The repeated prisoner's dilemma and tit for tat, explained

The repeated prisoner's dilemma is the prisoner's dilemma played over and over by the same two players. In each round, each player chooses to cooperate or defect. In Robert Axelrod's own summary, mutual cooperation pays $3 each and mutual defection $1 each, while a defector facing a cooperator gets $5 and the cooperator nothing. Defection pays more whatever the other player does, yet two defectors do worse than two cooperators. Axelrod invited experts to submit computer programs to play the game against each other, and the simplest entry, tit for tat, won. The same game is now used to test how language-model agents trust, punish, and forgive.

Axelrod's two tournaments

A 2015 PLOS ONE reanalysis by Amnon Rapoport, Darryl Seale and Andrew Colman sets out the design. In 1979 Axelrod invited 14 scientists, all with records of studying the game, to submit programs to a round-robin tournament. Each program played exactly 200 rounds against each other program, against a copy of itself, and against RANDOM, which cooperates or defects with equal probability. The payoffs were 5, 3, 1, and 0 points. If both programs in a pairing always cooperate, each earns 600 points; if both always defect, each earns 200.

Tit for tat cooperates on the first move and then copies the other player's previous move. The simplest of the 14 programs, it averaged 504 points per pairing and finished first. For a second tournament, entrants were told the first results, and the number of rounds was set at random to blunt end-game effects. Of 63 programs, including RANDOM, tit for tat again won.

Why tit for tat did well

Axelrod names four properties that tended to make a strategy succeed: avoiding unnecessary conflict by cooperating as long as the other player does, provocability after an uncalled-for defection, forgiveness after responding, and clarity, so the other player can recognize and adapt to the pattern. A "nice" strategy, in Axelrod's usage, is never the first to defect.

The length of play matters. Axelrod argues that if the game is played a known, finite number of times, neither player has a reason to cooperate on the last move, and the same logic unravels play back to mutual defection on the first. Cooperation needs an indefinite number of encounters and a large enough chance of meeting again, which Axelrod calls the shadow of the future.

Experiments with people support a narrower version. Pedro Dal Bó and Guillaume Fréchette, in the February 2011 American Economic Review, studied infinitely repeated games as subjects gained experience. They found that cooperation may prevail, but under conditions stricter than the subgame perfect equilibrium conditions usually considered, or even a condition based on risk dominance.

How far the result holds

Rapoport, Seale and Colman argue that the success of tit for tat depends on the format, the scoring rule, and the payoffs. Tit for tat can never beat a partner in a single pairing. Ranked by wins rather than total points, it came last in the first tournament, and the rank correlation between the two orderings was -0.103.

The authors also re-ran the first tournament's scores in all 756,756 ways of splitting the 15 programs into three groups for a two-stage contest. Tit for tat won 11.0 percent of these, behind two other programs at 30.0 and 24.8 percent. The ranking of the eight nice programs was largely set by two programs that were not nice, which Axelrod called kingmakers. Payoffs matter too: in seven payoff variants studied by Anatol Rapoport and Al Chammah, cooperation ranged from 26.8 to 77.4 percent.

Language models in repeated games

Akata and colleagues, in Nature Human Behaviour in May 2025, had language models play 144 two-by-two games for ten rounds each. The models did well in self-interested games such as the prisoner's dilemma family and poorly in games that required coordination. In the prisoner's dilemma, five models, including GPT-4 and Claude 2, played one another. GPT-4 never cooperated again with a partner that defected once and then always cooperated. With a known number of rounds, the authors note, defection can be the equilibrium. Telling GPT-4 that other players sometimes make mistakes led it to cooperate again. With 195 human players, prompting the model to predict the other player's move first raised mutual cooperation slightly. The stated limits are simple two-by-two games of known length.

Fontana, Pierri and Aiello ran 100-round games against random opponents of varying hostility. GPT3.5 and one other model were more cooperative than humans and forgiving when opponents defected less than 30 percent of the time, while a third model stayed uncooperative unless the opponent always cooperated.

Payne and Alloui-Cros ran seven evolutionary tournaments of classic strategies against models from OpenAI, Google, and Anthropic, producing almost 32,000 decisions with rationales. Each round ended the match with a set probability of 10, 25, or 75 percent. At 75 percent, the gemini-2.5-flash agent's cooperation rate fell to 2.2 percent and it spread, while the gpt-4o-mini agent cooperated 95.7 percent of the time and was eliminated. The authors read the rationales as reasoning about the time horizon and the opponent.

What to check

• Did the agents know the number of rounds, given that a known end can make defection the equilibrium?
• Is success scored by total points or by wins? Tit for tat ranked first on one and last on the other.
• Was the result rerun with a different field of opponents, a different format, and different payoffs?
• Does the agent forgive a single defection, which GPT-4 did not in ten-round games?
• Was the chance of the game ending varied, and did cooperation fall as it rose?

Azcuna's CALIBER puts AI agents in practice markets with play money and a news feed whose truth is known, and measures from their trades whether they are gullible, follow the crowd, overpay, or can be steered. It was proposed to DARPA under SBIR Phase I topic DPA26BZ06-DV026, and the proposal was submitted on October 21, 2026.

Sources

1. 1The Evolution of Cooperation · Robert Axelrod, adapted from the 1984 book, in Breakthrough: Emerging New Thinking (Walker, 1988), online edition hosted at Stanford University
2. 2Is Tit-for-Tat the Answer? On the Conclusions Drawn from Axelrod's Tournaments · Rapoport, Seale and Colman, PLOS ONE 10(7), e0134128, July 30, 2015 (PubMed Central)
3. 3The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence · Dal Bó and Fréchette, American Economic Review 101(1), February 2011
4. 4Playing repeated games with large language models · Akata, Schulz, Coda-Forno, Oh, Bethge and Schulz, Nature Human Behaviour, published May 8, 2025
5. 5Nicer Than Humans: How do Large Language Models Behave in the Prisoner's Dilemma? · arXiv (Fontana, Pierri and Aiello), version 2, September 2024
6. 6Strategic Intelligence in Large Language Models: Evidence from evolutionary Game Theory · arXiv (Payne and Alloui-Cros), version 1, July 2025

Where this shows up in our work

• CALIBER, the market testbed for AI agents measures from an AI agent's trades whether it is gullible, herds, overpays, or can be steered.
• LEDGER, auditable Army acquisition decisions turns a trade study into a package where every number cites its source and AI drafts but never decides.