Tactical tomes for choosy people

For more than three decades, non-cooperative game theory has shaped the scope, character and central concerns of modern economic theory. The theory has had a far-reaching impact on the social sciences, providing a coherent foundation for the study of strategic interaction and making great strides in our understanding of the evolution of social institutions.

Until recently, there were few texts for undergraduates. The first two books reviewed here buck this trend. Since the first edition in 1999, Avinash Dixit and Susan Skeath’s Games of Strategy has established itself as the definitive entry-level text. The authors write in a non-technical language but do not compromise rigour; they do not sidestep the task of clarifying the rationality requirements implicit in the solution concepts.

Alongside a thorough discussion of the basic equilibrium concepts, they introduce readers to advanced areas such as evolutionary games, as well as interesting applications including voting, bargaining and auctions. In this edition, the authors have extensively rewritten and reorganised the core material on equilibrium concepts to enhance clarity. It is superior to all other books in the category.

Fiona Carmichael presents a brief, informal overview of the central equilibrium concepts and application to bargaining. A Guide to Game Theory illustrates each idea with simple examples, which should prove useful for students and instructors. The book does not flesh out the rationality requirements behind the different solution concepts, and its pared-to-the-bone approach does not make for an exciting read. But it can be used as a set of lecture notes, and teachers can elaborate on the ideas.

The book is not free of conceptual mistakes. The use of the first-order condition for an interior maximum in deriving a mixed-strategy Nash equilibrium is a classic student mistake, but not one a text should make.

Game Theory: A Critical Introduction is a specialised book that focuses on methodological foundations and discusses the basic solution concepts, evolutionary games and application to bargaining.

A chapter on the recently developed area of psychological games is a worthy addition. But the presentation is often opaque. The discussion of mixed strategies suggests, misleadingly, that equilibria in such strategies have something to do with beliefs over pure strategy equilibria.
The book is further marred by a lack of enthusiasm. Part of the intellectual excitement of game theory derives from the enormous gains made in our understanding of institutions and design of mechanisms.

Such topics are missing here. But postgraduates conversant with game theory should find this a useful text that addresses issues standard texts largely ignore.

Despite its influence, game theory was considered even a few years ago too difficult to be taught to undergraduates. The range of entry-level texts is a testimonial to the persuasive power of the theory. One hopes that these will pave the way for game theory to be taught in schools.

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