The Evolution of Cooperation

Axelrod's Iterated Prisoner's Dilemma tournaments, strategies and replicability analysis.

Period
1980 to the modern era
Format
Interactive laboratory: six modules and a live match simulator

The Game-Theoretic Foundations of the IPD

The Prisoner’s Dilemma models the tension between individual self-interest and collective rationality. In a single-round game, mutual defection strictly dominates cooperation. However, when iterated under the "shadow of the future" (discount probability ω), conditional cooperation becomes mathematically sustainable.

Standard IPD Payoff Matrix

Constraint: T > R > P > S and 2R > T + S

Test the fundamental inequality conditions: T Temptation (5), R Reward (3), P Punishment (1), S Sucker (0).

Player A \ BCooperate (C)Defect (D)
Cooperate (C)R, R (3, 3)S, T (0, 5)
Defect (D)T, S (5, 0)P, P (1, 1)

Round Score Evaluator

Result: Mutual Cooperation yields 3 points to Player A and 3 points to Player B.

Core Mathematical Conditions

1. Strict Inequality Condition (T > R > P > S)

Ensures that defection strictly dominates in a one-shot game. 5 > 3 > 1 > 0 guarantees that defection yields a higher payoff regardless of the opponent's choice.

2. Mutual Cooperation Incentive (2R > T + S)

Prevents players from alternating between exploitation and being exploited. Here, 2(3) = 6 > 5 + 0 = 5. Sustained mutual cooperation yields higher utility than split exploitation.

3. Shadow of the Future (ω) & Backward Induction

If the game has a known finite horizon N, players defect on round N. By backward induction, cooperation collapses to move 1. If the end is probabilistic with continuing probability ω, cooperation persists when ω ≥ (T - R)/(T - P).

4. Replicator Dynamics

In population models, the proportion of a strategy grows proportionally to its average payoff relative to the population's mean score. High mutual utility drives ecological dominance.

Synthesized from historical archives, Fortran reproductions, and Press-Dyson ZD theory.