Game Theory Basics

Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.

1. Nim and Combinatorial Games; 2. Congestion Games; 3. Games in Strategic Form; 4. Game Trees with Perfect Information; 5. Expected Utility; 6. Mixed Equilibrium; 7. Brouwer's Fixed-Point Theorem; 8. Zero-Sum Games; 9. Geometry of Equilibria in Bimatrix Games; 10. Game Trees with Imperfect Information; 11. Bargaining; 12. Correlated Equilibrium.

Bernhard von Stengel, educated in the US and Germany, is a mathematical game theorist at London School of Economics and Political Science, and an authority on computational and geometric methods for solving games. He chaired the 2016 World Congress of the Game Theory Society, and is a senior editor for leading journals on mathematical game theory.