Prison breakthrough

JOHN NASH arrived at Princeton University in 1948 to start his PhD with a one-sentence recommendation: “He is a mathematical genius”. He did not disappoint. Aged 19 and with just one undergraduate economics course to his name, in his first 14 months as a graduate he produced the work that would end up, in 1994, winning him a Nobel prize in economics for his contribution to game theory.

On November 16th 1949, Nash sent a note barely longer than a page to the Proceedings of the National Academy of Sciences, in which he laid out the concept that has since become known as the “Nash equilibrium”. This concept describes a stable outcome that results from people or institutions making rational choices based on what they think others will do. In a Nash equilibrium, no one is able to improve their own situation by changing strategy: each person is doing as well as they possibly can, even if that does not mean the optimal outcome for society. With a flourish of elegant mathematics, Nash showed that every “game” with a finite number of players, each with a finite number of options to choose from, would have at least one such equilibrium.