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I have read a bunch of book on Game Theory, and I find that one of the best is the the book of Osborne and Rubinstein. Nevertheless, all books which I found are not made for mathematician, meaning that they do not assume prior knowledge, in particular they do not assume measure theory, functional/complex analysis etc.

Is there any really formal and well-written book about game theory made for mathematician? Thanks in advance

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    $\begingroup$ You can try Fudenberg and Tirole. $\endgroup$ – Rob Feb 17 '16 at 20:01
  • $\begingroup$ If you mean the one linked below, it is a rather standard textbook :/ read.pudn.com/downloads146/ebook/635671/… $\endgroup$ – user207096 Feb 17 '16 at 20:10
  • $\begingroup$ This is hot these days, and presume a fair amount of knowledge: springer.com/us/book/9781461485070 $\endgroup$ – parsiad Feb 17 '16 at 20:59
  • $\begingroup$ Try Gintis, Game Theory Evolving $\endgroup$ – Olórin Feb 17 '16 at 21:33
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I do not know what you mean by prior knowledge, but I would give a couple of books which requires more mathematical sophistication than Osborne and Rubinstein. If you are looking for a specific area in game theory then this list may not be useful for you.

  1. Game Theory by Maschler, Solan and Zamir: This book is relatively new and it includes almost everything one needs to know about game theory (both cooperative and non-cooperative). In the mathematical appendix it covers necessary background for existence theorem.

  2. Game Theory for Economic Analysis by Ichiishi: This is a pretty old book, but it is very well written and it assumes a great deal of mathematical knowledge. Yet, the initial chapters discuss continuity notions for set valued maps(uhc-lhc), properties of convex sets and fixed points.

  3. Game Theory by Owen: This is also another old book, but it is still used in various courses in different places. It has traditional definition-theorem-proof structure.

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