References for Nash's game theory

  • Thread starter Einj
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  • #1
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Main Question or Discussion Point

Hi all. I recently watched a documentary about John Nash's game theory and I'd like to study more about that. My present mathematical knowledge is that of a particle physics student at his fourth year. Is my preparation enough? If so, can someone advise some references where I could study?
 

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  • #3
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Actually I was thinking about something more specific that could explain the mathematical foundations of the theory. Still I'm not sure if I have the right requirements in order to understand it. What level of math does it require?
 
  • #4
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Here's a quote from the historical section of the above link:
The modern game-theoretic concept of Nash Equilibrium is instead defined in terms of mixed strategies, where players choose a probability distribution over possible actions. The concept of the mixed strategy Nash Equilibrium was introduced by John von Neumann and Oskar Morgenstern in their 1944 book The Theory of Games and Economic Behavior. However, their analysis was restricted to the special case of zero-sum games. They showed that a mixed-strategy Nash Equilibrium will exist for any zero-sum game with a finite set of actions. The contribution of John Forbes Nash in his 1951 article Non-Cooperative Games was to define a mixed strategy Nash Equilibrium for any game with a finite set of actions and prove that at least one (mixed strategy) Nash Equilibrium must exist in such a game.
I think John von Neumann is a pioneer in the field of game theory, and the quoted book may be a reputable source on the matter.

EDIT:
Here's a link from Google Books to look inside the book:
http://books.google.com/books/about/Theory_of_Games_and_Economic_Behavior_Co.html?id=_aIGYI-jGEcC
 
  • #5
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Thank you. I'll definitely look at it, but isn't Nash's theory been developed after this book?
 
  • #6
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Thank you. I'll definitely look at it, but isn't Nash's theory been developed after this book?
I don't know if there is such a thing as "Nash's game theory". I know he proved a theorem generalizing the one proven by von Neumann. That is why I linked you to this pioneering work. If you feel comfortable with the contents of this work, you are welcome to explore further.
 
  • #7
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I'll see. However, thank you very much.
 

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