ny 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 encoding their strategy. The twist was that each digital player would be played against each other player 200 times, to simulate a situation where we encounter the same people repeatedly. These computer programs could remember what had happened on previous encounters with their opponent, and tailor their behaviour accordingly.
The aim is to score as many points as possible over the whole tournament. This is not the same as ‘winning’: indeed the strategy that wins most often is to always defect, which will beat any opponent who does not always defect, and equalise with one who does. But this is typically a poor sort of winning in which neither player scores very many points, and the programs that did best overall in Axelrod’s tournament turned out to be those that were most effective at eliciting mutual cooperation.
The overall winner was a very simple strategy – the simplest of all the entries in that first tournament – called Tit for Tat. The tit-for-tat strategy is simply to cooperate the first time you meet someone new, and thereafter to do whatever they did the previous time. This strategy will cooperate with a co-player who is willing to cooperate, and yet cannot be much taken advantage of by one that is not.
After the tournament was over, and Axelrod had published the results in great detail, another tournament was announced for which entries were solicited from computer hobbyists as well as from professional mathematicians. There were 62 entries, again including Tit for Tat which was again submitted by its inventor, the psychologist Anatol Rapoport; and also including many subtle strategies that it could be proven would have won in the first tournament had they been there. The tournament was played, and Tit for Tat won again. This second victory showed the robustness of Tit for Tat, that it remained unbeaten even when all the competitors knew it was the one to beat.
And there matters rested, more or less, until this year. A few things were learned in the interim: it was found, for example, that sometimes a sligh