In May 1950, a 22-year old mathematics student at Princeton University submitted a PhD thesis titled “Non-cooperative Games.” It was only 26 pages long, making it one of the shortest doctoral theses of renown ever written. The student was John Forbes Nash Jr. and the central result of his thesis established that every finite game has at least one “resting point” or equilibrium when mixed strategies are allowed. More specifically, what Nash proved was the following: a group of players will reach a Nash equilibrium when no individual can improve their outcome by changing their strategy, assuming everyone else keeps their choices unchanged.

Consider two competing businesses deciding their prices. Each firm’s best decision depends on what its competitor does. An equilibrium occurs when neither has an incentive to change its decision unilaterally. This simple idea of the existence of an equilibrium in adversarial games changed the course of social science, beginning with economics then spreading to political science. Indeed, the concept of a Nash equilibrium also has unexpected applications in important areas of computer science!

 John Forbes Nash Jr. was born in 1928 in Bluefield Virginia. As a boy Nash was already showing brilliance in understanding abstract math concepts that stumped his peers and impressed his teachers. Nash would go on to make pathbreaking contributions in many areas of math, including geometric analysis and nonlinear partial differential equations for which he was awarded the highly prestigious Abel Prize in 2015. By then, he was already something of a celebrity beyond the narrow confines of mathematics. Eleven years before his Abel Prize, Nash was awarded the Nobel Prize in Economic Sciences for his contribution to game theory, and in 2001, he was the subject of the Oscar-winning biopic, A Beautiful Mind played by Russell Crowe.

As mentioned, the Nash equilibrium would have a ripple effect in diverse fields beyond economics. The concept revolutionized conflict modeling in political science. In biology, it provided a framework for thinking about the evolutionary dynamics of species. In computer science, it laid the foundation for the structural design of the internet (e.g., efficient data routing) and multi-agent artificial intelligence where an important goal is to ensure stable decision-making when many independent agents such as neural networks act. Unfortunately, Nash’s personal life was marked by tragedies. He suffered from paranoid schizophrenia for many years before being well enough to resume academic duties in the early 1990s. And shortly after receiving the Abel Prize, he and his wife Alicia died in a car accident in May 2015. He was 86.

Here is an immensely watchable YouTube video on the life of John Nash.