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 many of his writings of this period.)
We meet again
The Prisoner’s Dilemma challenges our moral sensibility too. For example, watch this clip from the British game show Golden Balls, in which two people play a Prisoner’s Dilemma-like game for high stakes:
It is hard not to feel that the winning player has done something morally questionable here, even though both are abiding by the rules of the game.
This is perhaps related to the fact that cooperation very often is the rational strategy in real-life situations. Whenever I go to the corner shop for a pint of milk, I have to choose whether to cooperate by paying for the milk, or defect by running away without paying. I could probably get away with stealing it: I think I could outrun the shopkeeper, who would in any case be reluctant to leave his shop unmanned for too long, and the police would be unlikely to devote much effort to the investigation of such a petty crime. But the inconvenience of this would outweigh the benefits. I would never be able to go back to the shop, so I would have to go further afield next time I need milk, and even passing by would risk the shopkeeper recognising me and calling the police, so I would have to walk my daughter to school by an inconveniently roundabout route. These practical considerations mean that, quite apart from any moral qualms I may have, stealing the milk would not be a net win for me. By contrast if I were passing through a distant Scottish village to which I was sure I would never return, then perhaps stealing a pint of milk from the village shop would be the rational course of action, since the inconvenience of being unable to go back to the same shop would be no inconvenience at all.
In short, cooperation may be the rational strategy if you encounter the same people time after time. The political scientist Robert Axelrod put this to the test in a famous experiment conducted in 1979. Axelrod set up a Prisoner’s Dilemma tournament, by computer, and invited a number of game theorists to submit computer programs encodi