The game-theoretic revolution of the past three decades left in its wake formidable barriers to entry for those without formal training in game theory. In recent years, the barriers have been lowered by the publication of several excellent graduate and advanced undergraduate textbooks. However, choosing an introductory undergraduate text, or a book for a friend who wished to fully understand game theory and its applications to economic, political, and social interactions, has remained an awkward compromise between depth, accessibility, and appropriateness of coverage. Most graduate and advanced undergraduate game theory texts assume some familiarity with game theory and considerable mathematical background, including at least multivariable calculus. Others offer elementary expositions for specialized audiences, with goals too sharply focused for most students or for readers seeking a general introduction. And the best books targeted at general audiences motivate and illustrate game-theoretic analyses without fully explaining its methods.
Games of Strategy makes the compromise much easier. It conveys a deep understanding of game theory and its applications with almost all of the accessibility and readability of my favorite book on game theory for general audiences, Thinking Strategically by Avinash Dixit and Barry Nalebuff (New York: W.W. Norton & Company, 1991). The exposition assumes no prior familiarity with game theory or economics; and it is mathematically elementary in that only knowledge of algebra is assumed, supplemented with some optional alternative arguments using calculus. This unusual combination of strengths makes Games of Strategy an ideal self-contained text for first- and second-year or more advanced undergraduates; excellent background reading for graduate students; and a good introduction for general readers. I believe that almost anyone with sufficient desire to understand and the patience to work through its arguments could read it with profit. Many readers will find it challenging because of the inherent difficulties of its subject, but there are no avoidable barriers to understanding.
The introductory chapter is a tour de force of motivating examples from economics, political science, sports, and daily life (some borrowed from Thinking Strategically), which provides a good illustration of the authors' expository strategy. Each example is artfully chosen to illustrate one of the central puzzles in the analysis of strategic behavior that a successful theory of games must resolve: the need for unpredictability in certain zero-sum games, the tension between individual incentives and efficiency in prisoner's dilemmas and related games, the difficulty of coordination, the value of commitment, the benefits of brinkmanship, and the importance of signaling. Collectively the examples create enough intellectual suspense that many readers who might otherwise be daunted by the material to come may find it difficult to put the book down.
The introductory chapter powerfully conveys the authors' conviction that game theory can usefully be applied in all aspects of life. This conviction pervades the book, and I suspect explains much of its power to engage students and general-interest readers. It apparently extends even to the interaction between authors and readers, for the first chapter's examples are a kind of up-front payment whose ultimate value is immediately apparent, but can only be realized by reading further—a stratagem to entice readers to make a risky but highly productive investment.
I cannot resist mentioning a more amusing illustration of the authors' faith in the universality of game theory, from a footnote to the discussion of the "dollar" or "all-pay" auction on p. 504: It seems that Dixit once whimsically sought to augment his students' customary round of polite end-of-course applause by offering $20 to the one who applauded continually the longest. Most students dropped out quickly, as expected, but three kept applauding for four and one half hours! The "once" in the authors' account of this episode made me wonder what the unfailingly courteous Dixit did during all that time, and whether the experience produced an unwelcome experimental discovery that even artificially induced courtesy can compel costly reciprocation.
In subsequent chapters the authors use the ideas and methods their examples so vividly evoke to organize a meticulous and exceptionally clear exposition of the basic ideas of game theory and some of its leading applications, which provides a strong foundation for further study. Their exposition of the theory is frequently supplemented by careful discussion of pertinent experimental results, an indicator of the increasing integration of theoretical and experimental methods in game theory. The result is an account rigorously organized around core theoretical ideas and principles, each introduced, clarified, and enlivened by concrete examples of evident relevance. Of particular note are the excellent treatments of games in which players can change the rules; Thomas Schelling's theory of strategic moves; brinkmanship and the Cuban Missile crisis, incorporating some fascinating historical information that became available after the excellent discussion in Thinking Strategically was written; and Schelling's theory of games played repeatedly in populations, the social-science analogue of evolutionary game theory.
Games of Strategy is a detailed, accurate, and highly entertaining exposition, which will open up a new world for novices and has the potential to change the way even specialists think about the uses of game theory as a tool for analyzing economic, political, and social interactions.
Vincent P. Crawford
University of California, San Diego