Game Theory

Cambridge University Press are up to their old tricks again. The description of the book states that a solution manual comes with this edition. However the solution manual is for lecturers only; only available to those who use the book as a set text.

Este é um livro acadêmico e pressupõe conhecimentos de matemática e álgebra linear. É um verdadeiro compêndio de Teoria dos Jogos, escrito por alguns dos maiores colaboradores pela evolução deste ramo da ciência.

I own a hardcover version of the first edition of this excellent book. I decided to purchase the second edition (also hardcover) for the additional topics and the errata present in the earlier edition and print. The production quality of this second edition is definitely inferior to the first edition for two reasons - paper quality and the binding (see photo). It is a real pity that Cambridge University Press did not pay attention to the production of this excellent book. I can imagine the authors will be disappointed as well.

Sometimes you buy these expensive textbooks that look like they were printed on one-ply toilet paper, this book is no such case.

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.

Es de los mejores libros de teoría de juegos, Pero asume que sabes muchas cosas que no tienes porqué saber. No creo que sea un libro pensado para estudiarlo de manera autodidacta como es mi caso. Si tienes pensado empezar con la teoría de juegos no creo que sea una buena idea empezar por este libro porque además las explicaciones matemáticas no tienen todos los pasos explícitos.