Game Theory

For the past twenty years, I have taught an advanced undergraduate mathematics course on game theory. I have therefore examined most of the available textbooks on the subject, always searching for the best possible course text. Over the years, I have found a number of strong, well written textbooks for the first course in game theory, but in my estimation, the book "Game Theory" by Maschler, Solan and Zamir (MSZ) ranks well above the scores of other books I have examined; the clarity of writing, the command of the subject shown by the authors, and the amazing breadth of coverage (in just over 1,000 pages!) place this book in a class by itself.When my students (and occasionally, some of my colleagues) ask for my opinion on the best reference for independent study in game theory, I always recommend MSZ. This book is an ideal reference for any sufficiently well-prepared reader who wants to first learn the basic concepts of cooperative and non-cooperative game theory, and then explore some of the most exciting developments and applications of the subject. The book will serve the independent learner quite well, continuing to function as a definitive reference long after the basics have been mastered. For a student currently enrolled in a game theory course, MSZ will make an authoritative secondary reference to complement the course textbook.Prospective reader always worry about prerequisites. It is remarkable that considerable progress can be made in game theory with only a minimal background in undergraduate mathematics. Solid coursework in single and multivariable calculus, linear algebra, and basic probability theory provides adequate preparation to read many chapters in this book. Of course, there are some deeper results in the subject that draw upon more advanced mathematics; one example is Sperner's Lemma and the various fixed point theorems that are so foundational to this subject, as presented in Section 24.1. Readers who are not prepared for these more advanced proofs may omit them on a first study without suffering too strong a penalty; they may then return to these theorems later, as their mathematical background progresses.It is important to observe that all three authors are or were highly regarded mathematicians who conduct research in various areas of game theory (Maschler died in 2008). There are many books on game theory written by economists, social scientists, biologists, or practitioners of other academic disciplines. Quite naturally, these books tend to differ in style and substance from game theory books written by mathematicians. I will quote Maschler, Solan and Zamir [page xxvi] on this essential point:"This book was composed by mathematicians; the writing is therefore mathematically oriented, and every theorem in the book is presented with a proof. Nevertheless, an effort has been made to make the material clear and transparent, and every concept is illustrated with examples intended to impart as much intuition and motivation as possible."I can assure the prospective reader that the authors succeed in their efforts; the examples are numerous and selected from a broad spectrum of applications, and the writing, while precise in the manner that characterizes most mathematical prose, is engaging and accessible. Prospective readers may be assured that this is not a dusty, dessicated mathematical treatise of the "Theorem-Proof-Lemma-Proof" variety; it is an extremely engaging, pedagogically sound introduction to a remarkable subject, written with the necessary level of mathematical rigor in those places where rigor is necessary.A final observation is that at just over 1,000 pages, MSZ provides an ambitious breadth of coverage that is simply not found in any other introductory text. Game theory has undergone explosive expansion and development since its introduction in the 1944 book "The Theory of Games and Economic Behavior," by John von Neumann and Oskar Morgenstern. To date, approximately fifteen Nobel prizes have been awarded to researchers who applied game theory to economics and other social sciences, and one researcher received the Crafoord prize for work in evolutionary game theory. The economist and social scientist Herbert Gintis (1940--2023), who was a passionate supporter for the integrative use of game theory across all the social sciences, argued in his his 2009 book "The Bounds of Reason" that game theory could serve as the common language to bring about a "grand unification" of the behavioral sciences. All of this is to indicate that that game theoretic techniques reach deeply into economics, biology, anthropology, political science, sociology, social psychology, linguistics, and other academic areas. MSZ provides a wealth of fascinating examples and exercises drawn from each of these academic areas, thus introducing the reader to many of the most exciting applications of game theory currently under consideration.The second edition of MSZ differs from the first through the following additions: a new Section 5.8 on rationalizability and a new Section 5.10 on the dependence of Nash equilibria on the payoffs of the game; a new Section 13.7 on subgame perfectness in Chapter 13 on repeated games; and an entirely new Chapter 15 on stochastic games. Perhaps most importantly, many errors in the first edition have been corrected. For the reader who does not believe that these changes are essential to her or his purposes, copies of the first edition are still available (at the time of this review) at significantly discounted prices.

I'm hoping to get some useful information out of this book, but to call it an "undergraduate" text is totally inappropriate. The math is quite advanced throughout this book from beginning to end. It really only seems appropriate for extremely mathematically capable undergraduate students (like none I've ever known, but then I wasn't a math major--just subjects that relied heavily on applied, as opposed to, basic math). To me, this is clearly a graduate level text which presumes the knowledge of a ton of hard-core basic mathematics (and, again, I'm not mathematically illiterate). The text would have been vastly improved with more general summations of the implications of the mathematical results in non-mathematical terms. Only buy this if your mathematical abilities are top-notch.One last thing. If, like me, your interest in this subject is particularly due to finance, economics, and investing, this should be the last nail in the coffin that you should stick to index funds. Take into account, when you are going up against Wall Street, your competition is a huge number of highly-compensated people who have no trouble reading this book, and they still typically lose vs. the overall market returns. If you think you can do better, you're almost certainly dreaming--just go for the index.I'm keeping it, because I think I can get my money's worth out of the parts I can understand, and by sitting on my shelf this book does an excellent job of reminding me that I'm not as smart as I think I am, which is the best self-knowledge that nearly all investors can ever have drilled into their heads.

El mejor libro que se ha escrito sobre teoría de juegos en muchas dimensiones

Examples are spot on

The authors provide a solid foundation by introducing the basic concepts and techniques of game theory, including strategic games, extensive games, and coalitional games. They then delve into advanced topics such as Bayesian games, repeated games, and mechanism design, allowing readers to develop a deep understanding of the subject.The clarity of explanations is a standout feature of this book. The authors have taken great care to present complex concepts in a straightforward manner, using intuitive explanations and concrete examples. The inclusion of numerous real-world applications throughout the book helps to demonstrate the relevance and practicality of game theory in various domains. The authors also provide step-by-step solutions to exercises, enabling readers to reinforce their understanding and apply the concepts in practice."Game Theory" incorporates insights from recent research, making it a valuable resource for both newcomers and experienced researchers in the field. The authors include discussions on cutting-edge topics such as evolutionary game theory, network games, and learning in games, providing readers with a comprehensive overview of the latest advancements in game theory. This integration of contemporary research ensures that the book remains relevant and up-to-date.In comparison to other notable game theory textbooks, such as "Game Theory" by Drew Fudenberg and Jean Tirole, and "Game Theory: Analysis of Conflict" by Roger B. Myerson, "Game Theory" stands out for its comprehensive coverage, clear explanations, and inclusion of recent research. While Fudenberg and Tirole's book emphasizes economic applications and strategic analysis, and Myerson's book focuses on the mathematical foundations of game theory, Maschler, Solan, and Zamir's book strikes a balance between theory and applications, offering a broader perspective on the subject.