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Game Theory

Game Theory

Game Theory

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Páginas:169 páginas
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Stop! This is a set of lecture notes. It is not a book. Go away and come back when you have a real textbook on Game Theory. Okay, do you have a book? Alright, let's move on then. This is a set of lecture notes for Math 486-Penn State's undergraduate Game Theory course. Since I use these notes while I teach, there may be typographical errors that I noticed in class, but did not fix in the notes. If you see a typo, send me an e-mail and I'll add an acknowledgement. There may be many typos, that's why you should have a real textbook.

The lecture notes are loosely based on Luce and Raiffa's Games and Decisions: Introduction and Critical Survey. This is the same book Nash used when he taught (or so I've heard). There are elements from Myerson's book on Game Theory (more appropriate for economists) as well as Morris' book on Game Theory. Naturally, I've also included elements from Von Neuman and Morgenstern's classic tome. Most of these books are reasonably good, but each has some thing that I didn't like. Luce and Raiffa is not as rigorous as one would like for a math course; Myerson's book is not written for mathematicians; Morris' book has a host of problems, not the least of which is that it does not include a modern treatment of general sum games; Von Neumann's book is excellent but too thick and frightening for a first course{also it's old. If you choose any collection of books, you can find something wrong with them, I've picked on these only because I had them at hand when writing these notes. I also draw on other books referenced in the bibliography.

This set of notes corrects some of the problems I mention by presenting the material in a format for that can be used easily in an undergraduate mathematics class. Many of the proofs in this set of notes are adapted from the textbooks with some minor additions. One thing that is included in these notes is a treatment of the use of quadratic programs in general sum games two player games. This does not appear in many textbooks.

In order to use these notes successfully, you should have taken a course in: matrix algebra (Math 220 at Penn State), though courses in Linear Programming (Math 484 at Penn State) and Vector Calculus (Math 230/231 at Penn State) wouldn't hurt. I review a substantial amount of the material you will need, but it's always good to have covered prerequisites before you get to a class. That being said, I hope you enjoy using these notes!



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