Economic and Game Theory
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Dear Dr. Levine,
I am an eighth grader at The Buckley School in New York City. My math teacher has assigned a research paper due in three weeks. We are to choose a theory in mathematics. I have chosen game theory.
My paper is supposed to be six to nine pages in length: a brief history (900-1800 words) and a results section which includes theorems, definitions, and/or graphs. I have been told to "Provide proofs and explanations of your results, as appropriate. And then, apply your theorems to problems in your theory."
I have visited several sites including yours (levine.sscnet.ucla) and have gotten a lot of information -- much of it I do not understand. Your articles, "What is Game Theory" (at www.levine.sscnet.ucla.edu/general/whatis.htm) and "Game Theory" (submitted to the Nature Publishing Group) were helpful. Game Theory by Aner Sela at www.sfb504.unimannheim.de/glassary/game.htm was a repeat of your two articles, but the repetition was helpful. I am trying to read "Game Theory" written by Don Ross of the University of Cape Town found at plato.stanford.edu/entries/game-theory.
At this point, I know I can understand and write about only the basics, so I plan to limit my paper to zero sum games with two rational players with a limited number of choices which lead to a well defined outcome. If I understand what I have read, I will be using strategic or normal form games. Because I know very little about probability, I do not think I can deal with mixed strategy games. I have read about Prisoners' Dilemma in several articles and have played rock, paper, scissors (at www.emf.net/~estephen/roshambo).
Can you tell me if all authors use 3rd person singular she or her when writing about game theory and, if so, why?
When I read your bibliography listed at the end of "Game Theory," I found Games and Decisions by R. Luce and H. Raiffa listed as published in 1857. Is this correct? I have asked my librarian to try and locate a copy of Thinking Strategically, by Dixit and Nalebuff because I read that it was "an accessible introduction" to game theory.
Can you offer me in guidance or direct me to any other material which I might understand?
Thank you very much for your time and any advice you can give me.