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Game Theory Basics
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Table of Contents

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.

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

About the Author

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.

Reviews

'This looks like a fine introduction to game theory, inter alia emphasizing methods for computing equilibria, and mathematical aspects in general. Especially worthy of note is the chapter devoted to correlated equilibria, a topic of central importance not normally covered in introductory texts.' Robert Aumann, The Hebrew University of Jerusalem
'This book is a delightful adventure into the mathematics of game theory. Without any heavy apparatus, it lets us into the secrets of a whole range of exciting results that are usually thought too advanced for the common herd. It is not only undergraduate students who will benefit from reading this book. Professional game theorists will find it very useful too.' Ken Binmore, University College London
'Bernhard von Stengel's book will enable students to become intimately familiar with game theoretic reasoning, which is mathematical by nature. The text comes at the right time: Game theory has become so popular in economics and political science that teachers could be tempted to put the cart before the horse. Here, the basic noncooperative game models are studied gradually and thoroughly, in a unified way, while providing the algorithms that can be used to solve interactive decision problems.' Francoise Forges, Universite Paris-Dauphine
'This is a rather reader-friendly, engaging, and polished superior creation. It illustrates, explains, motivates every definition, theorem, proof. Interesting and unique choice of topics, such as a delightful introductory chapter on combinatorial games. Highly recommended.' Aviezri Fraenkel, Weizmann Institute of Science, Israel
'A masterful presentation of mathematical game theory in all its beauty and elegance, from basic notions to advanced techniques. It fills the gaps left by the many textbooks that cover concepts and applications, but devote only the bare minimum to the mathematical tools and insights, without which game theory would not have become the success it is today.' Sergiu Hart, The Hebrew University of Jerusalem
'Game Theory is the child of mathematicians, as this textbook demonstrates through self-contained, elegant proofs of all seminal Theorems. The lively and rigorous exposition of carefully selected models, such as bargaining, combinatorial and congestion games (the latter two rarely the stuff of textbooks) explains its success far beyond mathematics. To reach deep results on both sides of the theory, Bernhard von Stengel's marvellous learning tool uses uncompromising, yet accessible mathematics and chooses examples to maximal effect.' Herve Moulin, University of Glasgow
'This will become a classic textbook on non-cooperative game theory. It is very useful for mathematicians, computer scientists, and economic theorists. Each chapter has a clear learning structure, with motivating examples and a central main theorem. The author's long teaching experience and expertise in game theory is apparent on every page.' Abraham Neyman, The Hebrew University of Jerusalem
'Attractively covers of a lot of important material, in particular for students of mathematics and computer science.' Eva Tardos, Cornell University
'This book is a gem. The presentation is clear and well structured, often with nice geometric illustrations. It moves step by step from basics to powerful concepts, methods and results. It is ideal for students of mathematics, computer science and economics who are curious about what game theory is and how it can be used.' Joergen Weibull, Stockholm School of Economics
'This excellent text develops with clarity and precision the basic concepts and mathematical tools of game theory, enhanced by well-motivated examples, exercises, and practical applications.' Robert Wilson, Stanford University
'An exceptionally lucid introduction to the fundamentals of game theory, enlivened by examples that are sure to captivate students.' Peyton Young, University of Oxford
'This is a rigorous, yet accessible introduction to mathematical non-cooperative game theory. In addition to the coverage of the basic concepts and results, it includes special and advanced topics and applications usually not contained in game theory textbooks, such as combinatorial games, congestion games and inspection games. The special emphasis on algorithmic and computational techniques make this textbook, just like its author, a valuable bridge between game theory and computer sciences.' Shmuel Zamir, The Hebrew University of Jerusalem

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