Prisoner's Dilemma I

A Nash Equilibrium occurs when all players choose strategies that are best for them, given the strategies chosen by others. No player can benefit from changing their strategy while others keep theirs unchanged. This concept is central to understanding strategic interactions where each player's decision is the optimal response to others' choices.

In the prisoner's dilemma, rational players choose to betray because each fears the other will confess first. Even though mutual cooperation yields better outcomes than mutual betrayal, the incentive structure rewards individual defection. Each player acts defensively, resulting in worse collective outcomes than if both had cooperated, demonstrating how trust absence undermines cooperation.

The prisoner's dilemma has four outcomes: both suspects stay silent and receive one year each; one confesses while the other stays silent, with the confessor going free and the silent suspect receiving a harsh sentence; both confess and receive two years each; or mutual silence, which is collectively optimal but individually risky due to betrayal incentives.

Two firms accused of price-fixing face similar choices: deny involvement or confess. If both deny, they receive minimal penalties. If one confesses while the other denies, the confessor escapes penalty while the denier faces severe consequences. If both confess, they receive moderate fines. The Nash Equilibrium occurs when both confess, even though mutual denial would benefit them more.

The Nash Equilibrium in the prisoner's dilemma occurs when both players confess or betray. Each player chooses this strategy because it is their best response to the other's potential action, even though both would be better off cooperating. This equilibrium demonstrates how incentive structures can lead rational individuals to suboptimal collective outcomes.

Mutual silence is not a Nash Equilibrium because each player has an incentive to deviate. If one suspect stays silent while the other confesses, the confessor goes free while the silent suspect receives a harsh sentence. This temptation to betray means neither player can trust the other to maintain silence, making mutual cooperation unstable.

The prisoner's dilemma shows that without communication and trust, rational players choose defensive strategies that harm everyone. When suspects are questioned separately with no ability to coordinate, each assumes the worst about the other's choice. This absence of trust and communication mechanisms prevents players from achieving the mutually beneficial outcome of cooperation.