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Differential games in economics and management science
Dockner E. (ed), Jørgensen S. (ed), Van Long N. (ed), Sorger G. (ed), Cambridge University Press, New York, NY, 2000. 382 pp. Type: Book (9780521631259)
Date Reviewed: Jan 1 2002

Game theory has broad applications in applied mathematics, statistics and economics as well as operations management. It relies heavily on mathematical modeling. This text uses the principles of game theory to investigate problem solutions in economics and management science. The book is designed for graduate students and advanced undergraduates as well as practitioners of game theory in their respective industries. While the authors assume no prior knowledge of game theory to benefit from the book, a background in mathematics is probably essential for optimum benefit.

The text is divided into a theoretical section and a section on practical applications. After an introduction presenting an overview of the text, chapter 2 describes the basic concepts of game theory. The treatment is classical.

Chapter 3 discusses control theoretic methods and chapter 4 explains Markovian equilibria with simultaneous play. Chapter 5 continues with the theory of games by discussing differential games with hierarchical play. There is a chapter each on trigger strategy equilibria, differential games with special structures, and stochastic differential games.

Part 2 is the application section, using the theory developed in Part 1 in a practical setting. Chapter 9 contains applications on capital accumulation games. Chapter 10 explores industrial organization and oligopoly games.

The last two chapters, 11 and 12, treat differential games in marketing and differential games in resources and environmental economics. Of special interest to the reader is the further reading section found at the end of each chapter. This is well done and quite professional. There is also a series of exercises at the end of each chapter making the text appropriate for classroom use.

Reviewer:  James Van Speybroeck Review #: CR125602 (0201-0016)
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