Game Theory and Gun Violence

Erik Engheim
4 min readFeb 28, 2018


Why do Americans keep getting more guns, despite the problem it causes? What if there was a simple, but formal principle to explain it? Turns out that there is. It is called the prisoners dilemma. The prisoners dilemma is an example of a non-cooperative game. Anyone who follows me will know this is one of my favorite explanation for many of the problems we face in society today.

The prisoner’s dilemma explains why we get arms races, such as the build up of nuclear stockpiles in the Soviet Union and the US during the cold war. When two sides in a struggle can’t trust each other, they easily start engaging in an escalation to the detriment of themselves and all of society.

Gun violence could just as well be analyzed as a prisoners dilemma game. The two players are “the law abiding citizen” and “the criminal.” Lets look at the different ways the game can be played. Keep in mind this is a simplification, and not reality. We exclude other forms of violence, knives etc. What we are interested in here, is the principles and the optimal strategies to pursue. Here are the possible outcomes of the game:

  1. Both can chose to not have a gun. When the criminal attempts to rob the law abiding citizen, neither risk getting killed.
  2. Both can be armed and risk getting shot and killed during the robbery.
  3. The robber is armed and the good guy isn’t. The robber is safe but the good guy will more likely get robbed and killed.
  4. The bad guy is unarmed but the good guy isn’t. The robber will likely both fail to rob the good guy and risk getting shot and killed.

In game theory we talk about both optimal global choices and Nash-equilibriums. The global optimum strategy for both players in this game would be that neither one have a gun. That means nobody risk getting killed, when interacting with the other guy.

However if the players cannot cooperate and has to pick the most optimal strategy for themselves, we end up with both players choosing to have a gun. This the Nash-equilibrium.

We can see how the logic of this game plays out in different societies. In Japan there are few guns and gun laws are strict. This means good guys won’t feel a strong inclination to get a gun, because they know criminals are unlikely to have one as well. Criminals likewise don’t have a strong inclination to get a gun either, because they know they are unlikely to face an armed victim. This means when crime happens it is unlikely to be fatal.

An entirely different strategy dominates if playing the game in an American society. Gun laws are lax and there is a massive proliferation of guns. The good guy will know that the criminals are likely armed and will deem the most optimal strategy is to arm oneself. Criminals in contrast will assume that given easy access to guns for law abiding citizens, they must assume their potential victim is armed as well. Hence every criminal will make sure they are well armed. Anything else would be far too risky.

Of course the problem is that both end up as losers. Criminals are more likely to get shot and killed in the US, just as victims are more likely to get shot and killed.

The Broken Logic of an Arms Race

Thus what happens in American society is an arms race between civilians and criminals. A criminal might start with something like a bat or knife in a normal society. But if they know the civilians are armed they will have to get a gun as well. Not only that but they will have to get a better gun to even the odds in their favor.

If they know their opponent has a handgun they might want to upgrade to a semi-automatic rifle. This isn’t purely theoretical but has been observed in practice.

The 1930s gangsters ended up in an arms race with each other which culminated in the Thompson machine gun, or Tommy gun for short. The police at the time usually used pistols or regular rifles. However they found they got consistently outgunned by gangsters wielding Tommy guns. So they had to upgrade as well, making the conflict between police and gangsters even more bloody.

The insane violence of the 1930s gangster rule would not have happened without lose gun regulation and the broken logic that law abiding citizens, need more guns to protect themselves. Because the Thompson machine gun failed to sell to the military, it got marketed towards civilians for protection. This had the complete opposite effect. By selling the gun in the civilian market, gangster got hold of the Thompson machine gun. Ironically the attempt at arming law abiding citizens resulted in a massive firepower upgrade for criminals.



Erik Engheim

Geek dad, living in Oslo, Norway with passion for UX, Julia programming, science, teaching, reading and writing.