I'd also recommend Ken Binmore's Game Theory: A Very Short Introduction.
His book is also great (http://gametheory101.com/textbooks/), but mostly a reiteration of the videos.
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.
https://www.youtube.com/playlist?list=PL6EF60E1027E1A10B
24 excellent lectures by Ben Polak.
Does anyone ever read Theory of Games by von Neumann?
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.