In October 1983 I walked into my first lecture and encountered “girls”—many more than I had ever seen before and conveniently all in one place. Thanks to the female-dominated intake of a pharmacology course, girls made up nearly two-thirds of the six hundred people now crammed around me in the lecture hall. Having been educated at an all-boys school, I thought I was in paradise. Among the handful of chemistry students was Ursula, who like me was struggling to keep pace with the university’s intensive introduction to mathematics. Six years later, we were married. I still wonder whether I was selected for my ability to solve mathematical problems.
As I became besotted at the University of Vienna, the emphasis of my studies gradually changed. I adored physics in the first year, then physical chemistry in the second year. In the third year, I had the great good fortune to be lectured on theoretical chemistry by the formidable Peter Schuster, who helped to establish the Viennese school of mathematical biology and, later, would become the president of the illustrious Austrian Academy of Sciences and deliver a lecture to Pope Benedict XVI on the science of evolution. I knew immediately that I wanted to work with Peter. In the fourth year, I began to study with him for a diploma thesis. An ebullient character, he was supremely knowledgeable and his interests extended well beyond science. Once, when we went mountain climbing together, he declared: “There’s no such thing as bad weather, only insufficient equipment.”
The moment when I realized that I was well and truly smitten by mathematics came a year later, while on an Alpine jaunt with Peter. It was March 1988, during my early days as a doctoral student, and I was on a retreat. With me was a fresh crop of talent, including Walter Fontana, who today is a prominent biologist at Harvard Medical School. Our group was staying in a primitive wooden hut in the Austrian mountains to enjoy lots of fresh air, work, and play. We skied, we listened to lectures, we drank beer and wine, and we contemplated the mysteries of life. Best of all, we discussed new problems and theory, whether in the cozy warmth of the little hut or outside, in the chilled Alpine air. As the ideas tumbled out at high altitude, our breath condensed into vapor. I can’t remember if they were mathematical dreams or just clouds of hot air. But the experience was exhilarating.
The mix of bright-eyed students was enriched with impressive academics. Among them was Karl Sigmund, a mathematician from the University of Vienna. With his wild shock of hair, bottle-brush mustache, and spectacles, Karl looked aloof and unapproachable. He was cool, more like a student than a professor. Karl would deliver all his lectures from memory with a hypnotic, almost incantatory rhythm. On the last day of that heady Alpine meeting, he gave a talk on a fascinating problem that he himself had only just read about in a newspaper article.
The article described work in a field known as game theory. Despite some earlier glimmerings, most historians give the credit for developing and popularizing this field to the great Hungarian-born mathematician John von Neumann, who published his first paper on the subject in 1928. Von Neumann went on to hone his ideas and apply them to economics with the help of Oskar Morgenstern, an Austrian economist who had fled Nazi persecution to work in the United States. Von Neumann would use his methods to model the cold war interaction between the United States and the Soviet Union. Others seized on this approach too, notably the RAND Corporation, for which von Neumann had been a consultant. The original “think tank,” the RAND (Research and Development) Corporation was founded as Project RAND in December 1945 by the U.S. Army Air Force and by defense contractors to think the unthinkable.
In his talk, Karl described the latest work that had been done on the Prisoner’s Dilemma, an intriguing game that was first devised in 1950 by Merrill Flood and Melvin Dresher, who worked at RAND in Santa Monica, California. Karl was excited about the Dilemma because, as its inventors had come to realize, it is a powerful mathematical cartoon of a struggle that is central to life, one between conflict and cooperation, between the individual and the collective good.
The Dilemma is so named because, in its classic form, it considers the following scenario. Imagine that you and your accomplice are both held prisoner, having been captured by the police and charged with a serious crime. The prosecutor interrogates you separately and offers each of you a deal. This offer lies at the heart of the Dilemma and goes as follows: If one of you, the defector, incriminates the other, while the partner remains silent, then the defector will be convicted of a lesser crime and his sentence cut to one year for providing enough information to jail his partner. Meanwhile, his silent confederate will be convicted of a more serious crime and burdened with a four-year sentence.
If you both remain silent, and thus cooperate with each other, there will be insufficient evidence to convict either of you of the more serious crime, and you will each receive a sentence of two years for a lesser offense. If, on the other hand, you both defect by incriminating each other, you will both be convicted of the more serious crime, but given reduced sentences of three years for at least being willing to provide information.
In the literature, you will find endless variants of the Dilemma in terms of the circumstances, the punishments and temptations, the details of imprisonment, and so on. Whatever the formulation, there is a simple central idea that can be represented by a table of options, known as a payoff matrix. This can sum up all four possible outcomes of the game, written down as two entries on each of the two lines of the matrix. This can sum up the basic tensions of everyday life too.
Let’s begin with the top line of the payoff matrix: You both cooperate (that means a sentence of two years each and I will write this as –2 to underline the years of normal life that you lose). You cooperate and your partner defects (–4 years for you, –1 for him). On the second line come the other possible variants: You defect, and your partner cooperates (–1 for you, –4 for him). You both defect (–3 years each). From a purely selfish point of view, the best outcome for you is the third, then the first, then the fourth, and finally the second option. For your confederate the second is the best option, followed by the first, fourth, and third.
What should you do, if you cast yourself as a rational, selfish individual who looks after number one? Your reasoning should go like this. Your partner will either defect or cooperate. If he defects, you should too, to avoid the worst possible outcome for you. If he cooperates, then you should defect, as you will get the smallest possible sentence, your preferred outcome. Thus, no matter what your partner does, it is best for you to defect.
Defecting is called a dominant strategy in a game with this payoff matrix. By this, the theorists mean that the strategy is always the best one to adopt, regardless of what strategy is used by the other player. This is why: If you both cooperate, you get two years in prison but you only get one year in prison if you defect. If the other person defects and you hold your tongue, then you get four years in prison, but you only get three years if you both defect. Thus no matter what the other person does, it is better for you to defect.
But there’s a problem with this chain of reasoning. Your confederate is no chump and is chewing over the Dilemma in precisely the same way as you, reaching exactly the same conclusion. As a consequence, you both defect. That means spending three years in jail. The Dilemma comes because if you both follow the best, most rational dominant strategy it leaves both of you worse off than if you had both remained silent! You both end up with the third best outcome, whereas if you had both cooperated you would have both enjoyed the second best outcome.
That, in a bitter nutshell, is the Prisoner’s Dilemma. If only you had trusted each other, by cooperating, you would both be better off than if you had both acted selfishly. With the help of the Dilemma, we can now clearly appreciate what it means to cooperate: one individual pays a cost so that another receives a benefit. In this case, if both cooperate, they forfeit the best outcome—a one-year sentence—and both