Nash Equilibrium


Mykyta Khairudinov

National technical university of Ukraine “KPI”


Doing science is always hard. Besides sturdy knowledge base and extremely high intelligence level, you need a lot of labor and tenacity to do this. Science is often compared with a fight and this fight is always with yourself. In my report I’d like to tell about one of the greatest mathematician and economist of the present, about the man, who recovered after a serious mental disorder and a little changed this world, 1994 Nobel Prize laureate – John Forbes Nash.

Nash is known to the general audience and to non-economist people through the book of a student, who has been inspired by his exiting life. “The Beautiful Mind” – a film, which won 4 Oscars, is based exactly on this book. The story of John’s life is really intriguing.

John Nash was born in the midst of economic crises, in 1928 in a tiny town Bluefield, West Virginia. His parents were strict Catholics; maybe this is why he grew up such a clever person. As most geniuses the world knows, at school Nash didn’t study that well and math for him was like an excruciation. But when John was 14, he read a “Men of Mathematics” by Eric Temple Bell and without any help proved the Fermat’s little theorem. He finished school and went to Carnegie Institute of Technology, where he tried to study chemistry and international economics. But by then math had completely occupied his heart and mind. Later the university rector gave him a laconic recommendation: “This man is genius”, and Nash went to Princeton University. There he got to know the Games Theory, and later he got a Nobel Prize for working with it.

The Games Theory is a mathematical method of optimal strategies analysis in games. A game is a process between two or more people, who uphold their own interests. Every player has their own target and their own strategy of how to reach the goal. Before Nash, this theory had another form. It was called a “Zero Sum Game” and supposed a victory to one player and a defeat to another. Later John von Neumann used this concept in his works of informatics and cybernetics (wining –“1”, losing – “0”). Nash got a new method of how to resolve this problem: no one can win changing their own decision if other players do not change their ones. For example, a trivial situation: salary discussion. It can be finished with a strike, a situation that is bad for both (0-0), or with a conclusion of mutually beneficial decision (1-1). This method is named after its author — “Nash Equilibrium”.

Nash’s works mathematically prove Karl Marx’s labour theory of value, which was banned in the USA that time. The government started to be interested in Nash. Later he got recruited by RAND – national safety organization. There John worked with the government and used his theory of games for waging cold war between the USA and the USSR.

When he was 30 years old, he got seek. Paranoia (paranoid schizophrenia) is a difficult illness and Nash fated to live with it for the rest of his life. He couldn’t recover but he learnt how to live with it. Maybe it was based on his own mathematical method, who knows. Anyway, he came to stay in economics world and in 1994 Nash got a Nobel Prize for researching in non-cooperative games. Life of John Nash shows us how great human mind is. He presented the society theory, which is used every day: in our simple lives and by the biggest corporations, in doing business, in finding compromises and it really is inspiring. When you enter the market with your product – it’s a game, when you get a new job – it’s a game, every contention is a game. It is difficult to imagine a game without rules, and exactly these rules were created by John Nash. It is impossible to overestimate his contribution to modern economics. John’s life inspirited a lot of young economists and scientists, and continues doing it.


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