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.
A lively introduction to Game Theory, ideal for students in mathematics, computer science, or economics.
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.
'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.' Françoise
Forges, Université 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.' Hervé 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.' Jörgen
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
'… 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
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