Game Theory and Public Policy Roger A. McCain Edward Elgar, 2010, 272 pp., £15.96 (pb), ISBN 9781849805711

This is not the usual game theory textbook or reference, which requires the reader to pull out a paper and pencil if he or she is to follow the arguments developed by the author. Nor is it a beginner's text, with examples so easy that advanced high school students can easily follow the analysis. Rather, this book should be considered the ‘thinking man's’ game theory textbook or reference. McCain provides a very readable overview of a very wide range of the game theory literature. He explores both cooperative and non-cooperative games along with more abstruse equilibrium concepts of interest mainly to game theorists and perhaps a few experimentalists, and he does so with intuitive prose and illustrations that get the principles across without much mathematical clutter. His examples are often from public policy, which provides the link between game theory and public policy suggested by the title. However, the book is clearly more about game theory than about the use of game theory to think about public policy issues.

The book is organized as follows. Chapter 1 provides an overview of the project, which in the author's words is ‘to survey and advance our understanding of game theory as a tool of public policy analysis’ (p. 3). Chapter 2 provides an overview of several ways to represent games and of the main behavioural assumptions of game theory. By the end of Chapter 2, it is clear that this is not a beginner's book, although little formal mathematics is used and the prose is eminently readable. In just a few pages, McCain discusses extended and normal forms of games, non-cooperative and cooperative games, and alternative informational assumptions.

Chapter 3 provides a very nice condensed survey of the literature that focuses for the most part on the period after Von Neumann and Morgenstern's classic 1944 book, the Theory of Games and Economic Behavior. The summaries of classic work are often subtle, and McCain notes cases in which one author is responsible for an idea's formulation and other authors for developing it in a manner that attracts attention from other theorists and/or experimentalists. The chapter includes a good deal of coverage of important applications of game theory in economics and political science, selected from among work that also advances game theory. Among economic pieces, it includes summaries of work by Shapely and Shubik, Schelling, Nutter, Myerson, and Bernheim. Among work relevant for political scientists, it includes work by Aumann, Axelrod, Gibbard, and Satterwaite. In a few cases, one must know a bit about the mathematics of the papers and books surveyed to understand the contribution being summarized. In most cases, however, the summaries are so clear that a reader who is somewhat familiar with the main strands of applied game theory will gain a new appreciation for the manner in which various ideas entered into the game theoretic literature and lexicon. The chapter also notes several innovations that failed to catch on and/or were replaced by minor refinements deemed to be more useful than the original. In general, the survey focuses on ideas that played important roles in the development of game theory rather than on how ideas from game theory clarified or created new issues for social science or public policy analysis.

Chapter 4 covers what many political scientists and economists regard as the most useful of the tools from game theory: social dilemma and coordination games, and pure and mixed strategy equilibria. Chapter 5 covers games with correlated equilibria, that is to say, games in which many Nash equilibria exist and game players somehow manage to choose probabilistic strategies that are similar (correlated) to one another. Chapter 6 covers sequential and repeated games, and provides overviews of sub-game perfection, the folk theorem, and trembling hand equilibria. Again the choice of illustrations and careful writing allows a good deal of ground to be covered in a few pages without immersing readers in mathematical notation, proofs, or lemmas. Chapter 7 provides a brief overview of game theory's use in the mechanism design literature. In such cases, games are designed to promote particular ends, rather than be used as models of pre-existing social settings, although such designs are not always possible, as McCain's overview of the Arrow Impossibility Theorem suggests.

Chapter 8 provides an overview of coalition formation in cooperative games, covering such topics as the core, the nucleolus, and Shapely values. From this point on, the analysis necessarily becomes a bit more mathematical. Chapter 9 analyzes cases in which coalitions have different strategies available to them than the individual members had when acting alone, as may be said of specialization within firms and the internalization of other externalities in formal organizations. Chapter 10 provides a nice overview of the implicit assumptions of game theoretic representations of social circumstances. Among the topics covered are weakness of will, imperfect recall, and bounded rationality. This sort of chapter is rare in game theory textbooks and, as in much of the rest of the volume, the prose and illustrations are clear.

The next three chapters examine what the author refers to as encapsulated cooperation, games in which groups of players form more or less stable coalitions that select strategies to maximize joint interests of the members. The group members cooperate, but may engage in non-cooperative games with those outside the group. These are the most technical chapters in the book. The main points developed are that groups, rather than individuals, often engage in the selection of strategies, that some groups are more stable than others, and that assumptions about the behaviour of members (for example, degree of information and rationality) will affect the equilibria that may emerge. One point of particular interest is that some partitions (assignment of individuals to groups or coalitions) often yield greater total output (aggregate payoffs) than others. If these are stable, one may expect (or at least hope) that such partitions dominate others.

The concluding chapters apply some basic game theory models to characterize government and governmental decisions. Chapter 15 provides a nice coalition-based analysis of the Hobbesian dilemma. Chapter 16 provides a novel coalition-based analysis of class-based politics grounded in economic interests. These are mostly of interest as exercises that show how such models can be assembled in a more or less consistent manner using concepts developed earlier in the book. They demonstrate that cooperative and non-cooperative game theory can be combined to shed new light on old questions.

Overall, the McCain book is a thoughtful and thought-provoking survey of the post-war game theoretic literature. It is notable for its clear exposition, its willingness to acknowledge weaknesses and ambiguities of game theory, and its many illustrations. It would make an excellent text for students who have already learned a bit of game theory in earlier classes and who are open to broader issues than those covered in more mathematical and more elementary books. It is also good bedtime reading for academics who use a bit of game theory in their own work and for theorists who are interested in methodological issues associated with rational choice models. A pencil is occasionally useful, but mostly for underlining points of interest.