GAME THEORY EXPLAINED: A Mathematical Introduction with Optimization

This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.

Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash's proof of the existence of mixed strategy equilibria in general sum games. On the way, u...