SuperCooperators. Roger Highfield
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.
These probabilistic games are always different in detail. But there was a pattern overall. Karl and I would always see the same strategies wax and others wane. Overall, the cycles play out in a predictable way, sweeping from all defectors to Tit for Tat, to Generous Tit for Tat, then all cooperators. Finally, with a great crash, the makeup of the community lurches back to being dominated by dastardly defectors all over again.
The good news is that a reasonably nice strategy dominates the tournament. When you average out the strategies over the entire duration of a game, the most common is Generous Tit for Tat. The bad news is that, in the real world, these cycles could sweep out over years, decades, or even centuries. Plenty of anecdotal evidence suggests that these cycles turn in human history too. Kingdoms come and go. Empires spread, decline, and crumble into a dark age. Companies rise up to dominate a market and then fragment and splinter away again in the face of thrusting, innovative competitors.
Just as these tournaments never see one strategy emerge with total victory, so it seems that a mix of cooperators (law-abiding citizens) and defectors (criminals) will always persist in human societies. The same goes for beliefs. One faith rises and another declines, the very scenario that prompted Augustine to write The City of God (De civitate Dei) after Rome was sacked by the Visigoths in 410. Augustine wanted to counter claims that Rome had been weakened by adopting Christianity, but as our computer tournaments made clear, great empires are destined to decline and fall: it was more a case of delapsus resurgam—when I fall I shall rise—and vice versa.
As the latest recession has vividly underlined, and as has been noted over the past few decades, there are economic cycles too. Regulations are introduced, then people figure out clever ways to evade them over the years. Periods of hard work and grinding toil are followed by those of leniency, when people slacken, take time off, and exploit the system. In our computer simulations, had we stumbled upon a mathematical explanation for the fundamental cycles of life that endlessly whirl around phases of cooperation and defection?
GOODBYE VIENNA
After four papers and a little more than one year of collaboration, Karl told me that I had done enough research to complete my thesis on the evolution of cooperation. I immediately got on with typing up my work. A few days later, I handed him my thesis. He held it up and closely examined the slender document from the side, shook his head, and declared that it was too thin: “A PhD thesis has to be thicker.” The next day I gave him the same thesis, only this time the font was bigger and the line spacing doubled. Karl was not fooled. But he was a pragmatist. He looked at it once again and said: “That’s all right.”
Karl suggested that I apply for a position with the leading figure in our field, Bob May at the University of Oxford. At that time, Bob was famous for the way in which he had injected the rigor of math into biology to reveal the underlying order in the living world. He had studied whether stability is the cause of the diversity of ecosystems, or whether it is the other way round (it turns out that populating an ecosystem with a diverse range of living things does not automatically mean stability). He charted the relationships between insects and their parasites. Using mathematical models, Bob had revealed how connections between species could lead to fluctuations in the number of individuals. In this way Bob had introduced chaos into biology—revealing how apparently random and complex behavior is ordered by simple underlying rules (I am writing this at home while sitting at the very same desk at which Bob made this discovery—a gift from him to help furnish my first house).
Karl did not rate my chances of moving to Oxford very highly, so I had also applied to Berkeley and Göttingen. My future life, career, and everything now depended on insubstantial aerograms. As these air mail letters winged their way around the world my predicament was both romantic and sad. I was about to marry Ursula and our time in Vienna was drawing to a close. The melancholy of leaving home was tempered by the excitement of a new adventure. Neither of us knew where on the planet we would end up.
Initially, Karl’s judgment seemed spot on. Bob rejected me, saying he did not have a group. Nor did he work much with postdoctoral students. I wrote to him again, pointing out that I might bring along my own funding, an Erwin Schrödinger Fellowship. By this time, Karl was lobbying Bob too. Eventually, to my delight, he agreed. At last the next step in my career was clear—up to a point. I had absolutely no idea what to expect at Oxford.
Ursula and I got married in Vienna the month before our move. We said our goodbyes after the service and went home to our respective parents until the time came to catch a train for what would turn out to be a nine-year honeymoon, starting in 1989. The day of departure saw us laden with seven suitcases and two bikes. It was cold and windy. A battleship grey sky threatened a torrential downpour. Our families saw us off that night from the Westbahnhof in Vienna. A friend stiffly stood before me and formally shook my hand. “Don’t embarrass us,” he joked. As the train pulled out into the darkness, my new wife cried.
The next day, once the cross-Channel ferry had set us down, I caught my first glimpse of Britain. It was not William Blake’s green and pleasant land. The soil was cracked and dry. The grass and foliage were brown and the country was in the grip of a drought. Reservoirs were drained and there were hosepipe bans and fines for anyone found washing a car. In Plymouth, flower beds were being showered with treated sewage effluent. In one British zoo, dirty water from the penguin pool was being sprinkled on parched putting greens. As our train waited, a fire was put out on the tracks ahead.
My expectations took a sharp departure from reality once again, when I eventually walked into my new place of work, the Zoology Department at the University of Oxford, an unlovely concrete pile on South Parks Road. There were posters showing birds and other animals. But there was not an equation or diagram in sight. Was I in the right place? I was. And I would discover that I was lucky to be there. There was little in the way of formalities. Unlike the hierarchical Austrian academic system, which discourages lowly students from bothering busy Herr Professors, I found myself having an informal chat over a cup of coffee or afternoon tea with many influential figures, from the great Bill Hamilton, who did pioneering work on cooperation, to Sir Richard Southwood, Richard Dawkins, Paul Harvey, and John (later, Lord) Krebs. This was a wonderful, heady intellectual atmosphere. I fell in love with the place.
Bob May would sometimes play soccer with everybody—all the students and professors were as obsessed by games as I was. This was a worry, given that he was so intensely competitive. In the British tradition, winning was beside the point and taking soccer too seriously was frowned upon. But not when it came to this wiry, quick Australian. Fortunately for the rest of us, he was somewhat ineffective. Appropriately enough, the goddess of randomness did smile on him from time to time, however. During one early encounter, when the score was seven all and I was the goalkeeper, Bob kicked the ball past me in