Repeated Games & Tournaments

Pit strategies against each other in iterated Prisoner's Dilemma tournaments

When Games Repeat

In a one-shot Prisoner's Dilemma, defection is the dominant strategy. But when the game is played repeatedly, cooperation can emerge. The shadow of the future changes the calculus — being nice today can pay off in future rounds.

In 1984, political scientist Robert Axelrod ran a famous computer tournament, inviting experts to submit strategies for the iterated Prisoner's Dilemma. The winner? Tit-for-Tat — the simplest strategy of all: cooperate on the first move, then copy whatever the opponent did last round.

Axelrod-Style Tournament

Select which strategies to include, set the number of rounds, and run a round-robin tournament. Every strategy plays every other strategy. Click any matchup to see the round-by-round cooperation/defection pattern.

Key insight: Tit-for-Tat succeeds because it is nice(starts with cooperation), retaliatory (punishes defection immediately),forgiving (returns to cooperation if opponent does), and clear(opponent can easily understand its behavior).

Strategy Profiles

  • Tit-for-Tat — Cooperate first, then mirror opponent. Simple and effective.
  • Grim Trigger — Cooperate until opponent defects once, then defect forever. Unforgiving.
  • Pavlov — Repeat last move if it was rewarded (both same), switch otherwise.
  • Suspicious Tit-for-Tat — Like TfT but starts with defection. Struggles against itself.
  • Tit-for-Two-Tats — Only retaliates after two consecutive defections. Very forgiving.
  • Always Defect — Exploits cooperators but scores poorly against itself.
  • Random — 50/50 coin flip each round. The baseline.

Key Takeaways

  • Repetition enables cooperation — the threat of future punishment sustains it
  • Tit-for-Tat wins — nice, retaliatory, forgiving, and clear
  • Environment matters — the best strategy depends on the population it faces