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Reviewer: Constantin S Chassapis

"The Internet is an equilibrium, we just have to identify the game." This quote from Scott Shenker appears in Christos Papadimitriou's dense and thought-provoking foreword to this book. The book discusses games (approached in the general way of being situations in which multiple participants interact or affect each other's outcomes), game equilibria, and the efficiency of computing the equilibrium of various games (that usually have an exponentially exploding solution-strategy space), including market equilibria, learning, graphical games, online auctions, routing games, peer-to-peer systems, manipulation-resistant reputation systems, and prediction markets. The book's theme, algorithmic information theory, is a relatively new discipline, which exists at the intersection of computer science, game theory, and economic theory. This is a big book at almost 800 pages, containing 29 state-of-the-art, lengthy papers written by more than 40 contributors. The papers are organized into four parts: "Computing in Games," "Algorithmic Mechanism Design," "Quantifying the Inefficiency of Equilibria," and "Additional Topics." The second part, which I found especially interesting, discusses how to design games whose equilibria can be efficiently computed. In this part, the algorithmic efficiency and computational complexity of a solution come into play; the epistemological benefits of game theory and computer science cross-fertilization are clearly shown. This very interesting book is capable of serving as a textbook for a two-semester course, since many chapters have exercises. In addition, there are basic chapters on game theory, algorithmic methods for equilibria, mechanism design, and combinatorial auctions. There are also more advanced chapters, written by top researchers in the field, on incentives and pricing, cost sharing, information markets, and cryptography and security. This book is well suited for the informed student, researcher, or professional. Online Computing Reviews Service

Reviewer: Jeremy A Hansen

The field of algorithmic game theory has its roots in efforts to probe the strategic social and economic interactions of the Internet, according to this book. The field, roughly ten years old, is an amalgam of game theory and algorithms, and has applications in economics, information security, network routing, and peer-to-peer networks. The text is broken up into four explicit parts: “Computing in Games,” “Algorithmic Mechanism Design,” “Quantifying the Inefficiency of Equilibria,” and “Additional Topics.” A more detailed table of contents, and an overview of the individual chapters, can be found online (http://theory.stanford.edu/~tim/agt/toc_brief.html). The first three sections (22 chapters) are fairly dense, and might be daunting to readers not already on a solid footing in theoretical computer science, algorithms, and game theory. The editors claim that their target audience is beginning computer science graduate students, but several of the chapters, particularly those discussing mechanism design, may be inaccessible to nonspecialist students. To be fair, the first few chapters do a reasonably good job of introducing the relevant topics required to understand the later chapters. Throughout these first three sections, one gets the feeling that the editors spent a good deal of time ensuring the cohesiveness of the individual chapters, as they flow well. Several times I noticed that a chapter left a thread of a topic hanging, only to discover that thread picked up in a later chapter. Sprinkled throughout the first three sections, and more frequently in the final seven chapters, are interesting applied topics. These topics include auctions, distributed protocol design, cryptographic applications of game theory, peer-to-peer systems, incentives in information security, and prediction markets. As this is intended to be a textbook, most chapters have exercises, but several do not. Tangentially, this is the first book where I have seen open problems posed as exercises for students to work through as far as they can, a feature I would love to see in other computer science texts. Besides exercises for those chapters missing them, something that would help the reader in the next edition of this book would be a glossary of terms across all of the chapters, especially for courses that cover the chapters out of order. I appreciate the open problems also included in many of the chapters, separate from the exercises: I am certain that several of the gems presented would turn into great theses should enterprising graduate students decide to pursue them. Overall, this is a solid, useful book that will serve seasoned graduate students well (even if not in the context of a course), both in rounding out their depth, and potentially as a source of thesis topics in the intersection of the fields of algorithms and game theory. Online Computing Reviews Service