Number of words: 691

Now Karl and I could sit back and watch the strategies slug it out in our creation over thousands and thousands of generations. Our fervent hope was that one strategy would emerge victorious. Even though no evolutionary trajectory ever quite repeated itself, there were overall patterns and consistency in what we observed. The tournament always began with a state of “primordial chaos.” By this I mean that there were just random strategies. Out of this mess, one, Always Defect, would inevitably take an early lead: as is so often seen in many Hollywood movies, the baddies get off to a flying start.

For one hundred generations or so, the Always Defect strategy dominated our tournament. The plot of life seemed to have a depressing preface in which nature appeared cold-eyed and uncooperative. But there was one glimmer of hope. In the face of this unrelenting enemy, a beleaguered minority of Tit for Tat players clung on at the edge of extinction. Like any Hollywood hero, their time in the sun would eventually come: when the exploiters were left with no one left to exploit, and all the suckers had been wiped out, the game would suddenly reverse direction. Karl and I took great pleasure in watching the Always Defectors weaken and then die out, clearing a way for the triumphant rise of cooperation.

When thrown into a holdout of die-hard defectors, a solitary Tit for Tat will do less well than defecting rotters, because it has to learn the hard way, always losing the first round, before switching into retaliatory mode. But when playing other Tit for Taters, it will do significantly better than Always Defect and other inveterate hard-liners. In a mixture of players who adopt Always Defect and Tit for Tat, even if the latter only makes up a small percentage of the population, the “nice” policy will start multiplying and quickly take over the game. Often the defectors do so poorly that they eventually die out, leaving behind a cooperative population consisting entirely of Tit for Tat.  But Karl and I were in for a surprise. In our computer tournaments, Tit for Taters did not ultimately inherit the Earth. They eventually lost out to their nicer cousins, who exploited Tit for Tat’s fatal flaw of not being forgiving enough to stomach the occasional mishap. After a few generations, evolution will settle on yet another strategy, which we called Generous Tit for Tat, where natural selection has tuned the optimum level of forgiveness: always meet cooperation with cooperation, and when facing defection, cooperate for one in every three encounters (the precise details actually depend on the value of the payoffs being used). So as not to let your opponent know exactly when you were going to be nice, which would be a mistake (John Maynard Smith’s Tit for Two Tats strategy could be easily exploited by alternating cooperation and defection), the recipe for forgiveness was probabilistic, so that the prospect of letting bygones be bygones after a bad move was a matter of chance, not a certainty.

Generous Tit for Tat works in this way: never forget a good turn, but occasionally forgive a bad one. Generous Tit for Tat can easily wipe out Tit for Tat and defend itself against being exploited by defectors. The Generous strategy dominates for a very long time. But, due to the randomness in our tournaments, it does not rule forever. We observed how slowly, almost imperceptibly, a population of Generous Tit for Tat mutates and drifts toward more and more lenient strategies. Ultimately, the population becomes uniformly nice: all cooperate. The reason is that when everybody tries to be nice, forgiveness pays handsomely. There is always an incentive to forgive quicker and quicker because the highest rewards come from having many productive (that is, cooperative) interactions. Now, at last, defectors have a chance to rise up again, with the help of the right mutation. A population of nice players who always cooperate is dry tinder for an invasion by any lingering or newly emerged defector. In this way, the cycle starts anew.

Excerpted from page 35-36of ‘Super co-operators ’ by Martin Nowak