ng 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 slight variant may fare better than plain Tit for Tat, the so-called Generous Tit for Tat in which an opponent’s defection is forgiven 10% of the time. Then there was a suggestion in 1993 that “win-stay, lose-shift” fares slightly better than generous Tit for Tat most of the time. (I am grateful to James Junghanns for drawing my attention to this, in the comments below.)
Still, it is reassuring to find that merely playing the game repeatedly with the same people is enough to favour strategies that resemble decent human behaviour, rather than the stark sociopathic logic that seems to reign when playing only once, and this is a comfortable place to rest.
But we can rest no longer! In a paper published earlier this year, Bill Press and Freeman Dyson outline a series of startling mathematical results that change forever our understanding of the game. And, if the game is a model of human affairs, does that change our understanding of the world more generally too?
Press and Dyson uncovered a class of strategies for the iterated Prisoner’s Dilemma – that is, the game where the Prisoner’s Dilemma is played repeatedly with the same other player – that have strange, almost unbelievable properties. One will force the other player’s score, on average, to be a certain number; and nothing she can do will change that score, however she chooses to play. Another type, which Press and Dyson dub “extortionate”, is able to take advantage of the other player’s self-interest. Against an extortionate opponent, the more you allow yourself to be taken advantage of the better you will score. So a purely self-interested player, who will modify his play only to increase his own score, can be taken for a ride by an “extortionist” who is able to use the other player’s self-interest against him.
All this is heady stuff, and it is hard to say precisely what the broader implications are. I have made a little interactive toy where you can pit yourself against both these types of strategy, if you would like to see how they work in practice. Click the t