Prisoner’s Dilemma

The Prisoner’s Dilemma is a foundational concept in game theory, a field of mathematics and economics that studies strategic decision-making in situations where the outcome for one person depends on the choices of others.

It’s a thought experiment that perfectly illustrates the conflict between individual self-interest and collective well-being.

The Classic Scenario

Imagine two suspects, let’s call them Alex and Ben, who have been arrested for a crime and are being interrogated in separate rooms. They can’t communicate with each other. The police offer each of them the same deal:

• If you confess and your partner stays silent, you will be set free, and your partner will get a full 3-year prison sentence.
• If you both confess, you will both get a 2-year prison sentence.
• If you both stay silent, there isn’t enough evidence for the main crime, so you will both get a minor 1-year sentence for a lesser charge.

The Dilemma: Individual vs. Collective Rationality

Let’s look at Alex’s thought process, knowing that Ben is facing the same choices and is a rational, self-interested individual:

• Case 1: Ben stays silent. If Ben stays silent, Alex has a choice. If Alex also stays silent, he gets 1 year. But if Alex confesses, he gets off scot-free. Alex’s best move in this case is to confess.
• Case 2: Ben confesses. If Ben confesses, Alex again has a choice. If Alex stays silent, he gets the full 3-year sentence. But if Alex also confesses, he only gets 2 years. Alex’s best move in this case is also to confess.

Regardless of what Ben chooses, Alex is always better off confessing. Confessing is the dominant strategy for Alex. Since Ben is a rational agent facing the exact same dilemma, his dominant strategy is also to confess.

The paradoxical outcome is that when both Alex and Ben act in their own self-interest, they both confess and end up with a 2-year prison sentence. This is a worse outcome for them collectively than if they had both cooperated by staying silent, which would have only resulted in a 1-year sentence each.

Application in Economics and Cartels

The Prisoner’s Dilemma is a powerful tool for understanding why cooperation is so difficult to maintain, especially in business. It’s a perfect analogy for how cartels work (or, more often, fail to work).

Imagine two competing companies, Firm A and Firm B, in a duopoly (a market with only two firms). They have secretly agreed to form a cartel to keep prices high and split the market.

• Cooperate (Stick to the agreement): If both firms keep their prices high, they both earn a large profit. This is the equivalent of the prisoners both staying silent.
• Defect (Cheat on the agreement): If one firm secretly lowers its prices, it can capture a large portion of the market and make an even larger profit in the short term. The other firm, which kept its price high, loses a significant amount of business. This is the equivalent of one prisoner confessing and the other staying silent.
• Mutual Defection: If both firms cheat and lower their prices, they will trigger a price war. This will drive prices down to competitive levels, and both firms will earn much lower profits than if they had cooperated. This is the equivalent of both prisoners confessing.

Just like Alex and Ben, each firm has a powerful incentive to cheat on the agreement, regardless of what the other firm does. The dominant strategy for each firm is to lower its price. This leads to the predictable outcome of both firms cheating, resulting in lower profits for both—a situation that is worse for them than if they had cooperated.

This is why cartels are so inherently unstable. They require constant monitoring and a credible threat of punishment to prevent members from cheating.

The Prisoner’s Dilemma highlights that in the absence of trust and a strong enforcement mechanism, self-interest will almost always lead to an outcome that is suboptimal for the group as a whole.