Ranking: average points per round
3 = always cooperating together, 1 = always defecting together. ⚔ = nasty (will defect first). W/L: matches scored higher / lower than the opponent. Click a strategy to read about it.
Who scores what against whom
Each square: the points per round that the strategy on the left got against the one on top (red 0, yellow 2.5, green 3, bright 5). Click a square to watch that match.
Watch a match
Evolution: good scores have more children
Each generation, every strategy's share grows or shrinks with its average score against the current population (Axelrod's "ecological tournament"). Below 1 in a million it dies out.
60 × 60 people, one strategy each. Every generation each plays its 8 neighbours, then copies whoever scored best nearby (itself included). Click to drop a group of the strategy picked below.
Play it yourself
What Axelrod found, and what this page finds
In 1980 the political scientist Robert Axelrod invited game theorists to send in computer programs for the repeated prisoner's dilemma. 14 programs (and a coin flipper) played everyone, 200 rounds each. The shortest one, Tit for Tat (four lines of Fortran), won. In a second tournament 62 entrants knew that result and tried to beat it; it won again.
| other cooperates | other defects | |
|---|---|---|
| you cooperate | 3 each | you 0, other 5 |
| you defect | you 5, other 0 | 1 each |
Whatever the other does, defecting gives you more (5 > 3, 1 > 0). So two clever players both defect and get 1 each, when they could have had 3. In a single game nothing beats defecting: try "Just one round".
Tit for Tat never scores more than the player it is facing: it can only tie or lose by one sucker's payoff. Always defect never scores less. Yet Always defect comes near the bottom and Tit for Tat near the top. The tournament is not about beating your opponent; it is about how many points you make together. Look at the W and L columns.
Nice: never be the first to defect. Retaliate: hit back at once, or you get exploited (Always cooperate). Forgive: go back to cooperating once the other does, or one slip means war forever (Grudger). Clear: be simple enough that the other can figure you out. In every setting with long enough games, the top of the ranking is full of nice strategies.
Cooperation only pays if you will meet again. If both players know which round is the last, defecting in it costs nothing, so the Last-round traitor quietly takes over (try "Everyone knows the end"). Then the round before becomes the last real one, and so on: in theory it unravels to the start. With a secret or random end there is no last round to betray, and nice strategies win, as long as another round is likely enough.
With a little noise, two Tit for Tats fall into an echo: one slip, then they take turns punishing each other. Strategies that forgive (Soft majority, Tit for Two Tats, Generous Tit for Tat) move to the top and Tit for Tat drops to the middle; Hard Tit for Tat and Two Tits for Tat fall to the bottom, Grudger into the bottom third. This is the point of the Veritasium video about the tournaments: in a noisy world, be a bit more forgiving than tit for tat.
Which strategy comes first depends on who else is playing. Among these 25, Gradual (punish harder for each new defection, then make peace) edges out Tit for Tat, as it did in Beaufils, Delahaye and Mathieu's 1996 tournaments. But the winners always share the four rules above, and nasty strategies never win once the games are long.
Go further: The Evolution of Trust by Nicky Case. A beautiful 30-minute interactive explainer of the same game theory. It shows why trust grows when the game is non-zero-sum (both can win) and repeated, why it collapses when people play only once or the game turns zero-sum, and how a little noise (misunderstandings) changes which strategy wins. A great companion to this page.
Play it at ncase.me/trust ↗