it on the prisoners (3rd worst outcome, since it's harder to prove).

Seeing that, the best option is to get control of the device yourself. Since any button pushing would likely have consequences on you anyway. Therefore take control of the decision yourself.

Once that step is reached, he has a new choice: press the button and guarantee retribution (social or legal) to yourself, or do not press the button, and risk death. Except, if he does not press the button - he also has a hidden reward if they are rescued. If he's the one attributed with the decision, he gains social equity from all people who have 20:20 insight and are thankful they didn't press the button. If effect, he could have his sentence reduced, or even wiped entirely. This is clearly the best overall outcome for him. (This is without even taking into account altruistic factors, such as guilt over past crimes, or not wanting innocent blood on his hands again)

For a convict with many of his years in jail - possibly life - a gamble between social (and possibly legal) redemption against death doesn't seem like all that much of a stretch. To me, it makes perfect sense he would do it - and I think one can see it even with a pessimistic mind. Though perhaps not a cynical one...

I would have personally pushed the button. The Joker was trying to prove a point, he wanted to see the morally upright people of Gotham reveal their inner selfishness. I have no reason to believe he is being dishonest (how am I to know about the trick he pulled on Batman?), but I have every reason to believe my life is at stake.

If any of you are accustomed to the work of Ayn Rand, there is something to be said for virtuous, or at least rational, selfishness.

However, by even invoking her name I'll spark another debate, but at least one thing we can all acknowledge, and one of the main points of her philosophy, is the inherent selfishness of man. Whether you believe man must struggle against this urge for the sake of altruism or embrace it is one debate, but given the situation, I am compelled to believe people on both boats would act without much thought beyond "I want to see my kids/dog/light of day, I don't want to die."

Perhaps a small lapse would take place as society's values were shrugged off in the face of imminent doom, but the result would be the same: one of the boats would have been destroyed. Perhaps I'm pessimistic, but I took the Joker seriously (har har). People will abandon their ideals for mere self-survival, but outside near-death situations, morality has its place.

By ProfessionalDi… (not verified) on 23 Aug 2008 #permalink

I mean, come on, a guy on the prisoner ship throws the bomb detonator out the window. Really?

There has been a few explanations here in the comments why the prisoner might have done what he did but I think that everyone missed a very obvious answer.

The prisoner is religious and believes in some sort of afterlife (this is true of the vast majority of prisoners in the US). Now the potential infinite reward or punishment trumps any of the normal outcomes of the game. We know that belief in heaven and hell does not guarantee moral behaviour (he is in prison after all), but in an immediate life or death situation like this it is not inconceivable that concerns about the afterlife would be his foremost consideration.

Also, unlike the Rand-bot in the previous post might suggest even an unbeliever might not want to push the button. Many people do have moral standards that are not just motivated by self interest. I can definitely imagine people arguing that "I would rather die than live with the knowledge that I killed x number of people"

i still wish Katie Holmes had stayed on board as Rachel Dawes for the Dark Knight; it was like the time spent getting familiar with her character in Batman Begins was wasted...

I simply refuse to let this post die!!!!!!!!!!! BUMP BUMP BUMP BUMP, LMAO. GREAT POST AND GREAT COMMENTS. Is there anymore like this?

Here's a related problem I heard on Car Talk:
Their answer was interesting, but, were I in that situation, I would spend most of my time trying to get through to my fellow inmates, that even if someone has been to the room twice, that doesn't mean we all have been once!

Excellent post overall, it makes for excellent reading, but there's one fundamental thing everyone seems to forget before we even get into the analysis of the parallels between situations in the movie, and Game Theory. Suspension of disbelief / judgment, which I think even the filmmakers take a dig at in the film. To begin with, it's a comic book movie, a morality tale, so we know the good guy has to win. The good guy dresses up like a bat and the bad guy wears war paint on his face. Moreover, we have as Lucius Fox himself describes, one of the wealthiest, most powerful men in the world who spends his nights dressed as a vigilante beating criminals to a pulp with his bare hands. Then he applies the concept of sonar to spying on and tapping into 30 million people's conversations and locations. Right after taking down an 18-wheeler or something using nothing more than the Batpod, which survived a catastrophic crash; after The Joker takes an entire police station hostage using nothing but a shard of glass and an IED (where he's the only one uninjured); after Batman neutralises Gotham's SWAT team as well as Joker's disguised henchmen. These are just a few instances, the basic premise of the movie itself requires massive suspension of disbelief. So a noble-minded prisoner isn't really that hard to fathom. Great movie though, very entertaining. Not as deep as many make it out to be, but certainly smart.

By Anonymous Content (not verified) on 28 Sep 2010 #permalink