What's the best reference for rigorous study of mixed-strategy nash equilibrium? I am studying game theory, but I feel like I do not understand mixed-strategy equilibrium all that much. Yes, I know how to find them in 2x2 cases, and in some 3xn (n &lt;= 2) cases as well where the normal form has been artificially constructed to make finding the mixed strategies very easily (e.g., one of the actions can conveniently be ignored because it's dominated).

But if I were to write down an nxn matrix right now, n >= 3, I wouldn't be able to solve for it's mixed strategies.

So I am looking for a really good really rigorous really thorough reference to understand mixed strategy equilibria. Any recommendations?
The book by Gibbons that Tobias mentions is titled "A Primer in Game Theory" in Europe. It is excellent, especially in its coverage of more advanced games of imperfect/incomplete information. But it is quite concise in its treatment of games of complete information like the ones you are studying. The book by Osborne might therefore be a better choice. Both of these books are aimed at the introductory graduate level and are therefore quite rigorous.*

However, I feel compelled to say that it sounds like you are taking a first course in game theory, so I would be inclined to suggest also the book "Strategies and Games: Theory and Practice" bu Dutta. It is more verbose, but I think also provides a more gentle introduction to topics like Nash equilibrium and mixed strategies. Game theory, like much of economics is often best learnt by first obtaining a firm grasp of the intuition, and later supplementing it with sufficient rigor.



(*) There is also "Game Thoery" by Fudenberg and Tirole, which is less of a textbook and more of a reference. But it is, perhaps, even more rigorous as a result.