Robert Axelrod

Robert Axelrod is presented as a political scientist whose computer tournaments made the repeated Prisoner’s Dilemma a practical way to study cooperation. His central contribution was not simply to identify a winning program: he showed how a strategy’s success depends on its opponents, and helped connect tournament results to evolutionary stability, where success is measured by persistence and reproduction rather than points alone.

The Prisoner’s Dilemma and reciprocal cooperation

Axelrod extended the idea of reciprocal altruism into a formal contest among rules for action. The Prisoner’s Dilemma gives each of two players a choice between cooperating and defecting, with the result for each depending on both choices. In its human version, a banker reveals the players’ cards and pays out according to the pairing. Though a single encounter makes defection the rational choice, repeated encounters create room for strategies that respond to earlier behavior.

The book treats the game as relevant well beyond human calculation. Animals, plants, and genes can participate in evolutionary versions of it without consciously planning: strategies are rules built into behavior, and their success is reflected in how many descendants they leave. Axelrod’s work with W. D. Hamilton helped extend reciprocal altruism in this direction, linking repeated interaction to biological questions rather than restricting it to human bargaining.

The computer tournaments

For Axelrod’s first tournament, fourteen experts submitted strategies as computer programs. Axelrod translated them into a common programming language and added a fifteenth entry, Random, which chose cooperation or defection at random as a baseline. Each program played each of the fifteen strategies, including a copy of itself, producing 225 pairings. Every pairing lasted 200 moves; the scores were then added across opponents to determine the overall ranking.

The winning entry was Tit for Tat, submitted by Anatol Rapoport. Its rule was spare: cooperate on the first move, then copy the other player’s previous move. Against another copy of itself, the two programs began by cooperating and continued to do so, each attaining the full 600-point benchmark. The strategy’s success was notable because it did not seek to outwit opponents with elaborate rules; its opening cooperation and responsive retaliation let it sustain mutually beneficial play with cooperative partners.

The second tournament tested whether contestants would adapt after seeing the first results. Axelrod received 62 entries and again added Random, making 63 strategies. Unlike the first contest, the number of moves in each game was left open. Competitors divided between those who submitted nice, forgiving strategies and those who expected others to do so and hoped to exploit them. Tit for Tat again won, scoring 96 percent of the benchmark. All but one of the top fifteen strategies were nice, while all but one of the bottom fifteen were nasty.

That result did not establish that the most forgiving strategy always wins. Tit for Two Tats, which tolerates two defections in a row before retaliating, would have won the first tournament had it been entered; in the second, it ranked well down the list because subtler exploitative strategies could prey on its exceptional softness. Axelrod’s tournaments therefore showed both the advantage of cooperation under many conditions and the dependence of a strategy’s rank on the particular field of competitors.

From tournament ranking to evolutionary stability

Axelrod’s round-robin method matched every strategy against every other submitted strategy equally. It rewarded robustness: doing well against a wide range of opponents in the arbitrarily assembled field. But a different collection of entries could produce a different winner. The book points out that six of the first tournament’s fourteen submitted strategies were nasty; if nearly all had been nasty, Tit for Tat might not have won. Tournament scores thus depended partly on the choices of human submitters, not on a universal ordering of strategies.

The evolutionary question is different. A strategy that has become common must do well in a population dominated by copies of itself, because biological winnings are offspring, not points. The author suggested that Axelrod contact W. D. Hamilton, who was in another department at the University of Michigan. Axelrod did so, and their collaboration produced a joint paper published in Science in 1981, which received the Newcomb Cleveland Prize of the American Association for the Advancement of Science. The paper discussed biological examples of repeated dilemmas and gave explicit recognition to the evolutionary stable strategy approach.

Axelrod also tested the strategies through an evolutionary succession, using the same 63 entries from the second tournament rather than soliciting a new set. Initially each strategy was equally represented. At the end of each generation, points became offspring identical to the parent strategy; as strategies grew more or less common, the competitive climate changed with them. After about 1,000 generations, the proportions stopped changing. Most strategies had gone extinct by generation 200. Some nasty entries initially rose, but their success was temporary; Harrington, the only nasty strategy to survive beyond generation 200, increased steeply for roughly 150 generations before declining gradually toward extinction around generation 1,000.

Tit for Tat is not, strictly speaking, a true evolutionarily stable strategy. Axelrod coined “collectively stable strategy” for it: a strategy, or combination of strategies, capable of maintaining a stable population. More than one such state can exist. Always Defect is stable too, because in a population already dominated by it, no alternative does better. The population can therefore be bistable, with either persistent defection or Tit for Tat and similar mostly cooperative, retaliatory strategies becoming dominant. Which state prevails depends on the population’s starting point and on whether it crosses a critical frequency at which selection begins to favor the other strategy.

Cooperation, rules, and consequences

The implications in the book reach beyond the computer. A divorce can look like a zero-sum contest even when the couple could benefit from cooperation. In England and, until recently, throughout the United States, a lawyer’s professional code did not permit one lawyer to represent both members of a couple. Each had to seek separate counsel, and the case was framed as adversarial even when the couple wished to remain amicable. The clients could lose jointly through mounting fees while the lawyers’ separate roles enabled a mutually profitable process. The example shows how rules and institutional arrangements can shape incentives, turning a potentially cooperative situation into a contest whose payoffs fall unevenly on participants.

A football match can change character when circumstances change. On May 18, 1977, Bristol and Coventry were both at risk of relegation, but the result of Sunderland’s game determined whether a draw between them would be enough for both to remain in the First Division. The Bristol–Coventry match was running five minutes late, so Sunderland’s loss became known before it ended. With two minutes remaining, the Coventry manager had the news displayed on the stadium’s electronic message board. Once the players understood that a draw would save both teams, they stopped pressing for goals and played to preserve the shared result. A contest that had been zero-sum became nonzero-sum because outside information changed what each side needed.

For cooperation to be sustained, the interaction must be repeated and its ending unpredictable. If both players know that a game lasts exactly 100 rounds, the last round becomes a one-off dilemma in which each has reason to defect. The same reasoning then works backward through the earlier rounds, making defection appear rational throughout. Axelrod’s framework therefore depends on the “shadow of the future”: each player must face the prospect of further dealings without knowing exactly when they will end. When people believe the final encounter is near, the temptation to defect can grow; the prospect of continued interaction supports cooperation.

The author also characterizes Tit for Tat as “nice,” “forgiving,” and “not envious.” It never defects first, has a short memory for past misdeeds, and does not seek to earn more than its partner at the cost of a mutually higher return. It cannot score more than an opponent in any individual game, because it defects only in retaliation, but it can draw while both players earn a high shared score. In a nonzero-sum game, this refusal to treat the other player’s gain as one’s own loss is a source of success. Axelrod’s work thus gives cooperation a precise, conditional form: it can thrive without denying the selfish-gene framework, when interaction repeats, mutual benefit is possible, and strategies respond to one another’s behavior.