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I recently got interested in game theory but I don't know where should I start.

Can anyone recommend any references and textbooks? And what are the prerequisites of game theory?

YCor
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Axiom
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    You should read the Wikipedia page on game theory, check the references there, decide what doesn't make sense to you, and provide some information on your background, for otherwise your question is a little vague and probably the answers you get won't be terribly helpful. – Jason Polak Mar 19 '10 at 20:48
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    Actually I already did what you said but there were a lot of references and I didn't know which one I should choose. That's why I came here and asked this question. – Axiom Mar 19 '10 at 20:54
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    Why the downvoting? If Soheil had said he wanted to study, let's say randomly (!) Algebraic Geometry, he would have had 20 upvotes and answers fiercely discussing the relative merits of Shafarevich and Fulton over Hartshorne and Eisenbud-Harris ... – Georges Elencwajg Mar 19 '10 at 21:49
  • What's wrong with the game theory Georges? – Axiom Mar 19 '10 at 21:58
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    The downvotes are encouragement to study a more popular subject. This has a lot of sense behind it. The users of Math Overflow want Soheil to get a good job at a good university surrounded by other good researchers. Maybe if we all downvoted every question that wasn't close enough - Riemann's hypothesis would be solved by now! – Dror Speiser Mar 19 '10 at 22:19
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    @Georges: This is funny, your comment is getting more votes than the question itself - while people agree with you, they still really don't care for game theory. – Dror Speiser Mar 19 '10 at 23:30
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    @Soheil, I believe that J. Polak was in part asking that you provide more information in your question, so that readers don't have to guess at what would be a helpful answer. I agree. – Jonas Meyer Mar 20 '10 at 01:17
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    @Dror: with due respect that's got to be a terrible motivation to get someone to study algebraic geometry. The idea of consecrating one's efforts to Proper Stuff And Not That Other Stuff is, when made dogmatic, quite damaging IMHO. (I mean, why should people in the 70s and 80s have studied the local theory of Banach spaces rather than motivic cohomology?) – Yemon Choi Mar 20 '10 at 03:28
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    @Dror: I think your reading of the relative number of votes for Georges' comment and for the question itself, is way off base. (It's not the topic of Soheil's question that I refrain from upvoting; it is, as Jonas seems to also think, its lack of well-defined & attainable targets.) – Yemon Choi Mar 20 '10 at 03:31
  • Yemon, you understood Dror's first comment to be serious? Here I was giving it an up-vote on the grounds that it was clever tongue-in-cheek. I mean, surely that last sentence is the tip-off, no? – JBL Mar 21 '10 at 14:29
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    @JBL Ah, if that was irony from Dror, then I apologize for my sense-of-humour failure; I can only excuse it by saying that I've seen attitudes like that, for given values of X=good and Y=infra dig, dispiritingly often. – Yemon Choi Mar 21 '10 at 17:45

9 Answers9

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"A course in game theory" by Martin J. Osborne and Ariel Rubinstein is probably the standard more mathematical starting point. A more concise, more modern, and slightly CS-leaning text is "Essentials of Game Theory -- A Concise, Multidisciplinary Introduction" by Kevin Leyton-Brown and Yoav Shoham.

Noam
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    This book is one of the main textbooks used in a recent and free online course of Game Theory from Stanford: https://www.coursera.org/course/gametheory – Tadashi Jan 06 '14 at 13:29
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I asked this same question about a year ago, so I'm very slightly ahead of you. Here's what I know:

As you probably know, there are two major branches for game theory. There's (for lack of a better term) "economics" game theory dealing with real world situations, economics, politics and the like. I know next to nothing about that. However, I do know a decent amount about combinatorial game theory, which is a little bit more ground in mathematics, and deals with two player games such as Go, Chess, Nim, or Tic-Tac-Toe.

The best introductory text is going to be Conway's Winning Ways, any of the volumes 1-4. These are the books to read to get into any other subset of combinatorial games, in my opinion.

My personal specialization thus far is generalizations of Tic-Tac-Toe called achievement games, which you can read about (along with much more) in Tic-Tac-Toe Theory.

However, if you want to go even further in these studies, you are a little bit out of luck. What's very exciting to me about combinatorial game theory is that it's pretty much a brand new field of mathematics, and right now the best techniques we have to study it are educated guessing/brute-forcing and a little bit of discrete mathematics. Although it's disenchanting sometimes, this also means that there is potentially a world of possible links and connections to other branches of math that we don't know about, and is just out there waiting to be discovered.

Ian Douglas
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    I second the distinction Ian makes. "Economics" game theory (in the tradition of Nash and von Neumann), and combinatorial game theory (in the tradition of Conway, and applied to semantics of programming languages) are as far as I know pretty much disjoint subjects. – Tom Leinster Mar 20 '10 at 13:49
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    ...and to ask the obvious question to the orginal questioner: do you know which of these two branches of game theory you're interested in? – Tom Leinster Mar 20 '10 at 13:49
  • @Axiom, Also see same question at http://math.stackexchange.com/q/76096/13733 – Pacerier Aug 09 '15 at 15:53
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There is a new (well, the English translation is) book that treats both noncooperative and cooperative (but not combinatorial) game theory on a high level, is extremely well written, mathematically rigorous and fairly comprehensive: Game Theory by Michael Maschler, Eilon Solan, and Shmuel Zamir. For someone who knows some undergraduate real analysis and linear algebra, the book should be self contained (with a few exceptions, where reference literature is recommended in the book). The book doesn't contain everything (there is very little on refinements), but it contains enough to get one near the frontier of research fast.

Book cover

Michael Greinecker
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G. Owen, GAME THEORY

background is basic linear algebra I believe

Gerald Edgar
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I've found Tom Ferguson's text to be a good introduction. His Linear Programming (pdf) text is a useful supplement. Both are freely available from his website.

Jason Bandlow
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The Wikipedia article on Game theory is a general introduction to the field. In it I found an a link for Theory of Games and Economic Behavior. Also here are lecture notes from a graduate level course.

Kristal Cantwell
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One area that's really fascinating from a game theory angle is algorithmic game theory, and there's an excellent book out on this topic. While this focuses more on the computational aspects of game theory, it's extremely relevant to a ton of work on the internet and e-commerce, and weaves together game theory, economics and theoretical computer science in a fascinating manner.

The book is: Algorithmic Game Theory

Suresh Venkat
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I recently had to write a report about this and one of my main sources was http://www.math.ucla.edu/~tom/Game_Theory/comb.pdf I found it to be fairly comprehensive and it included some practice exercises

SkippyNBS
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This is not a reference for starting game theory. But its title attract my attention. Moreover the references therein contains some references for starting game theory for example Handbooks of Game theory, etc.

But I think that geometric approach to this theory is an exciting and interesting point.

https://hal.science/hal-01382281/document

Ali Taghavi
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