I often find myself deliberately avoiding books that are based on university courses. In my experience, such books tend to feel rushed and thrown together rather than carefully planned out. So it was with some trepidation that I sat down to read Tim Roughgarden’s *Twenty lectures on algorithmic game theory*, a book that grew from his Stanford course on algorithmic game theory. Within a few pages it became clear that this was not like other books based on university courses; it is an engaging, practical, and well-thought-out text.

The book’s 20 chapters aim to introduce the reader to the key concepts that lie at the intersection of computer science, game theory, and economics. Each “lecture” (chapter) focuses on a single topic of interest, starting with basic concepts central to game theory such as optimal behavior and mechanism design; the later chapters then deal with topics in more detail, specifically the price of anarchy theory and the computation of equilibria.

One of the strong points of this book is that each chapter follows a similar structure, making it effective as both a general reader in the topic area and a quick reference. A chapter begins with a brief sentence or two outlining its content and purpose. The main body of each chapter covers the details of the topic in question (more on which later), and the chapter ends with notes, exercises, and a useful “upshot” box. The upshot box contains a list of key points from the lecture. I found these simple devices incredibly useful, as they allowed me to check whether I had understood everything that was highlighted as an upshot of the chapter. It is worth pointing out that the exercises and problems are among the best I have seen in an academic text of this kind. In some texts, the exercises at the end of each chapter can feel forced and do nothing to aid the reader in understanding the topic further. In this book, the exercises are well thought out and challenging. Hints to selected exercises and problems are provided at the end of the book to help the reader if they get stuck.

So, what about the main text of this book? I have already mentioned that the start and end of each chapter are strong. It is worth reinforcing at the start what Roughgarden mentions in the preface: the content is deliberately condensed and terse. This means that time is needed to think through and unpack what is being taught. I found it useful to read this book with a pen and paper in hand, scribbling notes that I could refer to later on. This should not be seen as a negative; in fact, it forces the reader to spend time understanding the concepts (while keeping the book to an approachable length).

I found this book to be an engaging introduction to the field of algorithmic game theory, but the reader must be willing to spend time unpacking the content and undertaking the exercises to get the most from it. I would happily recommend it to any advanced-level undergraduate or postgraduate with a solid mathematical grounding who is interested in learning more about this field. It is worth noting that there is also a series of online videos relating to the lectures on which this book is based [1].

Do not be put off; this is not like other textbooks based on university courses. I would recommend anyone with a passing interest in game theory to pick up this book and read it through; I don’t think you will be disappointed.

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