In a single round of the prisoners dilemma, betraying the other player is better no matter what they do. That is not an opinion, it is arithmetic. Yet when Robert Axelrod ran a tournament in 1980 where the same players met again and again, the winner was the simplest program submitted: four lines that cooperate first and then copy whatever you did last. Everything below is that tournament, run live, with the payoffs Axelrod used.
Click any square. Whatever the other player has chosen, look down your own column: defecting always pays you more. 5 beats 3, and 1 beats 0. That is what makes this a dilemma rather than a puzzle — the reasoning is airtight, both players follow it, and both end up on 1 when they could have had 3. Notice the second condition too: 2 x 3 is more than 5 + 0, so taking turns exploiting each other is worse than simply cooperating.
| they cooperate | they defect | |
|---|---|---|
| you cooperate | 3 / 3reward | 0 / 5sucker |
| you defect | 5 / 0temptation | 1 / 1punishment |
Every column is one round; the top band is the first player, the bottom the second. Green is cooperate, red is defect. Run tit for tat against always-defect and watch it lose the first round and then never lose another — it ends one point behind, forever. Run it against itself and nothing ever goes wrong. Then turn the noise up in the panel above and run tit for tat against itself again: a single mistaken move starts an echo that neither player can stop.
Everyone plays everyone, including a copy of itself, and the scores are added up. Tit for tat never defects first and never beats anybody head to head — the best it can ever manage against one opponent is a draw. It wins anyway, because a tournament is not a duel. The column on the right is the giveaway: with the default roster, the five strategies that never defect first take the top five places and the five that do take the bottom five.
| # | strategy | points per round | defects first? |
|---|
Who does what to whom. Each cell is the row strategy scoring against the column strategy — bright is a good outcome for the row, dark is a bad one. The block of green at the top left is what actually decides the tournament: nice strategies get 3 a round off each other, and there are more of them than there are victims to exploit.
Real players mistype, misremember and are misunderstood. Sweep the noise from 0 to 25% and the ranking rearranges itself. Grudger falls off a cliff — one accidental defection and it writes the opponent off for good, including a copy of itself. Tit for tat sags too, for the same reason in slower motion. The winner at high noise is Pavlov, which asks a different question: not "what did you just do to me" but "did what I just did work?" — and so it stops punishing once punishing stops paying.
Now stop scoring and start breeding. Each generation, every strategys share of the population grows in proportion to how well it did against the population as it currently stands. Always-defect does well at first, while there are still naive cooperators to eat — and that is exactly what kills it, because it eats them all and is then left with nothing but other defectors. Always-cooperate cannot survive on its own either. What is left at the end is the strategies that cooperate with each other and refuse to be exploited.
The payoffs are Axelrods: 5 for defecting on a cooperator, 3 each for mutual cooperation, 1 each for mutual defection, 0 for being defected on, with 200 rounds a meeting and self-play included. On the default ten-strategy roster tit for tat finishes first on every random seed we tried, at 2.795 points a round against 2.711 for tit for two tats, and the five nice strategies fill the top five places — which is the actual finding from 1980, not a coincidence we arranged. Everything is driven by a seeded mulberry32 generator, so the same settings give the same table twice.
Where it would mislead you: a tournament result depends entirely on who entered. Swap the roster to the classic seven and Grudger beats tit for tat, because with only seven players Random carries a seventh of everyones score and punishing it forever pays better than forgiving it. That is a real property of these tournaments and a reason to distrust any single league table. The population model is the deterministic replicator equation — infinite population, everyone meets everyone with equal probability, no mutation and no spatial structure. Real cooperation leans heavily on the things left out here: relatives, reputation, gossip, the ability to walk away from a bad partner, and neighbours you meet more often than strangers. And the players here cannot see how many rounds remain; if they could, the last round would be a one-shot dilemma, and the logic would unravel backwards from there.