Review of Game Theory, Alive

Game Theory, Alive is a wonderful book and is to be highly recommended, either for teaching or self-study. By way of comparison, it covers fewer topics and is less advanced than the well known book Game Theory, by M. Maschler, E. Solan, and S. Zamir. For this reason, it seems ideal for a first course on Game Theory at the undergraduate level. Since Game Theory, Alive assumes some basic knowledge of probability theory (in addition to discrete math), students should have some probability theory as a background, though much of the book is still very accessible without it. This reviewer would not be surprised if Game Theory, Alive becomes the standard text for an introductory course on Game Theory. It is very well written and fun to read. The numerous figures, cartoons (see, e.g., Figure 6 on page xxi), photos, anecdotes, and especially, the historical summaries at the end of each chapter as well as the backgrounds of the mathematicians, statisticians, and economists whose results now go into Game Theory, is one of the loveliest features of this book. Wikipedia notwithstanding, we often don't learn enough about the 'players' themselves, their history and/or the evolution of how a result came into being (at least in this reviewer's primary field of study, which is not game theory or even probability theory), and this book very nicely bucks that trend. The most important caveat I should state here is that I am not myself in game theory or combinatorics, so my review of this book cannot be as deep as that of a practitioner in either of these fields. That is unfortunate, but the plus side of this is that I can make the following comment: to me, the most beautiful feature of this book is how nicely-and yet how compactly-the authors convey intuition and motivation, which is the most important thing a textbook can do for someone approaching the field for the first time. And to do so while at the same time presenting everything mathematically-definitions, theorems, proofs-is not easy.