The Dover reprint of Steven Brams’ Game Theory and Politics wraps a shiny new cover around an influential thirty year-old classic. While the mathematically inclined reader may not find much theory or proof, the book is highly effective in achieving its goal “to demonstrate, mostly by example, the relevance of the mathematical theory to the explication of strategic features of actual political situations.” This makes it a valuable reference for much of the early work done in applied game theory and a catalog of all sorts of interesting examples.
Supported by an assortment of tables and figures (about 25 of each), the book introduces and develops many standard topics of the theory through the author’s own categorization of games (international, voting, vote-trading, coalition, and election) and power indices. The reader will encounter major developments such as Arrow’s theorem (alias, the paradox of voting) alongside specialized models and applications such as the battle of Bismarck Sea. For those who desire an introduction to or enhancement of game theory that flows from examples, especially political examples, Game Theory and Politics has much to offer.
It goes without saying (but I say it anyway), that there have been dramatic developments in game theory over the past thirty years not treated in this reprint. This detracts little from the book’s very helpful glossary, but its nicely annotated bibliography cannot help but come up short in view of the many developments in game theory over the past several decades. Nonetheless, there may be a new generation of students and scholars who can benefit from keeping this book in print.
Ed Packel is Volwiler Professor of Mathematics at Lake Forest College. He has published four books and approximately 40 papers in areas that include functional analysis, social choice theory, game theory, and information-based complexity.