Applying Game Theory to Stand-Your-Ground

Game theory is a method of studying strategic decision making. It helps us model conflict and cooperation between intelligent rational decision-makers. It is commonly used in economic and business. I thought I would attempt to apply it to conflict in neutral territory in precincts with and without stand-your-ground laws. Of course models always over simplify real-world situations but they do help us think through situations and how the rules of the game change decision making.

I used the normal (or strategic form) game which is represented by a matrix which shows the players, strategies, and pay-offs. In this game, Tom and Bill are at the point of conflict and the decision to stand or retreat must be made. The potential outcomes of those decisions are included in the matrices. I have added points to make it easier to see how decisions are made.

First, let’s look at the matrix for a state in which there is no stand-your-ground law and individuals are expected to retreat.

The matrix explains outcomes. If both players stand, depending on who is quicker, one will end up dead and the other in prison on a murder rap. That is 0 points each. If one retreats and the other stands, the one who retreats runs some risk by letting down his guard, but the risk is reduced. That is 2 points. The individual who stands is going to get arrested for, at least, assault. Since it isn’t a murder rap and he doesn’t risk getting killed, that is 1 point. If they both retreat, it is freedom for each which is worth 10 points each.

Assuming neither player knows what the other will do, they make a decision. Standing gets you either 0 points or 1 point. Retreating gets you either 2 points or 10 points. The strategy is clear. It is better to retreat. If social policy is to reduce violence and conflict, the rules of the game appropriately designed.

Now lets look at states with a stand your ground law.

In this game, there is no legal penalty for standing your ground. Therefore, if both players stand, one player will be dead and the other will be free. Since death is 0 pts and freedom is 10 pts, we will split the difference and assign this option 5 pts. If one retreats and the other stands, as in the other game, the one who retreats runs some risk by letting down his guard, but their is still risk. That is 2 points. The player who stands, however, has no risk since he has the right to stand. In this case, he is free and that is worth 10 points. As in the other game, if they both retreat, it is freedom for each which is worth 10 points each.

Again, we will assume that neither player knows what the other will do as they make their decisions. Now things have changed. Standing gets you either 5 points or 10 points. Retreating gets you either 2 points or 10 points. Now the best strategy is far less clear. It is, however, slightly better to stand. If social policy is to reduce violence and conflict, the rules of the game badly designed. The stand your ground law is badly designed.

We can change the point structure around but, assuming the points are rational, the stand-your-ground matrix will always be more conducive to violence than the no-stand-your-ground matrix.

Food for thought.

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14 Responses to Applying Game Theory to Stand-Your-Ground

  1. R.D. Walker says:

    Again, I want to reiterate that I strongly and wholeheartedly support castle laws. The above game applies to neutral territory – the street. The game changes radically when you are required to retreat from your home.

    In that matrix, the players aren’t equal and the outcomes aren’t the same. We are mostly concerned about the incentives on the home invader. Without the castle law, the game makes burglary, home invasion, rape – whatever – much more likely. It takes away the downside for the home invader. It is a completely different scenario.

    As you can see, homeowner retreating is of great benefit to the burglar no matter what he does. Policy should not force homeowners to take steps to benefit criminals.

  2. slinger says:

    Stand your ground should apply most to those least able to retreat … kind of like a stand your ground right-of-way …

    For instance, I have no problem retreating when I am out and about by myself. When I have my 5 year old and 3 year old with me, my ability to retreat is significantly reduced. Similarly, an old woman in a walker should have more right to stand her ground than a physically capable 30 year old man.

  3. R.D. Walker says:

    I agree Slinger, even in states that don’t have stand-your-ground laws (like Iowa) you can defend yourself if you can’t retreat. If you are cornered or have some other factor preventing retreat – little children, physical impairment – you can legally defend yourself and others.

    In Florida, you don’t have to retreat even if you are able to retreat.

  4. Bushido says:

    I understand where you are coming from RD, here is where my “however” comes into play. Situation should dictate your actions. Sometimes retreating is a better option, sometimes standing your ground is the better option. In my opinion the law shouldn’t be the deciding factor in your decision. This is the school yard argument that a kid didn’t fight back because he didn’t want to get into trouble.

    I think of it in terms of tactics. If I’m confronted by someone and I am legally bound to retreat I can be hurt even worse because of my actions. I could be pushed off balance, run into other people who then get into the confrontation, get backed into a corner. If this guy is pushing me he might push me back and I hit my head on the curb, stroke out and die. Did he mean to kill me? NO! Does it make me any less dead? NO! I just don’t want to be at a disadvantage because I was following “the law” and not the tactics I need to survive.

    On the flip side; just because you can stand your ground doesn’t mean that you should. In fact you may put yourself at a disadvantage because you did. This would be if you are far enough away to avoid the situation or if the situation escalates and you are out gunned or outmanned. I think this is what your graph illustrates nicely.

    My thoughts on this is I want the law behind me every step of the way if I am forced to protect myself. Stand your ground and the term Self-Defense is stictly a legal term. You are admitting to crime, but this was the reason for it so I’m OK!

  5. R.D. Walker says:

    The law, just like my game matrices, will never be able to accommodate all scenarios.

  6. W. C. Taqiyya says:

    Castle laws aside, except to say I agree that a person’s home is his castle, or should be. More food for thought. Forget the games and scenarios. The bottom line is that all the micromanagement laws in the world can’t protect shit or make anyone safer. In fact, they make the world more dangerous because they encourage people NOT to think for themselves. If you can’t figure out that attacking an unknown person on a darkened street is problematic, you SHOULD be dead because your brain already is. And screw Treyvon Martin, he killed himself.

  7. W. C. Taqiyya says:

    My post above. I think my time for editing expired and that undefined thing showed up. Without my edited comment. Fracking technology.

  8. R.D. Walker says:

    By the way, if Zimmerman was flat on his back with Martin on his chest dribbling his melon on the pavement like a basketball, stand-your-ground doesn’t really enter into the case, does it?

  9. rj says:

    Good write up and comments, yes RD if his head was getting thunked on hard dirt or concrete it is not stand your ground it is self defense which I believe is what he is claiming.

    In TX all else aside, if he tried to end a conflict by leaving or clearly indicating his intent to end the conflict and he is kept in the conflict by the more powerful one he can still claim self defense even if he started it.

    so if a bad guy approaches me to rob me with a knife or fist and I pull mu gun and he runs self defense goes out the window and I cant shoot him in his running back.

    If however I pick a bar fight and the big guy kicks my butt to the point I am trying to leave or on the ground covered up and shouting I quit and he keeps kicking me in the head I then have the right of self defense even though I provoked the fight.

  10. notamobster says:

    In all of the games a crime is being comitted, no? It may be more problematic to stand, but no one has the right to violate you or your God-given rights. The law should always err on the side of the individual’s rights, as endowed by their Creator, without regard to where the violation occurs.

  11. JJ says:

    Even when you have a “stand your ground” law, you don’t. Ask George Zimmerman. It all comes down to the right of self defense.

    I doubt that this specific SYG law entered Zimmerman’s mind during the encounter, and he is in jail anyway.

    With or Without this law, you are at risk if you have to defend yourself.

    Self defense is your God given right.

    Stand your ground laws are more of a response to irresponsible prosecution of persons who clearly are in the right to defend themselves by a prosecutor who thinks you have no such right of self defense.

    They won’t help you if you act stupid.

    The game changes when you begin to include intent for the players. The gain/loss formula changes when you take society into consideration by looking at the variety of the intentions of the players. The worst loss overall is when you have two people encounter each other who stand when neither intended harm. It is also the least likely to occur.

    When you have one of the two parties more likely to have intent for harm (evil player), they have a gain from the confrontation. If there is no risk of Standing from the other side (good player), society will see more activity from the evil party with intent to harm.

    If there is a greater risk to the evil player (because the good player may be more likely to stand), evil will have some dis-incentive to confrontation.

    It is a similar effect of increased concealed carry in correlation to localities with lower crime rates. The risk/reward calculation changes.

    If you have two evil players, such as with gang turf wars, the incentive for confrontation may be greater to stand than to retreat.

    The complexity of the game increases because you have to play more scenarios and weigh the points based on intent of the player.

    Sheep versus Sheep. Sheep versus Wolf. Sheepdog versus Wolf. The intent and nature of the player changes the risk/reward points.

    Simplified game theory can be like the “settled” science of AGW. The complexities soon exceed the simple theory.

    The bottom line will always come down to Self Defense. You have a right to it. Do everything you can to avoid having to use Self Defense. Don’t get yourself into a position that you must make the choice.
    If you are in a position that you have to employ Self Defense you are at risk when you don’t act, and when you do. You will have to live with the decision for the rest of your life. How long will that be?

  12. R.D. Walker says:

    All good and thoughtful comments.

    As I said in the lead in, the models oversimplify real life. They are intended to help us organize our thoughts and think through scenarios. They are not intended to predict any individual situation.

    I would never claim they predict specific outcomes. They assume rationality which is a pretty damned big assumption and they leave out untold numbers of variables.

    Still, they serve a purpose by allowing us to think about aspects of any situation “caeteris paribus” or with “all else equal.” In that sense, they are valuable tools we have in our tool set.

  13. slinger says:

    In one of the carry courses I took, the scenario was posed like this: “If after taking the shot, you find yourself in prison for life, you wife has divorced you, your kids don’t want anything to do with you, and your friends disown you … and you still would have taken the shot, then you did the right thing.” I try to think of that often, as I carry often.

  14. R.D. Walker says:

    The salience of that lesson is not to take the shot lightly, however. Very bad things can be the result. I would hate to be in prison for life, my wife divorced me, my kids not wanting anything to do with me, and my friends having disowned me, thinking, “man, I shouldn’t have taken that shot.”

    I would be surprised if right now Zimmerman isn’t thinking he should have just taken his chances with the ass whooping that night rather than taking his chances with the state for the rest of his life.

    If he did, he might be on the mend basking in the sympathy of his community while Martin sits in jail.

    Just sayin…