The epitaph is attributed to John Nash and game theory




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Died the famous American mathematician, Nobel prize laureate in Economics John Forbes Nash.

86-year-old Nash died in a car accident in new Jersey. Together with the great mathematician died in a car accident his wife, 82-year-old Alicia Nash. The driver of the taxi, which drove a couple, lost control while overtaking and crashed into the barrier. After impact, both passengers were literally thrown out because they were not wearing seat belts.

John Nash worked in Princeton University. The Nobel prize in Economics in 1994 he received for his work "Analysis of equilibria in the theory of non-cooperative games". Biography of genius mathematician who suffered from schizophrenia, was the basis for the Oscar-winning drama "a beautiful mind" with Russell Crowe in the title role.

About the prisoner's dilemma read? Detained two criminals. The conditions are: if one of them testifies against the other, and the other does not give such testimony, the one that gives goes free and the other gets ten years. This strategy is called treason. If both testify against each other, both get two years, but if none of them gives evidence for six months, the latter strategy is called cooperation. What strategy would you choose? I will deliver you from the pangs of conscience, we proceed from rational choice — it would not take long. This task is formulated without Nash, but the math suggested it. The objective of this classic game theory. To Nash was a well-developed mathematical apparatus of the theory of management. There is some function, for example, the gross domestic product per capita, and there are a lot of restrictions, so-called boundary conditions. We need to maximise objective function subject to all constraints. Our Leonid Kantorovich received the Nobel prize for one of the solutions to such problems. But in control theory there is only one function, in game theory there is interaction between players.

You may find that the task is too refined and abstract. But even this problem was solved in the cold war the USSR and the USA. If countries cooperate, both will save resources if both betray, they will have to spend reasonable money on the arms race. But if one country chooses to cooperate and the second one will deliver, it will win only one. This problem was solved by the Nash. He considered how to behave as a country from a mathematical point of view. Like Sakharov, Nash becomes a dissident, goes to Europe seeking political asylum, not getting it, was deported back to the States, ill with schizophrenia and forcibly treated in a psychiatric hospital. Twenty years not working, but receives the Nobel prize for the mathematical solution of the described class of problems. By the way, you would have done with his accomplice?

It turns out that the prisoner's dilemma is a classic problem of Economics. There are two companies that dominate the market. If companies cooperate and do not invest money in advertising — both get good profit. If both betray and inflate your advertising costs, then both reduce their profits. But if one cooperates, the second betrays, that one of the companies cover. Are you clear on what to do with your partner? Exactly the same is the case with the budgets of football clubs. Or all save on transfer budgets and cooperate or betray it all and pay for parasites big money.

The classic prisoner's dilemma is a classical solution — you need to bring. Only this strategy leads to minimal time in prison. If you cooperate, your partner, minimizing your time, will betray you and you go for 10 years, and he will be released. This solution explains why companies spend so much money on advertising, and football teams have transfer budgets. This solution explains the arms race and price wars in the economy.

A little more complicated, if the game is repeated many times. Then a winning strategy is complicated and becomes very interesting. Omitting Nash developed the mathematics, the conclusions are the following: to maximize the win you have to behave as behaved your accomplice/partner in the previous step. It is a strategy of vendetta. It is mathematically verified. Only in 1984, Robert Axelrod found a winning "altruistic" strategies.

Now let's add in our model several hundreds of players, instead of two, we introduce the probabilities and allow the players to share information. Here this mess Nash up and put in the formula. For which he was recognized as the greatest mathematician of modern times. His work concerns the non-zero-sum, prisoner's dilemma, only one of them. He formulated the "Nash equilibrium" — a situation in which deviation from the strategy of one of the players reduces the win everyone, including that player. It is a model of healthy competition.

Now you understand why the world is so full of shit. This is a winning strategy. And only an infinite number of iterations allows you to find the altruistic scenario. And so it appears a mathematical justification of the necessity of religion.

Nash crashed into a taxi, along with his wife Alicia Nash. She left him in 1962, unable to cope with the schizophrenia of her husband, she raised a son who also became ill with schizophrenia. In 1970, Alicia realized that I had betrayed her husband and, by implementing an altruistic strategy, the newly married John. They lived long and happily and died in one day.

Author: Yuri Stroilov

Source: m.saint-petersburg.ru/m/society/stro/336938/

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