Yet more players in game

Over the past 30 years, the development of game theory has revolutionised the nature and scope of economic analysis. Game theory investigates how individuals might think about strategic situations, and thereby builds theories of social interaction starting from the basic premise of individual self-interest. Wielding game-theoretical tools, economists have broadened their concerns to diverse areas such as the logic and design of institutions, design of law, voting and the structure of governance, evolution and even the foundations of social morality.

The rise of game theory to a central position in economic analysis has, over the past decade or so, led to a proliferation of textbooks on the subject. While these necessarily tend to repeat core material introducing solution concepts, the ever-expanding landscape of the field has led to some differentiation.

The book by Christian Montet and Daniel Serra is pitched at an undergraduate/advanced undergraduate audience and attempts the difficult task of presenting material with a minimum of formalism without abandoning logical rigour. While largely successful, at points the informality becomes too casual. For example, the analysis of repeated games is conducted without a clear definition of a strategy in such games. An abrupt reference to the revenue equivalence result, which appears with no explanation, is another case in point. Even a casual reading reveals other problems, such as confusion between "equilibrium" (which refers to strategies) and "outcome" (which refers to payoffs) in defining Nash equilibrium; the incorrect suggestion that the winning bid in a common-value auction is always greater than the value of the object. Such laxity detracts from the value of the book.

The main contributions are in chapters six and eight, which respectively introduce coalitions and experiments not covered by other texts. Students should find this a good starting point for an understanding of these important topics. Overall, the authors should be commended for approaching the difficult task of informal presentation of complex and subtle results.

Later editions should straighten out the kinks, making this a useful advanced undergraduate text.

Fernando Vega-Redondo's book is an authoritative text aimed at graduate students. He presents the basic material clearly, carefully explaining the rationality requirements implicit in the major solution concepts. The inclusion of a host of applications and a large number of exercises will please instructors and students.

Almost a third of the book is devoted to the analysis of evolution and learning, a first for a textbook at this level. The availability of such advanced material in a graduate text will have an impact on the content of many game theory courses. Given its clarity, thoroughness and breadth of coverage, this book will surely become one of the most valuable texts at graduate level, initiating a generation of students into the exhilarating pursuits of game theory.

Arup Daripa is lecturer in economics, Birkbeck, University of London.