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I am a starting Ph.D. student in computer science, and I am trying to understand some classic game-theory papers, such as those by Nash, Kalai and Smorodinsky. But I find it hard to understand the mathematical parts. It seems that these papers were written by mathematicians, for mathematicians.

Can you recommend a book that explains the mathematical preliminaries of game theory, to people without extensive mathematical background?

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    $\begingroup$ For the class on game theory that I took the past semester, one of the recommended readings was "a course in game theory" (osbourne & rubinstein). With around 300 pages, that seemed to be accessible. Another, more voluminous book on the matter would be "algorithmic game theory" by nisan et al. That one is roughly 800 pages and seems to be very detailed. You will find, however, that game theory is very much a mathematical discipline, as is most of theoretical computer science. The trouble you may have is that it requires more knowledge of analysis than for example efficient algorithms would. $\endgroup$
    – G. Bach
    Commented Sep 13, 2013 at 15:53
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    $\begingroup$ Try Algorithmic Game Theory. You should have some familiarity with linear algebra and linear programming, although not too much. $\endgroup$
    – adrianN
    Commented Sep 13, 2013 at 17:06
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    $\begingroup$ Almost every paper that has been written was written "by people in field X for people in field X." The purpose of most papers is to share knowledge with people in the field. $\endgroup$
    – David Richerby
    Commented Sep 15, 2013 at 23:26
  • $\begingroup$ We don't have a strict policy for list questions, but there is a general dislike. Please note also this and this discussion; you might want to improve your question as to avoid the problems explained there. $\endgroup$
    – Raphael
    Commented Sep 16, 2013 at 8:16

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[The reviews are based on my first hand experience with the materials.]

Quick Read:

  • Essentials of game theory (Leyton-Brown, Shoham) - This is a ~100 page book, which will give a strong intuition (and more) on Game theory, this mostly covers the basics, the math here is also pretty lightweight, and this is very much readable (even by a college junior). After this book the reader should be able to (atleast) sit through an advance GT Talk.

  • An Algorithmic Game Theory Primer (Tim Roughgarden) - A really nice survey by Tim Roughgarden. It talks about various disciplines like Mechanism Design, Complexity of Equilibria, among many other things.This should motivate the reader to identify the other areas of research.

Books:

  • Algorithmic Game Theory (Nisan et al) - This is perhaps the most popular book among Computational Game Theorists.. It covers a lot of ground, and the content is very rich. (IMHO) This is one of the books, that every researcher should read before diving into the subject.

  • Lectures in Game Theory for Computer Scientists (eds. Apt and Grädel) This is yet another book that contains essays from several authors and is rich in application content. As the name suggests, this is for a great resource for computer scientists who want to use game theory for their research.

Also, if you are done with these, want more advanced material take a look at the LNCS Proceedings of SAGT.

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    $\begingroup$ I'm currently working my way through Algorithmic Game Theory (Nisan). It's one of those books that doesn't lend itself to PDF format. Luckily, the hard copy book is relatively cheap. Unluckily, it's cheap because there's very little editing/revision. It's more like an ordered collection of research papers than a textbook, each chapter written by different authors. They can be very hit or miss, and the quality of writing is a roller-coaster ride (Chapter 4 made my eyes bleed). My advice: Don't be afraid to skip over sections or even chapters. $\endgroup$
    – Nobbynob Littlun
    Commented Sep 15, 2013 at 20:29
  • $\begingroup$ Also as G.Bach said, the book by Osbourne & Rubinstein is a very popular book, however since I haven't read it, I decided not to include it in my list, however most of the people I know in this field highly recommends this book. :) $\endgroup$
    – Subhayan
    Commented Sep 16, 2013 at 10:47

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