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

By Tom Siegfried

Hundreds of thousands have obvious the motion picture and millions have learn the ebook yet few have totally liked the maths constructed through John Nash's attractive brain. this day Nash's attractive math has develop into a common language for study 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 thought. on the time of Nash's early paintings, video game concept was once in short well known between a few mathematicians and chilly struggle analysts. however it remained imprecise until eventually the Seventies whilst evolutionary biologists started employing it to their paintings. within the Eighties economists started to embody video game thought. when you consider that then it has chanced on an ever increasing repertoire of purposes between quite a lot of clinical disciplines. this 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 take advantage of video games to higher comprehend social networks. a standard thread connecting a lot of this learn 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 by means of the past due Isaac Asimov. In a gorgeous Math, acclaimed technology author Tom Siegfried describes how online game concept hyperlinks the existence sciences, social sciences, and actual sciences in a manner which may deliver Asimov's dream towards truth

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

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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. ) And they both know that the bus will always beat walking. ” The numbers show how much the player on the left (Alice) wins.

And you’d have other rules for all the other situations. There’s one additional essential point about strategy in game theory—the distinction between “pure” strategies and “mixed” strategies. In tennis, you might rush the net after every serve (a pure strategy) or you might rush the net after one out of every three serves, staying back at the baseline two times out of three (a mixed strategy). Mixed strategies often turn out to be essential for making game theory work. 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.

So equating utility with money is a convenient simplifying assumption, allowing the theory to focus 40 A BEAUTIFUL MATH on the strategic aspects of how to achieve what you want, without worrying about the complications involved in defining what you want. However, there remained an important aspect of utility that von Neumann and Morgenstern had to address. Was it even possible, in the first place, to define utility in a numerical way, to make it susceptible to a mathematical theory? ) Money (which obviously is numerical) could really be a good stand-in for the more complex concept of utility only if utility can really be represented by a numerical concept.

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