Iterated Prisoner's Dilemma Tournament

About the Prisoner's Dilemma

The Prisoner's Dilemma is a fundamental problem in game theory that demonstrates why rational individuals might not cooperate, even when it's in their best interest to do so.

The Classic Scenario

Two suspects are arrested and interrogated separately. Each can either cooperate with their partner (stay silent) or defect (betray them). The payoffs create a dilemma: mutual defection is worse than mutual cooperation, yet defection is the dominant strategy in a single round.

Iterated Games

When the game is repeated, cooperation can emerge. Famous strategies include:

• Tit-for-Tat: Start by cooperating, then copy opponent's last move. Simple and effective.
• Always Cooperate: Pure altruism - vulnerable to exploitation.
• Always Defect: Pure selfishness - misses cooperative gains.
• Grudger: Cooperates until betrayed, then defects forever.
• Pavlov (Win-Stay, Lose-Shift): Repeat if you did well, change if you did poorly.
• Random: Cooperates or defects with 50% probability.
• Generous Tit-for-Tat: Like TFT but occasionally forgives defections.
• Suspicious Tit-for-Tat: Starts with defection, then copies opponent.

Axelrod's Tournament

Robert Axelrod's famous tournaments in the 1980s revealed that "nice" strategies (those that never defect first) tend to outperform purely selfish ones in iterated games. Tit-for-Tat won both tournaments, showing that being nice, retaliatory, forgiving, and clear is a winning combination.

Payoff Parameters

• R (Reward): Mutual cooperation payoff
• T (Temptation): Payoff for defecting while opponent cooperates
• S (Sucker): Payoff for cooperating while opponent defects
• P (Punishment): Mutual defection payoff

For a true dilemma: T > R > P > S and 2R > T + S (to prevent alternating defection).