Iterated Games
An iterated game is a repeated interaction between the same players — the same game played over many rounds, with each round's outcome carrying forward into the next. The repetition transforms what's strategically rational.
In a one-off prisoners-dilemma, defecting is the dominant-strategy. But in an iterated version, defecting has a cost that doesn't exist in a single encounter: it damages the relationship, invites retaliation, and forecloses future cooperation. The shadow of the future changes the math.
Axelrod's key insight: "What makes it possible for cooperation to emerge is the fact that the players might meet again."
What Repetition Changes
Reputation — each interaction creates information. Players who defect acquire a reputation for defecting; players who cooperate build trust. In a one-off game, reputation is irrelevant because there's no future. In iterated games, reputation is a resource.
Retaliation — a player who gets defected on can respond next round. This makes exploitation costly in a way it isn't in a single encounter. The threat of retaliation disciplines defectors.
Cooperation as equilibrium — when players know they'll interact again, cooperation can become stable. Neither player wants to trigger a defection spiral that leaves both worse off across all future rounds. The iterated structure makes the cooperative outcome self-enforcing.
The Unknown Horizon
In Axelrod's second tournament, the number of rounds per game was left undefined — players couldn't calculate backward from a known endpoint. This better mirrors real life: most interactions don't have a defined endpoint, so you can't reason about "the last round" and defect without consequence. An unknown horizon sustains cooperation.
Connections
- prisoners-dilemma — the game that becomes solvable through iteration
- dominant-strategy — defecting is dominant in one-off games; iteration eliminates that dominance
- tit-for-tat — the strategy that wins iterated games by exploiting the cooperation-sustaining properties of repeated interaction