18.8 : Prisoner's Dilemma I

The prisoner's dilemma is a fundamental example in game theory. It shows how two rational individuals might not cooperate, even when it's in their best interest to do so. It also demonstrates the concept of Nash equilibrium, where each player's choice is the best response to the other's decision.

Imagine two business rivals, Firm A and Firm B, that are accused of price-fixing. They are questioned separately and have two options: to confess (betray the other) or to deny (cooperate). The outcomes depend on their decisions:

1. If both firms deny involvement, they receive a minimal penalty, such as a small fine. The best collective outcome is when neither firm provides evidence against the other.
2. If Firm A confesses while Firm B denies, Firm A is rewarded with no penalty, while Firm B faces a severe penalty, like a hefty fine or further legal action. The reverse happens if Firm B confesses and Firm A denies.
3. If both firms confess, they receive moderate fines that are worse than if both had denied, but better than the severe punishment one would face alone.

The Nash equilibrium in this scenario occurs when both firms choose to confess. Even though denying would be better for both, each has the fear of cooperating with the other firm confessing. This leads them both to act defensively, resulting in each firm suffering a less favorable outcome than if they had both cooperated. This example illustrates how the structure of incentives can lead rational players to make decisions that do not maximize their joint benefit. The Prisoner's Dilemma game highlights the challenges of cooperation when trust and communication are absent.