Thinking Strategically by Avinash Dixit and Barry Nalebuff is a fantastic way to start. You can pick it up without any prior knowledge of game theory.

I'd also recommend Ken Binmore's Game Theory: A Very Short Introduction.

This youtube channel has proven invaluable to me: https://www.youtube.com/user/JimBobJenkins

His book is also great (http://gametheory101.com/textbooks/), but mostly a reiteration of the videos.

The last two lectures in the The Georgia Tech Machine Learning course on Udacity cover some basics of Game Theory. Just skip ahead, the game theory part is mostly self-contained. https://www.udacity.com/course/machine-learning--ud262 The Reinforcement Learning course includes some of the same (exactly the same) game theory content and then adds an additional lecture on further topics in game theory https://www.udacity.com/course/reinforcement-learning--ud600 Again, skip to the last couple lectures.

Kreps, Game Theory and Economic Modeling has a nice overview and contextualization as I recall. I also really like Brian Skyrm's little books (Evolution of the Social Contract and Stag Hunt) for an introduction to the evolutionary side.

Note, those aren't textbooks. They're applied/context works with introductions, and I think they're better for developing intuition before getting into a textbook.

For a really accessible textbook that (as I recall) isn't as math-heavy as some others, Morrow, Game Theory for Political Scientists.

I'm currently a TA in a basic game theory for MSc students at a technical university. For the basic theoretical concepts we use as a course book Leyton-Brown & Shoham (2008) Essentials of Game Theory: A Concise, Multidisciplinary Introduction. This book is great because it is short and to the point, precise without diving deep into everything. Introduces most important concepts in less than 100 pages.

The original: Theory of Games and Economic Behavior, published in 1944 by Princeton University Press, by John von Neumann and Oskar Morgenstern the text that created the interdisciplinary research field of game theory, is still worth reading.

I really enjoyed Gintis's 'Game Theory Evolving', which focuses on evolutionary game theory. Mind you, I was a biologist when I was working with it, so that was much more relevant to what I was thinking about.

I learned Game Theory from this Open Yale course:

https://www.youtube.com/playlist?list=PL6EF60E1027E1A10B

24 excellent lectures by Ben Polak.

MIRI recommends Game Theory: An Introduction by Steven Tadelis

https://intelligence.org/research-guide/

I'm building some games for this topic for my startup [1]. But we won't have them ready until the spring.

[1] http://www.simcase.io

I hope you'll post something here when you launch. I like the ideas presented on the site but they are a bit vague right now.

I had a professor once classify GT as a sub set of statistical decision theory. Might be worth picking up a SDT text.

Does anyone ever read Theory of Games by von Neumann?

This is backwards. Decision theory, which is the foundation of inference in statistics today (Bayesian, minimax, etc. are all special cases of it) is formulated as a one player game. Certain things mesh nicely when you realize this. For example, we know that there is a Nash equilibrium for large classes of games if we allow random strategies. Likewise, for decision theory with nonconvex loss functions, optimal procedures are almost always random.

But: game theory of two or more players is qualitatively different. For a one player game, we speak of optimal strategies. For multiplayer, noncooperative games, Nash equilibria take what would seem to be the obvious generalization of that and twist it in a whole new direction.

"Decision theory is 1-player game theory" -- I think I saw this on LessWrong, once, but I can't find it now.

Theory of games is VERY old, predating most other groundbreaking work (Nash, Shapley, Myerson, etc.)

Look up game theory lectures on coursera