Today’s post is a tribute to the late John Forbes Nash – mathematical genius, Nobel and ex-schizophrenic. I first came across Nash as with most famous economists in sophomore year during ECO 211 – Principles of microeconomics and yes it involved talk on the famous game ‘Prisoners Dilemma’. Nash would come to me later: firstly in the movie the Beautiful Mind and during my post-grad economics. A scene out of the beautiful mind illustrates the concept Nash uncovered – Nash and a set of friends were looking at a group of ladies in particular an eye-catcher when one of his friends dropped a Smithian line about self-interest, Nash counters by saying if everyone goes for her no one gets her rather target her friends. I’m not skillful in such matters and never still understood how going after a girl’s best friend gets you on dates with her but yeah that’s a way of explaining the idea. Nash equilibrium holds in zero sum games which are infinitely repeated. A game is called zero-sum if the sum of payoffs equals zero for any outcome. That means that the gains by winners are paid by the losses of the losers.
Nash’s discovery was to prove the existence of a set of moves or strategies in which no player was better off or worse off – a sort of equilibrium concept. Although before Nash, economists had hinted at the existence of such a state starting from Adam Smith, it was Nash’s mathematical proof which lay the foundation for other economists to sketch out the framework upon which all economics is based. If all economic activity occurred within markets where each agent is trying to maximize their utility subject to constraints then there must be some optimal strategies which generate an equilibrium outcome. This was the genius of John Nash.
Lest I forget this piece is an attempt at biography, John Forbes Nash was born two days from today eighty-seven years ago in Blue Field West Virginia to an electrical engineer of same name and a school teacher Margaret Virginia Nash. He took courses in Mathematics at an early age developing a devotion to it before gaining a scholarship to go to Carnegie Institute of Technology where the plan was to study Chemical Engineering. Nonetheless, his love for mathematics got the better and Nash ended up obtaining a Bachelors and Masters degree in Mathematics before the age of 20. With his genius background fully established he got admitted to Princeton snubbing an admission offer from Harvard. At Princeton, he set about proving his ideas.
Nash’s work stood on the works of Von Neumann and Morgenstern who derived utility functions of individuals. According to future Nobel Prize winner Rogers Myerson, Nash’s idea likely stemmed from undergraduate courses in international trade in 1948. A year later in 1949, Nash sent a note briefly outlining his thought process. Further research on the note yielded his 28-page PhD thesis aptly titled, ‘Equilibrium points in N-person games’ published in 1950. Three more papers followed establishing the framework of the existence of an equilibrium concept.
From there things turned blank literally as Nash began to experience bouts of paranoia resulting in his hospitalization over a long period of his life. Prior to this, unlike many famous economists he fathered two children from two different women one of whom he married, divorced and later remarried. His wife Alicia Lopez Harrison de-larde was at his side when he died – a grisly accident in a taxi after returning from Norway in New Jersey on the 23rd of May 2015.
History remembers a man who was infused a powerful concept central to the study of economics today. On the lesser side, his recovery from schizophrenia which resulted in the Nobel committee awarding the long overdue award in 1994 was truly remarkable.