“The greatest tragedy in social science? Whoever invented the Prisoner’s Dilemma neglected to name it after themselves.”

– Jo Wolff (professor of public policy at the Blavatnik School of Government, University of Oxford)

What is the Prisoner’s Dilemma?

The Prisoner’s Dilemma is a well-known concept in modern game theory. Game theory is a framework for modelling scenarios where different ‘players’ have conflicts of interest. The Prisoner’s Dilemma presents us with a paradox in decision analysis in which two individuals, acting in their own self-interest, fail to produce the optimal outcome.

It works like this:

Alex and Bobbi have been arrested following a bank robbery. They’ve been placed in separate isolation cells and can’t communicate in any way. Both Alex and Bobbi care more about their own freedom than about the welfare of the other. A clever prosecutor makes the following offer to each: 

“You may choose to confess or remain silent. If you choose to confess and your accomplice remains silent, I’ll drop all charges against you and your accomplice will serve three years in prison. Likewise, if your accomplice chooses to confess whist your remain silent, they will go free and you’ll serve the three years. If you both confess, you’ll each serve two years. If you both remain silent, you’ll each serve one year.” 

Therein lies the ‘dilemma’. Both Alex and Bobbi have an incentive to betray the other. But if they both confess they’ll each serve two years in prison – a worse outcome than had they both remained silent.

If we assume that Alex and Bobbi are both purely rational, then the only possible outcome is for them to betray each other – betraying the other offers a greater reward (freedom) than cooperation (prison). This is an interesting outcome: in pursuing individual reward, both Alex and Bobbi are now worse off.

Why is it useful?

The Prisoner’s Dilemma is often used to illustrate the conflict between competition and cooperation or, more narrowly, individual and group rationality. We can see how a group pursuing rational self-interest may actually end off worse than a group whose members act contrary to rational self-interest.

Much of the contemporary discussion around the Prisoner’s Dilemma (and related scenarios) has focused on working out the conditions under which players would or should make the ‘cooperative’ move (corresponding to remaining silent). After all, benefiting oneself is not always wrong – but in the Prisoner’s Dilemma, both players prefer the outcome with the altruistic moves to the selfish moves. To some, this says something important about the nature of morality.

Knife crime

Some elements of knife crime can be modelled on a Prisoner’s Dilemma. Take weapons amnesties, for example. There are three possible scenarios here. Firstly, if everyone hands in their weapons, then everyone is better off (safety). If some people hand in their knives and others do not, then they are safer at the expense of those who do (power imbalance). If no one hands in their knife, then everyone remains unsafe (danger).

This is one concept at the heart of knife crime. You get a knife to protect yourself because of the other knives around you – and you will only give up your knife if that’s what everyone else does. This is further complicated by the fact that you do not know for certain whether those around you have actually handed in their weapons or not.

Any system or process designed to facilitate mutually beneficial exchanges, like weapons amnesties, will need to overcome the Prisoner’s Dilemma or somehow avoid it.

Knife Crime?

It’s important to note that knives themselves are not strictly relevant to this model. Replace ‘knife’ with ‘gun, ‘hammer’, or a similar weapon and you end up in the same situation – safety, a power imbalance, or danger.

It’s often argued that knives are the weapon of choice because they’re accessible – they’re found in every kitchen across the country and anyone over the age of eighteen can buy one.  So what about getting rid of knives? Would this help? If we gave everyone in London a gun, knife crime could well disappear overnight. But shootings would increase dramatically.

We could get rid of the knives, but that wouldn’t stop the crime. Instead, we could see an increase in crimes involving other types of weapon. If we want to see reduced rates of knife crime, we need to treat the root causes – not the symptoms.