Isn't This a Straightforward Prisoner's Dilemma?

How often in movie's have you seen two enemies pointing pistols at each other from about ten feet apart, having a stand-off? Isn't the rational action here simply to shoot immediately? (Of course, there are sometimes complications: one guy is a cop, say, and he's not supposed to be shooting first, or the "enemy" is his brother, and he loves the dude, but can't let him leave with the diamonds. But let's just consider the cases without those complications, of which I have seen plenty.)

You can hardly expect to play Tit for Tat here, right? If your opponent has pulled the trigger from ten feet away, you are dead, correct? It would seem to me that there is no "threat" that if you shoot, I will too. But perhaps a reader more familiar with firearms than am I will set me straight here. Joe? Bob, do you and Woods ever have standoffs where you each threaten the other with your machine-gun-like wits? How do those resolve?


  1. Oddly enough, most human beings, including soldiers and cops, are lousy shots. The social science on this is pretty unambiguous, AFAICT.

    I'll grant you that many people with a gun in their hand won't recognize ex ante that they're lousy shots, which probably re-scrambles the calculus. But in a true free market - excuse me! in a Mexican standoff with perfect information, each side should recognize that even firing first is no guarantee that they are the one that lives.

    1. OK, Jim, I readily believe that. But do cops and gangsters really miss people when they are only separated by ten feet? Maybe they do: I'm certainly no expert! And perhaps one can set one's finger on the trigger so that, in the process of dying, one will shoot.

      I certainly don't know.

    2. Anonymous11:22 PM

      Keep in mind that when people get shot, they don't die right away. Often there is a long drawn out period of extreme pain, where they will be screaming, crying, or whatever until they bleed out. Unless you hit the brain, the heart or the spine (in a particular spot), chances are that the person being shot will be alive for some time afterward. Also, in some cases the adrenaline is so high that one doesn't even realize they've been shot. So, a person could certainly shoot a person and then that person shoots them back. In fact, there's a little story regarding Iraq that I will share.

      The Marines used to primarily use the standard M16. However, more recently the M4 has come into favor. The only real difference between these weapons is the barrel and the stock. The M16 has a standard stock while the M4 has a collapsable stock. As for the barrel, the standard M16 has a 20 inch barrel, while the M4 has a 14.5 inch barrel. When the barrel is a different length you must have a different twist rate to the rifling in the barrel, usually shorter barrels will have a faster twist rate due to the lower muzzle velocity.

      Anyhow, the ammunition used in the M16 and M4 is basically a .22 caliber projectile with a ginormous casing with lots of powder. Obviously a .22 cal projectile isn't the most damage-inflicting bullet that you can find. However, due to the fact that the projectile is of a boat-tail design, if it is traveling at a fast enough rate it will flip end over end when it hits flesh. When this happens the friction of the flesh will cause the bullet to fragment into pieces, thus inflicting major damage to tissue. This is why the 5.56 NATO round used in M16/M4 variant guns is so effective.

      Well, when the Marines first encountered Iraqi insurgents, the major problem that they encountered was that the M193 ammo that works great with the 20 inch barrel M16 wasn't very effective in the shorter barreled M4. The problem was that the bullets were not flipping end over end and fragmenting. So, the Marines would shoot these guys, but the bullets would just go in one side and out the other. Basically, they'd shoot these guys numerous times, but they'd keep on coming. They eventually solved this problem by creating the M855 variant of the 5.56 NATO, which has a heavier projectile.

      So, just because you've shot somebody, that doesn't mean that they stop in their tracks. Sometimes they keep coming. Personally, if I am going to shoot somebody, I am probably going to unload the magazine into them, and then reload. At least in a one on one situation.

      If you ever wonder why you hear stories of cops putting a very high number of rounds into somebody, this is why.

  2. I understand what you are saying, but I don't know the answer. I do remember thinking that the end of The Good, The Bad, and The Ugly was ridiculous.

  3. Anonymous9:49 PM

    Ha! There's nothing like being called out on a gun question. Shoot, even Lew asked if I'd write a gun article a month or so ago after a conversation that we had. As for Bob and Tom, I would guess that neither of them has ever fired a gun.

    I'm going to say that you're kind right, but mostly wrong. If the person is trained and shoots often, then more than likely they will hit the target with ease from ten feet away. However, this is not typically the case with most criminals. Also, the condition and choice of weapon is important. If the gun is not well maintained, has fouling, or the sights aren't zero'd in, then there is a good chance of missing. Even a movement of the barrel one inch to the left or right can cause a miss at ten feet of distance. Certainly, firing a gun well is not as simple as pointing and shooting, there's a lot more to it than that.

    Holding the gun correctly goes a long way. Most people assume that if you're right-handed that most of your grip pressure is going to come from your right hand. This is incorrect. You want your right hand to be as relaxed as possible while maintaining a good grip, because this allows your trigger pull to be smooth and free of jerks or twitches. I personally grip in such a way as to have my left hand (in a two-handed grip) account for roughly 60-70 of grip pressure so that all my right hand really needs to do is smoothly pull the trigger.

    Sighting and target acquisition is another thing that must be practiced. I don't use one eye to sight (I sight with both eyes) and I don't pay much attention to the rear sight. When I shoot I almost exclusively look at the front sight with both eyes open. The reason for this is that you can acquire a target much quicker with both eyes, you just have to train your brain to know how to focus your dominant eye onto the front sight. I usually spend about 5-10 minutes every day doing target acquisition and trigger pull exercises with an empty gun (i.e. dry firing), and this keeps me pretty sharp for my trips to the range every week or two. I also practice different positions and make sure to do a few one-handed drills with both weak and strong hand. Just so that you know, all military and police are trained to shoot at center of mass. There is no such thing as shooting to wound or aiming at particular appendages. That only happens in movies.

    Most of everything that I mentioned is going to be pretty standard stuff for a police officer or military personnel, so they are at a great advantage as compared to a criminal, who probably hasn't shot their gun very much and probably hasn't maintained it properly. However, police and military must follow certain rules, which can put them at a disadvantage under certain circumstances.

    In the military, if somebody has a gun you are going to shoot them. I don't think that police can do this, I think that their ROE requires an imminent threat to be present (i.e. somebody is reaching for a gun, or somebody is attempting to point a gun). Obviously, there are many situations that can arise and it depends upon the circumstances (and the person). Personally, if somebody has a weapon unholstered, I am not going to take a chance and hesitate. Further, if I am going to unholster my weapon, I will only do so if I intend to use it (if I am pulling it, the trigger will be pulled).

    1. Wonderful, Joseph! I knew you could come through here.

      So these stand-offs really would be filled with uncertainty, as I read you?

    2. Anonymous10:55 PM

      Yes, certainly. Obviously, there would be some minimal level of uncertainty no matter what the conditions, but it is actually much greater than one would think in most cases. Of course, if you have two highly trained marksmen at 10 feet of distance, then the uncertainty diminishes greatly. Still, you really only get one chance (one shot).

      I've had instances at the shooting range where my body made an unconscious movement at the exact moment that I pulled the trigger, causing me to miss the target completely (and I am a pretty proficient shooter). It certainly isn't inconceivable that this could happen during that one shot scenario.

    3. Anonymous11:26 PM

      Well, actually you don't always just get one shot. See above.

  4. Anonymous9:51 PM

    The last consideration is nerves. No matter what, when confronted with a situation in which you must use a weapon, you're going to be nervous and your adrenaline is going to be flowing. This will cause your hands to shake or to make unintended jerking movements. However, that is the point of training, to minimize these problems. With proper training, the movement of unholstering the weapon, acquiring the target and squeezing the trigger will occur in one fluid and smooth motion without even a single thought. Sure, the shooter will be nervous, but the procedure should be automatic.

    I live in a pretty bad neighborhood, but I don't worry too much because I am well-trained and I know that most everybody else around me isn't and probably cannot shoot worth a crap. This is a tremendous advantage on my part.

    As for the movies, well they have to keep your interest. And if they kill off the bad guy before your find out that he's the cops brother, then you're miss the drama. It's entertainment, and it is almost always out to lunch.

    1. "As for the movies, well they have to keep your interest."

      And yes, I understand that entertaining is the major goal. But I have also found that some media productions are able to entertain with intelligence (The Sopranos, The Wire) while others don't care how often they insult your intelligence so long as the receipts cover the production costs.

    2. Anonymous10:58 PM

      Well, of course there are some productions (usually drama or war) that are very accurate or realistic, but that isn't generally the rule. Film is weird in that it has certain things that are always done a certain way out of tradition. As I've said before, I am more of an audio guy, so that is what I notice the most. A few examples of what I am talking about is tires squealing on dirt, a wolf call whenever there is a moon shot, the "Wilhelm scream", etc. I think that it is kind of stupid, but that is just the way it is.

    3. Guest post request! Can you collect these comments into one post and I will put it up?!

    4. Anonymous11:40 PM

      Oh jeez, now you're putting me on the spot just like Lew did. I turned him down for two reasons: I don't like to speak as an authority on this topic (guns) and I don't want to be "that guy" (the gun nut).

      I think what happens is that I am a detail oriented person who likes to explain things without leaving things unanswered, so my comments on other people's blogs can often become longer than the blog post itself. What I really should be doing is writing my own blog, except every time I've tried I cannot think of anything to write about.

      I think that I am going to have to decline. I appreciate the offer, though.

  5. Good evening, Dr. C.

    Surely, JF has forgotten more about this than I will ever know, but I thought your original question was something like: "If A and B are 10 feet away and pointing guns at each other, doesn't the first to fire win?" It seems like the answer to that is a resounding: Yes.

    Of course, I am assuming the A and B are equal in skill. If this is true, then the first to fire should be the first to be able to fire all his bullets. Also, if it is hard for the unskilled to shoot accurately, then I imagine that it would be especially hard for the unskilled to shoot accurately when said unskilled person has just been shot in the leg, arm, foot, etc., or even when the unskilled has avoided being shot. The adrenaline rush would be too overwhelming.

    In terms of entertainment, I always found it funny that someone would "tie-up" their adversary and give them an opportunity for escape rather than simply dispatching them quickly and efficiently with a shot through the head.

    1. So, no, I now think not, as Joe and Tom have demonstrated: This is not a straight-forward, one-shot prisoner's dilemma at all. Instead, it is a probabilistic, repeated game: If I defect first, there may be a *somewhat* higher chance that I live than I do if my opponent defects first. But if neither of us defects, we both have a 100% chance of living. Depending on how you set up the payoff matrix, this may strongly indicate "cooperate."

  6. Well, if the situation is *really*, truly symmetric, then you both will make the decision, and so you can trust that your decision will match your opponents, so pick the one you'd rather both of you did.

    But of course, real world situations (I guess) don't capture that aspect either.

  7. Gene,

    As you are fond of pointing out, I am not a trained theologian. I am, however, a trained US Marine Corps marksmanship instructor, so my opinion on this may be a little more palatable to you than my opinions on the Pauline Heresy ;-)

    Yes, it is entirely possible for even a well-trained shooter to miss a human target at ten feet for any number of reasons, ranging from unsteady/improvised/ad hoc position, to the fact that in such a situation he probably has 55 gallons of adrenaline coursing through his veins and making him shake like a leaf, to the fact that killing another human being is, quite simply, an unnatural and mentally frazzling act that one's bodily functions tend to revolt against.

    That last one could also partially account for the movie "pause and stare at each other" effect, if that does indeed happen in real life (I've fortunately never been in such a situation involving guns).

    And to the extent that rational calculation enters into the matter, as one previous commenter points out, shooting is no guarantee of instantaneous incapacitation of your opponent even if you hit him.

  8. Others handled this really well, so I'll just cap things off with a link to Randall Collins.

  9. Here's what I don't understand: Joseph Fetz explained that in the military, you would shoot right away, and that with the police, you would shoot once a bad guy points a gun at you.

    And yet, he concluded that it makes sense in movies for a good guy and a bad guy to point guns at each other without shooting.

    I'm no gun expert (though I've been to the range once, Joseph), but this doesn't seem to add up.

    1. Anonymous4:32 PM

      Yes, I probably should have been more clear on that, but it really wasn't what I considered a larger point to address.

      All I was saying is that the ROE for military and police are different. In a warzone setting, you are authorized to shoot anybody with a gun. This is not true outside of a warzone (even for military). For instance, if I am guarding a Navy ship ported in San Diego, I cannot just shoot a guy because he is waving a gun around. I would have to conclude that he is an immediate threat to persons or property* (merely waving a gun is not enough). In neither case would you wait for somebody to actually point a gun at you. Now, if he is waving a gun and says, "I am going to shoot you", and I notice that as he is waving the gun that he begins to wave it in my direction (or that of another person), then I can shoot him. You must have intent in this case (and, you better be able to prove it).

      Yes, it does make sense in the movies for a good guy and a bad guy to have a standoff. The reason is for purposes of entertainment. If when the bad guy and good guy meet all that happens is the good guy immediately shoots and kills the bad guy, that would be quite a let down. I'm sure that even though this would be the more realistic scenario that most people would conclude that the movie was anti-climactic.

      * The ROE for military allows one to shoot a person who poses a threat to government property. Usually, there is a lot of ambiguity regarding this particular ROE, so the specifics are typically handled in what is called "standing orders", which are the command-specific orders as laid out by the commanding officer. So, if for instance I am on a classified installation, the commanding officer may state in his standing orders that I can shoot any persons who attempt to enter the perimeter of the property, this would obviously allow me to shoot anybody that so much as puts a toe across that blue line on the pavement. However, in almost all cases, if the person is attempting to destroy property and the destruction of that property can represent an addition danger to persons, then you can indeed shoot them (e.g. a guy taking a sledgehammer to a nuclear warhead). Also, just so that we're clear, ROE means "rules of engagement".

    2. Anonymous4:36 PM

      Keep in mind, I am talking about standard ROE procedures. The commanding officer can essentially make any changes that he wants in his standing orders just so long as they do not defy standard ROE. Basically, he can make the rules more strict, but he cannot make them more lax, and often a commanding officer will make the rules slightly more strist in many cases (because it is his ass if one of his men screw up).

    3. Anonymous4:36 PM


    4. "Yes, it does make sense in the movies for a good guy and a bad guy to have a standoff. The reason is for purposes of entertainment."

      I don't know: I don't find movie cliches I'm seeing repeated for the 500th time very entertaining, but since every action movie seems to feel the need to include a car chase, I recognize I am in the minority.

    5. Anonymous5:18 PM

      Just remember to park at the back of the lot when you go to the theater.

    6. Anonymous6:25 PM

      Wow, I just realized that what I said can be taken more than one way. I was actually referring to the fact that me, you and Murphy park toward the back of parking lots, because we would rather get in and out quickly than spend all day looking for a good spot (the fact that we do this puts us in the minority). However, I just realized that what I said could also be misconstrued as being related to minorities being forced to sit at the back of the bus. I surely didn't mean it in this latter sense, but it still works, I guess.

    7. Joe, we Irish are used to the back of the bus treatment. I took it in stride.

    8. Anonymous5:19 PM

      I am equal parts German, Hungarian, Irish and Sicilian; one half of me tells the other half to sit at the back, so I end up in the middle.


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