Download e-book for iPad: A Beautiful Math John Nash, Game Theory, and the Modern by Tom Siegfried

By Tom Siegfried

ISBN-10: 0309101921

ISBN-13: 9780309101929

Hundreds of thousands have noticeable the motion picture and millions have learn the ebook yet few have totally liked the maths invented through John Nash’s appealing brain. at the present time 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 received the 1994 Nobel Prize in economics for pioneering learn released within the Fifties on a brand new department of arithmetic often called online game thought. on the time of Nash’s early paintings, video game idea used to be in brief well known between a few mathematicians and chilly battle analysts. however it remained quite vague till the Nineteen Seventies, while evolutionary biologists started to locate it beneficial. within the Eighties economists started to embody video game concept. in view that then video game idea math has discovered an ever increasing repertoire of functions between quite a lot of clinical disciplines.

Today neuroscientists peer into online 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 make the most video games to higher comprehend social networks.

A universal thread connecting a lot of this study is its relevance to the traditional quest for a technology of human social habit, or "a Code of Nature," within the spirit of the fictitious technological know-how of psychohistory defined within the well-known origin novels through the overdue Isaac Asimov. In a stunning Math, acclaimed technology author Tom Siegfried describes how video game idea hyperlinks the existence sciences, social sciences and actual sciences in a fashion which can deliver Asimov’s dream in the direction of fact.

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

Sample text

If he has red, he might fold—and Alice will win with a red card. Bluffing sometimes pays off. On the other hand, Bob knows that Alice might be bluffing (since she is not a Vulcan), and so he may go ahead and call. The question is, how often should Alice bluff, and how often should Bob call her (possible) bluff ? Maybe von Neumann could have figured that out in his head, but I think most people would need game theory. VON NEUMANN’S GAMES 49 A matrix for this game would show that both players can choose from four strategies.

If he sent them south and the convoy went north, he would lose a day of bombing time (of only two bombing days available). If the recon planes went north, the bombers would still have time to get two bombing days in if the convoy went south. So the “payoff ” matrix looks like this, with the numbers giving the Allies’ “winnings” in days of bombing: Japanese North South North 2 2 South 1 3 Allies A BEAUTIFUL MATH 46 If you just look at this game matrix from the Allies’ point of view, you might not see instantly what the obvious strategy is.

This game puzzles Bob, too. Here’s the matrix. Bob Bus Walk Bus 3 6 Walk 5 4 Alice Bob realizes there is no simple strategy for playing this game. If he rides the bus, he might get off paying only $3. But Alice, realizing that, will probably walk, meaning Bob would have to pay her $5. VON NEUMANN’S GAMES 47 So Bob might decide to walk, hoping to pay only $4. But then Alice might figure that out and ride the bus, so Bob would have to pay her $6. Neither Bob nor Alice can be sure of what the other will do, so there is no obvious “best” strategy.

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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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