Read e-book online A Beautiful Math: John Nash, Game Theory, and the Modern PDF

By Tom Siegfried

Hundreds of thousands have noticeable the motion picture and hundreds of thousands have learn the booklet yet few have absolutely preferred the math built by means of John Nash's appealing brain. this present day Nash's appealing math has turn into a common language for learn within the social sciences and has infiltrated the nation-states of evolutionary biology, neuroscience, or even quantum physics. John Nash gained the 1994 Nobel Prize in economics for pioneering learn released within the Nineteen Fifties on a brand new department of arithmetic often called video game idea. on the time of Nash's early paintings, online game concept was once in short well known between a few mathematicians and chilly warfare analysts. however it remained vague till the Nineteen Seventies whilst evolutionary biologists all started making use of it to their paintings. within the Nineteen Eighties economists started to include video game concept. on account that then it has discovered an ever increasing repertoire of purposes between quite a lot of clinical disciplines. at the present time neuroscientists peer into video game gamers' brains, anthropologists play video games with humans from primitive cultures, biologists use video games to give an explanation for the evolution of human language, and mathematicians take advantage of video games to higher comprehend social networks. a typical thread connecting a lot of this study is its relevance to the traditional quest for a technological know-how of human social habit, or a Code of Nature, within the spirit of the fictitious technological know-how of psychohistory defined within the recognized beginning novels via the overdue Isaac Asimov. In a gorgeous Math, acclaimed technology author Tom Siegfried describes how online game conception hyperlinks the existence sciences, social sciences, and actual sciences in a manner which can deliver Asimov's dream in the direction of truth

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Extra resources for A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature

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1 UTILITY AND STRATEGY By most accounts, the invention of modern game theory came in a technical paper published by von Neumann in 1928. But the roots of game theory reach much deeper. After all, games are as old as humankind, and from time to time intelligent thinkers had considered how such games could most effectively be played. As a branch of mathematics, though, game theory did not appear in its modern form until the 20th century, with the merger of two rather simple ideas. The first is utility—a measure of what you want; the second is strategy—how to get what you want.

Say that Bob owes Alice $10. Bob proposes a game whereby if he wins, his debt will be reduced. ) But for purposes of illustrating game theory, she might agree. A BEAUTIFUL MATH 44 Bob suggests these rules: He and Alice will meet at the library. If he gets there first, he pays Alice $4; if she gets there first, he pays her $6. If they both arrive at the same time, he pays $5. ) Now, let’s say they live together, or at least live next door to each other. They both have two possible strategies for getting to the library—walking or taking the bus.

To arrive at his own evolutionary theory, Darwin required an alternative logic to explain the efficiency of life. Adam Smith, Gould concluded, supplied that logic. “In fact, I would advance the even stronger claim that the theory of natural selection is, in essence, Adam Smith’s economics transferred to nature,” Gould wrote. “Individual organisms engaged SMITH’S HAND 25 in the ‘struggle for existence’ act as the analog of firms in competition. ”16 In other words, as Smith argued, there is no need to design an efficient economy (and in fact, a designer would be a bad idea).

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