A Beautiful Math: John Nash, Game Theory, and the Modern by Tom Siegfried

By Tom Siegfried

Millions have noticeable the motion picture and hundreds of thousands have learn the e-book yet few have absolutely preferred the maths built by means of John Nash's attractive brain. this present day Nash's attractive math has develop into a common language for examine 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 examine released within the Fifties on a brand new department of arithmetic often called video game conception. on the time of Nash's early paintings, video game thought used to be in short well known between a few mathematicians and chilly conflict analysts. however it remained imprecise till the Nineteen Seventies whilst evolutionary biologists all started utilizing it to their paintings. within the Nineteen Eighties economists started to embody online game idea. due to the fact then it has chanced on an ever increasing repertoire of functions between quite a lot of clinical disciplines. this present day neuroscientists peer into video 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 raised comprehend social networks. a standard 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 starting place novels by means of the overdue Isaac Asimov. In a stunning Math, acclaimed technology author Tom Siegfried describes how online game conception hyperlinks the existence sciences, social sciences, and actual sciences in a manner which may deliver Asimov's dream towards reality.

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

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VON NEUMANN’S GAMES 49 A matrix for this game would show that both players can choose from four strategies. Alice can always pass, always bet, pass with red and bet with black, or bet with red and pass with black. Bob can always fold, always call, fold with red and call with black, or fold with black and call with red. If you calculate the payoffs, you will see that Alice should bet three-fifths of the time no matter what card she has; the other two-fifths of the time she should bet only if she has black.

Nash carried social science into a new world where a unified analytical structure can be found for studying all situations of conflict and cooperation,” writes University of Chicago economist Roger Myerson. ”1 So it’s not too outrageous to suggest that in a very real way, Nash’s math provides the foundation for a modern-day Code of Nature. But of course it’s not as simple as that. Since its inception, game theory has had a complicated and controversial history. Today it is worshiped by some but still ridiculed by others.

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. Utility is basically a measure of value, or preference. It’s an idea with a long and complex history, enmeshed in the philosophical doctrine known as utilitarianism.

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