The classical prisoner's dilemma

The Prisoner's Dilemma was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "Prisoner's Dilemma" name (Poundstone, 1992).

The classical prisoner's dilemma (PD) is as follows:

Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?

The dilemma can be summarized thus:

	Prisoner B Stays Silent	Prisoner B Betrays
Prisoner A Stays Silent	Each serves six months	Prisoner A serves ten years Prisoner B goes free
Prisoner A Betrays	Prisoner A goes free Prisoner B serves ten years	Each serves five years

The dilemma arises when one assumes that both prisoners only care about minimizing their own jail terms. Each prisoner has two and only two options: either to co-operate with his accomplice and stay quiet, or to defect from their implied pact and betray his accomplice in return for a lighter sentence. The outcome of each choice depends on the choice of the accomplice, but each prisoner must choose without knowing what his accomplice has chosen.

In deciding what to do in strategic situations, it is normally important to predict what others will do. This is not the case here. If you knew the other prisoner would stay silent, your best move is to betray as you then walk free instead of receiving the minor sentence. If you knew the other prisoner would betray, your best move is still to betray, as you receive a lesser sentence than by silence. Betraying is a dominant strategy. The other prisoner reasons similarly, and therefore also chooses to betray. Yet by both defecting they get a lower payoff than they would get by staying silent. So rational, self-interested play results in each prisoner being worse off than if they had stayed silent. In more technical language, this demonstrates very elegantly that in a non-zero sum game a Nash Equilibrium need not be a Pareto optimum.

Note that the paradox of the situation lies in that the prisoners are not defecting in hope that the other will not. Even when they both know the other to be rational and selfish, they will both play defect. Defect is what they will play no matter what, even though they know fully well that the other player is playing defect as well and that they will both be better off with a different result.

The "Stay Silent" and "Betray" strategies are also known as "don't confess" and "confess", or the more standard "cooperate" and "defect."

One experiment based on the simple dilemma found that approximately 40% of participants cooperated (i.e., stayed silent).^[1]