*The Evolution of Cooperation* is the title of a book by Robert Axelrod. It was published by Basic Books in 1984, and became an instant classic. It set the style in which modern scientists think about biological evolution, reducing the complicated and messy drama of the real world to a simple mathematical model that can be run on a computer. The model that Axelrod chose to describe evolution is called “The Prisoner’s Dilemma.” It is a game for two players, Alice and Bob. They are supposed to be interrogated separately by the police after they have committed a crime together. Each independently has the choice, either to remain silent or to say the other did it. The dilemma consists in the fact that each individually does better by testifying against the other, but they would collectively do better if they could both remain silent. When the game is played repeatedly by the same two players, it is called Iterated Prisoner’s Dilemma. In the iterated game, each player does better in the short run by talking, but does better in the long run by remaining silent. The switch from short-term selfishness to long-term altruism is supposed to be a model for the evolution of cooperation in social animals such as ants and humans.

Mathematics is always full of surprises. The Prisoner’s Dilemma appears to be an absurdly simple game, but Axelrod collected an amazing variety of strategies for playing it. He organized a tournament in which each of the strategies plays the iterated game against each of the others. The results of the tournament show that this game has a deep and subtle mathematical structure. There is no optimum strategy. No matter what Bob does, Alice can do better if she has a “Theory of Mind,” reconstructing Bob’s mental processes from her observation of his behavior.

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