The Prisoners’ Dilemma
The Prisoner’s Dilemma is a game, but a game that seems to bear lessons for the conduct of human affairs more generally, and it has attracted a great deal of attention from men not noted for their frivolity. It was discovered in 1950 at the RAND corporation, a military think-tank established after World War II by the United States Air Force to conduct a “program of study and research on the broad subject of intercontinental warfare”.
So it is a serious game, but a simple one for all that. It requires two players, let’s say you and me. There is only one move. Each of us must make a choice, to “cooperate” or “defect”, without knowing what the other has chosen. Perhaps each of us takes, from a chess board, one black and one white pawn, and as we face each other I put my hands behind my back and proffer a closed fist containing the pawn I have chosen. You make your choice, too, in the same way. Together we open our hands, and reveal what we have chosen. The black pawn represents the black heart of the defector, the white the innocence of the cooperator.
Now, the reckoning. Should we each reveal a white pawn, we have cooperated and each of us wins £20: a fair and happy outcome. If we both are blackhearts with black pawns in our hands, we win nothing. But wickedness is not without its rewards in this game, for if I hold black and you white then I win £40 – and you, looking sadly at the white pawn in your hand, must pay £10 for your naivety.
A troubling game
The troubling aspect of this game, the reason it is infamous, is that it seems clear that each player’s best strategy is always to defect. Whichever pawn is in my hand, you will do better by defecting: if I have cooperated, then defecting will make you £20 richer than you would be by cooperating, and if I have defected then your defecting will spare you a loss of £10. Yet we collectively are punished for our cold rationality, for if we both defect then we are both worse off than if we had both cooperated.
Douglas Hofstadter seems to have been especially troubled by this: “I found that I simply could not accept the seemingly flawless logical conclusion that says that a rational player … will always defect”, he wrote, and his Scientific American column of June 1983 explores this discomfort. Hofstadter sent a letter to 20 friends, inviting them to make a choice – to cooperate or defect – which would be used in a game of Prisoner’s Dilemma against each of the 19 others. So each person was to play 19 games, but had to choose one move that would be their move in each. These games were played for real (fairly small) sums of money.
The letter included a nod to the outcome Hofstadter had hoped for: “You’re very bright.”, he wrote. “So are all of you! About equally bright, I’d say, in fact.” In the event, most of the participants defected – 14 out of 20 – which, though it is the outcome most of us would expect, is not what Hofstadter had been hoping for. It is not easy to explain what he had been expecting, and I am not quite certain that it makes sense, but let me try: Hofstadter hoped that his friends would form what he called a ‘superrational’ cluster:
❝Superrational thinkers, by recursive definition, include in their calculations the fact that they are in a group of superrational thinkers.❞
In other words he hoped the players would realise that any answer arrived at by pure reason must be reached, too, in the same way, by all the other members of the group; and thence the players would realise that, since everyone must arrive at the same answer, there are only two possible outcomes: either all must cooperate, or all must defect; and that finally since of those two it is clearly preferable for everyone if everyone cooperates, the only rational move is to cooperate. Hofstadter later speculates that perhaps there are alien “civilisations to which cooperation appears axiomatic” that are destined to survive, whereas civilisations such as ours – “to which defection appears axiomatic” – shall not. (The Cold War threat of nuclear annihilation hangs gloomily over ma