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5.2 Turning Points essay turning points Prisoners of the dilemma When mathematics and biology met on a mountain. Martin A. Nowak nce a year, the theoretical chemist Peter Schuster used to take his stu- Odents from the University of Vienna to a small house in the Austrian mountains. During the day we skied, of course, but in the evening the emphasis was on science. I was a first-year PhD student looking for a project. The mathematician Karl Sigmund was there and gave a talk on what was a new topic for him: the prisoner’s dilemma. At the end of the talk I asked a question, and the next day we travelled back to Vienna, endlessly debat- ing this game. In subsequent days, I visited Karl’s office and we started to do calculations. We had become prisoners of the dilemma. I was amazed that mathematics could be used to explore the evolution of social inter- actions. In the prisoner’s dilemma, two play- An Austrian holiday led to iterated cooperation between Karl Sigmund (left) and Martin Nowak. ers have a choice between cooperation and defection. If both cooperate, they get more pleased my parents. But in the last vacation Within a year,we had conceived an evolu- than if both defect. But if one cooperates before university, I realized that my passion tionary description of probabilistic strate- while the other defects, the cooperator gets was to understand the natural laws of living gies in the prisoner’s dilemma struggling the lowest score and the defector the highest. systems, and I switched from medicine to bio- for cooperation by natural selection (see This is the dilemma. In a single game, defec- chemistry. My parents consulted a dictionary Nature 355, 250–253, 1992; Nature 364, tion is an unbeatable strategy. The game and discovered that biochemists work with 56–58, 1993). The prevailing paradigm, becomes complicated and fascinating, yeast, which was also used for fermentation. tit-for-tat, an unforgiving retaliator, was however if repeated.In his talk on the moun- They were worried about my future.At univer- replaced by generous tit-for-tat (which tain, Karl reported that a simple strategy, sity, I found labs disappointing — experi- always cooperates when the other person tit-for-tat (TFT), was victorious in two ments failed for no good reason. But theory has cooperated and sometimes even when ‘world championships’conducted by Robert was beautiful.You could do theory while walk- the other person has defected) and later Axelrod. Researchers from many disciplines ing through the forest or lying in the grass. by win–stay, lose–shift (which stays with had submitted computer programs to play Theory was not grey,but a golden tree of life. its current choice if the score is above an the repeated prisoner’s dilemma in a round My collaboration with Karl continued, aspiration level and changes otherwise). robin tournament. The surprise winner of and embarrassingly I had to tell my parents A byproduct of this work was adaptive the first tournament was the simplest of all I was now working on games. The mathe- dynamics, representing a new way to look strategies, TFT, submitted by game theorist matical institute of the University of Vienna at evolution of strategies in a continuous Anatol Rapoport. For the second tourna- was in the same building as the priests’ space. I handed in my thesis and asked Karl ment, others attempted to enter strategies seminary and was filled with tranquility and what to do next. He said Robert May was that were superior to TFT, but Rapoport, solemn peace. My impression was that second to none in theoretical biology, and (following the maxim of British soccer people in those halls certainly contemplated a few days later my train left for Oxford. leagues,‘Never change a winning team’) once distant and far greater worlds. My introduction to Karl Sigmund in the more fielded TFT,and again it won. The institute had only two computers that Austrian mountains was the turning point that TFT cooperates on the first move and students could use, but these were sufficient, brought together mathematics and biology. then copies whatever the opponent did in the and I was usually alone in the computer room. But it was not the only time that my thinking previous round. Immediately, we noted that Karl gave all his lectures from memory. He or approach to science has changed course. this strategy would be weak if errors were never carried anything with him except one Far from a linear path,my scientific career feels taken into account. Hence, we wanted to folded piece of paper that contained a long more like brownian motion,which is continu- calculate a new world championship that password and detailed instructions for how ous everywhere, but differentiable nowhere. was run by evolutionary dynamics in the to switch on a computer. Mathematicians There have been many turning points that presence of mistakes. Instead of a single were in a different league,I concluded. have sent me off in new directions, making round robin tournament,there was a biolog- We often met in coffee houses, the me forget what I had been doing at the time. ical population of strategies evolving over genius loci of past glory. Here Kurt Goedel I am no longer embarrassed to work on many generations. Successful strategies left announced his incompleteness theorem, games. They are the generic description of more offspring for the next generation. All Ludwig Boltzmann worked on entropy, and evolutionary interactions among genes,cells strategies were stochastic;they had ‘trembling Ludwig Wittgenstein challenged the Vienna and people. Children love games. Scientific hands’when implementing their rules. circle. Or we walked in the Vienna forest, creativity is to never stop playing. ■ Before encountering Karl, my speciality visiting a meadow called ‘Himmel’ (Heaven), Martin A. Nowak is at the Program for had been in biochemistry. I had wanted to where a sign noted that here Sigmund Freud Evolutionary Dynamics, One Brattle Square, study medicine since high school — which first understood the nature of dreams. Harvard University, Cambridge MA 02138, USA. NATURE | VOL 427 | 5 FEBRUARY2004 | www.nature.com/nature 491.
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