Game theorist John Nash

2024 Author: Henry Conors | [email protected]. Last modified: 2024-02-12 02:45

John Nash became widely known all over the world thanks to the movie "A Beautiful Mind". This is an amazingly touching, life-affirming film charged with faith in the power of human genius. This is a biography film, a shock film, a discovery film. He introduces the viewer into the world of the future, where the mind creates real miracles. A piercing interweaving of madness and genius in its unity and struggle. The collection of "Oscars" is evidence of this. The game theory created by this mathematician turned the foundations of corporate business on its head. The 27 pages of Nash's doctoral dissertation had the same impact on society and economics as Einstein's 21 pages of doctoral dissertation on theoretical physics.

The theory of Adam Smith, which traditionally follows the development of a liberal bourgeois society, in comparison with the way John Nash explores it, looks pale, not giving a clear explanation for many modern phenomena. The above theories are related in the same way that two-dimensional geometry is only a subset of three-dimensional.

Initiation

John was born on 1928-13-06 in Bluefield (West Virginia). At school he was not a "nerd", he studied averagely. By nature - closed, selfish.

Imagine a future mathematician (differential geometry and game theory) did not like this subject at school. At this stage, everything about him was suspiciously average. It was as if his intellect was sleeping and waiting for a push. And he still came.

At the age of 14, the teenager got into the hands of the book "Creators of Mathematics" by his compatriot Eric Bell, a mathematician and author of science fiction. The book very authentically told about the life of great mathematicians, about their motivation and contribution to progress.

What happened when he read the book? Who knows … However, it was like an initiation, after which, before that, quite an average "gray" schoolboy John Nash takes on the impossible and suddenly proves Fermat's little theorem for others. For non-specialists, the latter circumstance says little. But believe me, it was a miracle. What can it be compared to? Perhaps, with the fact that an amateur provincial actor had a chance, and he perfectly played Hamlet in the capital.

Polytechnic Institute

His father (his son dubbed his first and last name) was an educated man who worked as an electronics engineer in a commercial company. After proving Fermat's Theorem, it became quite obvious to the parent that John Nash Jr. would become a scientist.

Several brilliant research papers opened the door wide for the guy to the fairly prestigious Carnegie Polytechnic Institute, where the young man first chose chemistry, then international economics, and finally established his desire to become a mathematician. The diplomas he received, bachelor's and master's,corresponded to the speci alty "Theoretical and Applied Mathematics".

The recommendation given to him by educator Richard Duffin for admission to Princeton University speaks of how much he was appreciated by his institute teachers. Here is her text in full and verbatim: “This guy is a genius!”

Princeton University

And yet, thanks not to a recommendation, but to brilliantly passed exams, he entered John Nash University. His biography at that time creates the impression that fate really led him. How did it manifest?

What he didn't know, he was only nine years away from the milestone when madness would close him for thirty years with a dark veil of paranoid schizophrenia from the outside world, cross him out of society, destroy his family, deprive him of his job and home.

The young man did not know all this, just as he did not know where the fine line between genius and madness lies. He enthusiastically greeted the presentation of the new science of game theory, the brainchild of economists Oscar Morgenstern and John von Neumann, and immediately set to brainstorming headlong. The twenty-year-old genius managed to independently develop the fundamental tools of game theory, and at the age of 21 he completed work on the corresponding doctoral dissertation.

How could a young almost doctor of science know that in 45 years John Nash's theory would be awarded the Nobel Prize? It will take society almost half a century to understand: this was a breakthrough!

Work

Very early, in 1950–1953, a 22–25-year-old scientist beginsperiod of creative maturity. He writes several fundamental papers on the so-called non-zero-sum game theory. What it is? You will find a comment later in this article.

John Nash is a famous and successful mathematician. His place of work is very prestigious: the Massachusetts Institute of Technology, located in Cambridge. Then luck smiles at him: contact with the RAND corporation. He's tasting unlimited funding for the Cold War, becoming one of America's leading cold war experts.

What is game theory

The contribution of game theory to the modern regulation of society is difficult to overestimate. What is society in terms of macroeconomics? The interaction of many players. For example, aggregated: business, state, households. Even at this macro level, it is clear that each of them is pursuing a different strategy.

Businesses are potentially inclined to inflate their profits (crushing households) and minimize taxes (underpaying the state).

It is beneficial for the state to raise taxes (suppressing small and medium-sized businesses) and reduce the level of social protection (depriving the support of the unprotected sections of society).

Households are comfortable with excessive social support from the state and minimum prices for services and goods produced by businesses.

How to get these Swan, Cancer and Pike together and dynamically drag the cart, the name of which is society? Game theory defines it.

John Nash's brainchild - non-zero sum problems

The abovethe class of problems, when the gain of one of the parties is equal to the loss of the other, is called zero-sum problems. Both Morgenstern and Neumann were able to calculate it. However, we recall that for this class of problems John Nash created the tools and concepts.

But the ingenious mathematician did not stop at this model, he substantiated a more subtle class of problems (with a non-zero sum). For example, the conflict between the administration and trade unions, which put forward a demand for higher wages.

Inflaming the situation with a long strike, both sides will suffer losses. When used by both the trade unions and the administration, the ideal strategy will both benefit. This situation is called non-cooperative or Nash equilibrium. (Such tasks include diplomatic problems, trade wars.)

Modern highly competitive society demonstrates a truly endless range of interactions between different actors. Moreover, almost all of them lend themselves to mathematical analysis as problems with a non-zero sum.

Private life

Until the end of the 50s, the future Nobel laureate John Nash climbed the scientific and career ladder, so to speak, jumping over three steps. The main thing for him were ideas, not people. Coldly and cynically, he reacted to his MIT colleague Eleanor Stier, who fell in love with him. He was not touched by the fact that the woman bore him a child. He simply did not acknowledge his paternity. By the way, Nash had no friends in any team among his work colleagues. He was eccentric and strange, lived in a world of formulas invented by himself. All his attentionwas devoted to one thing - the development of ideal strategies.

Needless to say, the leading technologist of the Cold War, thirty-year-old John Nash, flourished. His photo during these years is very similar to the picture of the actor Russell Crowe who played him. A brunette with an intelligent face and a thoughtful look. Fortune magazine predicts fame and fame for him. In February 1957, he marries Alicia Lard, and two years later they have a son, Martin. However, at this seemingly high point in his career and personal well-being, John began to show symptoms of paranoid schizophrenia.

Disease

Further, a real nightmare began for John Nash: harsh insulin therapy at Trenton State Hospital, dismissal from his job, divorce after three years of illness from a desperate Alicia Lard, wandering around insane asylums.

In the 60s, he felt better, and Eleanor Stier gave a homeless scientist a roof over his head, he spent time in conversations with his first son. Nash seemed to be recovering and stopped taking antipsychotic medication. The disease has returned.

Then, in the 70s, he was given shelter by Alicia Lard. Colleagues gave him a job.

Road to recovery

At this point, he realized that he lives in an illusory world deformed by schizophrenia and paranoia, and began to fight the disease. But he was not a doctor, but a scientist. Therefore, it was not medical methods that became his weapon, but the theory of games developed by him. scientificallyJohn Nash consistently battled paranoia. The film with Russell Crowe as a genius clearly showed this. He fought the disease around the clock, uncompromisingly, as with an opponent in the game, ahead of the initiative, minimizing his chances, limiting the choice of moves, depriving him of the initiative. As a result of this most important game in his life, genius defeated madness: he achieved a permanent absolute minimization of an incurable disease.

Finally, in 1990, the long-awaited verdict was delivered by doctors: John Nash recovered. We must pay tribute to the scientific world of the United States, the genius was not forgotten, because all these more than fifty years they used the tools developed by Nash. In 1994, he won the Nobel Prize (for his student thesis, written at the age of 21!). In 2001, Nash tied the knot again with Alicia Lard. Today, the famous scientist continues his scientific activities in his Princeton office. He is interested in non-linear strategies for using computers.

Conclusion

This American genius is an amazingly whole person, his whole life is proof of game theory. In his fate came together and triumph, and love, and madness, and the victory of intellect over paranoia. To analyze the surrounding reality, John Nash invariably uses the scientific tools developed by him.

The genius of a scientist can be very clearly characterized by the phrase of Umberto Eco (the novel "Foucault's Pendulum") that a genius always plays on one component. However, his game is unique and unique. Because when heplays on it, then all other components are involved.