Game Theory Basics

A lively introduction to Game Theory, ideal for students in mathematics, computer science, or economics.

Bernhard von Stengel (Author)

9781108824231, Cambridge University Press

Paperback / softback, published 19 August 2021

374 pages
24.6 x 18.9 x 1.8 cm, 0.79 kg

'… while the textbook would be ideal for students of mathematics and computer science, the care with which any formal analysis is presented should also make it highly accessible to students from other fields, such as economics or political science.' Ronald Stauber, Economic Record

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.

Subject Areas: Algorithms & data structures [UMB], Game theory [PBUD], Microeconomics [KCC]