New PDF release: A Beautiful Math: John Nash, Game Theory, and the Modern

By Tom Siegfried

ISBN-10: 0309101921

ISBN-13: 9780309101929

ISBN-10: 0309659280

ISBN-13: 9780309659284

Thousands have noticeable the motion picture and hundreds of thousands have learn the publication yet few have totally preferred the maths built through John Nash's attractive brain. at the present time Nash's attractive math has turn into a common language for learn within the social sciences and has infiltrated the geographical regions of evolutionary biology, neuroscience, or even quantum physics. John Nash received the 1994 Nobel Prize in economics for pioneering learn released within the Fifties on a brand new department of arithmetic referred to as video game concept. on the time of Nash's early paintings, online game concept was once in short well known between a few mathematicians and chilly struggle analysts. however it remained imprecise till the Nineteen Seventies while evolutionary biologists begun making use of it to their paintings. within the Eighties economists started to embody online game thought. due to the fact that then it has came across an ever increasing repertoire of purposes between a variety of medical disciplines. at the present time neuroscientists peer into online game avid gamers' brains, anthropologists play video games with humans from primitive cultures, biologists use video games to provide an explanation for the evolution of human language, and mathematicians make the most video games to higher comprehend social networks. a typical thread connecting a lot of this examine 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 through the past due Isaac Asimov. In a gorgeous Math, acclaimed technological know-how author Tom Siegfried describes how video game concept hyperlinks the lifestyles sciences, social sciences, and actual sciences in a manner which may carry Asimov's dream in the direction of truth

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

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But in most walks of life (except perhaps publishing), money isn’t everything. So you need a general definition that makes it possible to express utility in a useful mathematical form. One mathematical approach to quantifying utility came along long before Bentham, in a famous 1738 result from Daniel Bernoulli, the Swiss mathematician (one of many famous Bernoullis of that era). In solving a mathematical paradox about gambling posed by his cousin Nicholas, Daniel realized that utility does not simply equate to quantity.

Or . . ” 2 So to VON NEUMANN’S GAMES 31 Bentham, utility was roughly identical to happiness or pleasure— in “maximizing their utility,” individual people would seek to increase pleasure and diminish pain. ”3 Bentham’s utilitarianism incorporated some of the philosophical views of David Hume, friend to Adam Smith. And one of Bentham’s influential followers was the British economist David Ricardo, who incorporated the idea of utility into his economic philosophy. In economics, utility’s usefulness depends on expressing it quantitatively.

In any event, the question isn’t whether there is always a good general strategy, but whether there is always an optimum set of VON NEUMANN’S GAMES 43 rules for strategic behavior that covers all eventualities. And in fact, there is—for two-person zero-sum games. You can find the best strategy using the minimax theorem that von Neumann published in 1928. His proof of that theorem was notoriously complicated. But its essence can be boiled down into something fairly easy to remember: When playing poker, sometimes you need to bluff.

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A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature by Tom Siegfried

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