The Prisoner’s Dilemma

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.

William Press, Professor at the University of Texas at Austin, is the author of Numerical Recipes, the cookbook for people who do serious scientific computing. He is the Julia Child of numerical cuisine. He recently invented a new class of Prisoner’s Dilemma strategies and tried them out numerically to see how they performed. He found that they behaved weirdly. They had a bad effect on his computer program, causing it to crash. He sent me an email asking whether I could understand what was going on. He is a modern calculator who works with numerical programs, while I am an ancient calculator who works with equations. So I wrote down the equations and did the math the old-fashioned way. I found a simple equation that told us when the behavior would be weird. I started a new career as a self-proclaimed expert in the theory of games. Press and I published a paper, “Iterated Prisoner’s Dilemma Contains Strategies that Dominate Any Evolutionary Opponent,” in the Proceedings of the National Academy of Sciences, May 22, 2012. This created quite a stir in the world of theoretical biology. As usual when you discover something new, the response comes in three waves. First, this is nonsense. Second, this is trivial. Third, this is important, and we did it before you did.

The most interesting of Press’s new strategies are the ones that he calls extortion strategies. As usual in the mathematical discussion of games, he uses a numerical payoff scheme to represent the value to Alice and Bob of talking to the police or remaining silent. If Alice uses an extortion strategy, she can arrange things so that, no matter what Bob does and no matter how much payoff he gets, she will get three times as much. The only way for Bob to get even is to accept zero payoff, in which case Alice also gets zero. If Bob acts so as to maximize his own payoff, Alice’s payoff is automatically maximized three times more generously. In a commentary published on the Edge website, William Poundstone, author of a book on the Prisoner’s Dilemma, summarized our work as follows: “Robert Axelrod’s 1980 tournaments of iterated prisoner’s dilemma strategies have been condensed into the slogan, Don’t be too clever, don’t be unfair. Press and Dyson have shown that cleverness and unfairness triumph after all.”

I am interested in a bigger question, the relative importance of individual selection and group selection in the evolution of cooperation. Individual selection is caused by the death of individuals who make bad choices. Group selection is caused by the extinction of tribes or species that make bad choices. The fashionable dogma among biologists says that individual selection is the driving force of evolution and group selection is negligible. Richard Dawkins is especially vehement in his denial of group selection. The Prisoner’s Dilemma is a model of evolution by individual selection only. That is why believers in the fashionable dogma take the model seriously.

I do not believe the fashionable dogma. Here is my argument to show that group selection is important. Imagine Alice and Bob to be two dodoes on the island of Mauritius before the arrival of human predators. Alice has superior individual fitness and has produced many grandchildren. Bob is individually unfit and unfertile. Then the predators arrive with their guns and massacre the progeny indiscriminately. The fitness of Alice and Bob is reduced to zero because their species made a bad choice long ago, putting on weight and forgetting how to fly. I do not take the Prisoner’s Dilemma seriously as a model of evolution of cooperation, because I consider it likely that groups lacking cooperation are like dodoes, losing the battle for survival collectively rather than individually.

Another reason why I believe in group selection is that I have vivid memories of childhood in England. For a child in England, there are two special days in the year, Christmas and Guy Fawkes. Christmas is the festival of love and forgiveness. Guy Fawkes is the festival of hate and punishment. Guy Fawkes was the notorious traitor who tried to blow up the King and Parliament with gunpowder in 1605. He was gruesomely tortured before he was burnt. Children celebrate his demise with big bonfires and fireworks. They look forward to Guy Fawkes more than to Christmas. Christmas is boring but Guy Fawkes is fun. Humans are born with genes that reward us with intense pleasure when we punish traitors. Punishing traitors is the group’s way of enforcing cooperation. We evolved cooperation by evolving a congenital delight in punishing sinners. The Prisoner’s Dilemma did not have much to do with it. 

Freeman Dyson, Professor Emeritus in the School of Natural Sciences, first came to the Institute as a Member in 1948 and was appointed a Professor in 1953. His work on quantum electrodynamics marked an epoch in physics. The techniques he used form the foundation for most modern theoretical work in elementary particle physics and the quantum many-body problem. He has made highly original and important contributions to an astonishing range of topics, from number theory to adaptive optics.