Repeated Prisoner’s Dilemma

The Repeated Prisoner’s Dilemma turns a one-off conflict between individually rational self-interest and mutual benefit into an ongoing relationship shaped by memory. With the same players meeting again, each move can influence what the other does next: cooperation may be reciprocated, betrayal punished, and trust gradually established or withdrawn. In the account developed by Robert Axelrod and W. D. Hamilton, this repeated structure helps explain how cooperation can persist in a world where strategies are selected for their effects on individual success.

From a single encounter to an ongoing game

In the human version, a banker adjudicates the game and pays the two players. Each has two cards, marked cooperate and defect. They choose simultaneously, laying their cards face down so neither can adjust a move after seeing the other's choice; only when the banker turns the cards over does each player learn the outcome. In the single-round game, the payoff depends on both choices, and the tension is that each player can do better by defecting whatever the opponent chooses, although both would do better if they cooperated. Without a way to ensure trust, the one-off game tends toward mutual defection and a poor result for both.

The repeated version changes the conditions rather than the available cards. The same two players play another round after each payout, and the cycle continues for an indefinite number of rounds. Their earlier moves become evidence about how they are likely to act again. This allows them to reciprocate, placate, forgive, or avenge; it also gives them a way to police one another through the prospect of future responses. Rather than trying to win at one another's expense in a single encounter, both can benefit over time at the banker's expense.

The difference is visible in a ten-round example. A player could theoretically win as much as $5,000 if the opponent cooperated every time while the player defected throughout, but that outcome requires the opponent to keep cooperating despite repeated exploitation. If both cooperate across all ten rounds, each can collect $3,000 without relying on saintly self-sacrifice: each can infer trustworthiness from the other's past play. If neither trusts the other, both may defect throughout, leaving the banker with $100 in fines from each. Partial trust and mixed sequences of cooperation and defection can produce intermediate totals.

Strategy, memory, and reciprocal exchange

Iteration opens a wider strategic field than the one-shot choice between cooperation and defection. A player might cooperate most of the time but defect randomly on 10 per cent of rounds; other strategies condition their next move on the game's history. The book's example of Grudger is fundamentally cooperative but remembers a defection and thereafter defects against the player responsible. More forgiving strategies can have shorter memories. Which strategy is best is not self-evident, because the record of earlier moves gives strategies scope to respond to one another.

The same structure can apply outside conscious human decision-making. Birds that remove ticks from one another's feathers illustrate the game: a bird cannot reach the top of its own head, so a companion can provide a useful service, but removing another bird's ticks costs time and energy. A bird that accepts grooming and then refuses to reciprocate gains the benefit without paying that cost. Mutual grooming is advantageous compared with mutual refusal, yet unilateral defection is tempting; and helping a partner without receiving help in return can be worse than neither helping nor being helped. The exchange therefore has the relevant payoff structure of a Prisoner's Dilemma, played across repeated interactions.

The game is presented as a pattern that can recur in animal and plant life, not as a claim that the organisms consciously calculate. Strategies may be understood in the Maynard Smithian sense: rules of action that genes could preprogramme. The biological example thus carries the argument beyond human intention. Cooperation need not mean that participants are acting from conscious generosity; it can arise from strategies whose success depends on what others did before and what they may do again.

Rules and circumstances reshape the payoff

The book also distinguishes the repeated game from other interactions whose rules make cooperation possible or impossible. In a divorce, a couple may have reasons to cooperate even after a marriage breaks down, including concern for children's welfare and the cost of paying two lawyers. Yet, in England and until recently in all fifty states of the United States, legal rules or lawyers' professional codes prevented one lawyer from advising both members of a couple. Each lawyer had to accept only one as a client, turning a possible shared interest into an adversarial arrangement. The case could be listed as “Smith versus Smith” even if the couple themselves did not want a fight; the lawyers, rather than the spouses, might be the only beneficiaries of treating it as a win-or-lose contest. The example shows that cooperation is not determined by preferences alone: institutional rules can channel participants into opposing sides.

The 1977 English Football League season supplies a contrasting case in which outside information changed what the players stood to gain. On May 18, Sunderland, Bristol, and Coventry were competing over the last First Division relegation place. Bristol and Coventry were playing one another, and if Sunderland lost, a draw between them would keep both in the First Division. Their match was running five minutes late, so the Sunderland result became known before it ended. With two minutes left, Sunderland's loss was announced on the stadium's electronic message board. A draw now served both teams; trying to score could weaken a defence and risk the very relegation they wanted to avoid. The players shifted from a fiercely contested 2–2 match to preserving the draw, while supporters who had been rivals joined in celebration. The game had not changed its football rules, but news from the other match transformed the teams' interests: an apparently zero-sum contest became one in which both could benefit from the same outcome.

The shadow of an uncertain ending

Repeated play does not guarantee cooperation. Its promise depends on players expecting that they may meet again, so that today's conduct can affect tomorrow's response. The book calls this expectation the “shadow of the future” and stresses that the end must not be known to the players. An indefinitely continuing game does not require infinite duration; it requires that the participants not know exactly when play will stop.

If two strictly rational players know that a game has exactly 100 rounds, backward reasoning removes the basis for cooperation. The hundredth round is effectively a one-off game, so each has reason to defect. Once that final round is predictable, the ninety-ninth becomes the last meaningful opportunity and the same reasoning applies; it can then be carried backward through the rounds. The result is defection throughout, even though cooperation could have benefited both players. For this reason, theorists treat the repeated game as one whose end is unpredictable to the players or known only to the banker.

Real interactions may still offer clues about how much time remains. A player who notices the banker fidgeting and looking at his watch may suspect that the game is about to end and feel tempted to defect. If that player also suspects the opponent has noticed the same signal, fear of the opponent's impending defection may make betrayal seem urgent. The future supports cooperation only while it remains a credible prospect; as the anticipated endpoint approaches, the incentives that made reciprocity worthwhile can unravel.