## Comment

Almost 58 years before this first lecture he gave at a Lindau Meeting on Economic Sciences, in September 1948, John Nash had arrived in Princeton as a twenty-year old student. He came from the Carnegie Institute of Technology in Pittsburgh where he „had learned and progressed so much in mathematics that they gave me an M. S. in addition to my B. S. when I graduated“.[1] The letter of recommendation from Richard Duffin, his teacher at Carnegie, contained just one sentence: „This main is a genius“.[2] Nash’s career in Princeton very soon proved Duffin’s assessment. Within roughly one year after his arrival, he had worked out a thesis on „Non-cooperative Games“ whose main results were submitted to the Proceedings of the National Academy of Sciences in November 1949. These main results were the distinction between cooperative and non-cooperative games; and the mathematical proof that for each finite non-cooperative game at least one solution can be found, an equilibrium, in which each player chooses his best response to what the other does. This „Nash equilibrium“ has become the game theoretic solution concept that is most frequently applied in economics. It were primarily these main results of his thesis for which Nash received a Nobel Memorial Prize 1994.

In this lecture, Nash focuses on an ambivalent and practically very important aspect of evolutionary and strategic interaction, namely the „paradoxical possibility of the natural evolution of cooperative behavior when the interacting organisms or species are presumed only to be endowed with self-interested motivations, thus motivations of a non-cooperative type“.[3] When he later published the considerations, which he shared with his audience in Lindau, he referred to the famous prisoner’s dilemma and described his motivation to study this paradox as follows: „The idea leading to this study originated some time ago when I talked at a gathering of high school graduates at a summer science camp. I spoke about the theme of „the evolution of cooperation“ (in Nature) and about how that topic was amenable to studies involving Game Theory (which, more frequently has been used in economics). After that event I was stimulated to think of the possibility of modeling cooperation in games through actions of acceptance in which one player could simply accept the „agency“ of another player or of an existing coalition of players. The action of acceptance would have the form of being entirely cooperative, as if „altruistic“, and not at all competitive, but there was also the idea that the game would be studied under circumstances of repetition and that every player would have the possibility of reacting in a non-cooperative fashion to any undesirable pattern of behavior of any another player. Thus the game studied would be analogous to the repeated games of ‚Prisoner’s Dilemma’ variety that have been studied in theoretical biology.“[4]

It must have been moving for the audience in Lindau to listen to Nash’s talk. They could tell from his face how deeply life had left its mark on him. Ten years after his brilliant thesis, Nash had fallen prey to schizophrenia, from which he suffered until the early 1990s. The story of his life, although not in a literal representation, was depicted in the movie “A beautiful mind”, which won four Academy Awards for 2001, and has made Nash one of the most popular scientists of his time.

Joachim Pietzsch

[1] Cf. http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1994/nash-bio.html

[2] Harold Kuhn in: The Work of John Nash in game theory. Nobel Seminar, December 8, 1994, p. 162.

[3] Nash JF. The agencies method for modeling coalitions and cooperation in games. International Game Theory Review, Vol. 10, No. 4 (2008), 539-564.

[4] Ibid., p. 539