Reddit mentions of Playing for Real: A Text on Game Theory

Given your background, you could read Ken Binmore's Game Theory: A Very Short Introduction (2007). It's really short, but it assumes the reader is familiar with probability theory and a fair amount of mathematics. Binmore has another textbook Playing for Real (2007) which is goes much more in depth. It assumes the reader is familiar with linear algebra.

One of the central results of von Neumann and Morgenstern's Theory of Games and Economic Behavior (1928) is the minimax theorem. This was John von Neumann's favorite theorem from that book. John Nash generalized this in his PhD thesis in 1950. The minimax theorem establishes the existence of Nash equilibrium for zero-sum games with finite players and strategies. Nash's extended this and showed that any normal form game with finite players and strategies has an equilibrium. You might have seen the movie A Beautiful Mind which depicted John Nash working on this. If you are interested, you can read about Nash's proof in Luce and Raiffa's Games and Decisions: Introduction and Critical Survey (1957). The proof does assumes the reader is familiar with point set topology.

Outside of economics, game theory is also applied to evolutionary biology. One of the best books on evolutionary game theory is Martin Nowak's Evolutionary Dynamics: Exploring the Equations of Life (2006). You might also like John Maynard Smith's Evolution and the Theory of Games (1982). Maynard Smith assumes the reader is familiar with homogenous differential equations.

Hope this helps!

this is a nice intro book with lots of cool examples and problems: Playing for Real