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Game Theory Basics

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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.

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  • A detailed, accessible introduction to the mathematics of games, written for students meeting the topic for the first time
  • Based on over 15 years of teaching experience, ensuring that it is ideal for both self-study and course use
  • Starts from examples and gives complete, self-contained and clear proofs as well as numerous exercises, fostering a solid understanding of the fundamentals of game theory
Author: von Stengel Bernhard
Publisher: CAMBRIDGE UNIVERSITY PRESS
Pages: 374
ISBN: 9781108824231
Cover: Paperback
Edition Number: 1
Release Year: 2021

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.

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