The prisoner's dilemma
The prisoner's dilemma is a classic example in game theory that illustrates the conflict between individual rationality and collective rationality. It is called a dilemma because it demonstrates how individuals can find themselves in a situation where cooperation would benefit the group as a whole, but the incentive to act in one's own self-interest often leads to a suboptimal outcome.
In the prisoner's dilemma, two suspects are being held in separate cells and are interrogated without being able to communicate with each other. The prosecution lacks sufficient evidence to convict them for the main charge, but they can be charged with a lesser offense. The authorities separately offer each prisoner a deal:
- If one prisoner confesses and implicates the other, they will receive a reduced sentence or immunity, while the other prisoner will face harsh consequences.
- If both prisoners stay silent and do not confess, they will each receive a moderate sentence.
- If both prisoners confess, they will each receive a slightly longer sentence compared to if both had stayed silent.
The dilemma arises because each prisoner must consider their own self-interest and decide whether to confess or remain silent, without knowing the other's decision. If both prisoners were to cooperate and remain silent, they could avoid harsher consequences. However, the temptation to betray the other prisoner becomes significant, as confessing could lead to either a reduced sentence or immunity.
The Nash equilibrium, which represents the most rational outcome given the circumstances, occurs when both prisoners choose to confess. In this scenario, neither prisoner can improve their individual outcome by deviating from their decision, even though the collective outcome would be better if both stayed silent.
The prisoner's dilemma has been used as a metaphor in various real-life situations, such as international relations, business negotiations, and social interactions. It highlights the challenges of cooperation and the inherent tension between individual and collective rationality.