Game theory. An introduction.

*(English)*Zbl 1142.91001
Wiley-Interscience. Hoboken, NJ: John Wiley & Sons (ISBN 978-0-470-17132-5/hbk; 978-1-118-03239-8/ebook). xx, 415 p. (2008).

This is a well-written introduction to the theory of games, with a strong mathematical flavor, but with a good selection of applications. It is appropriate as a textbook for an undergraduate course at the sophomore level or above; students should have had at least a year of calculus and some linear algebra and probability. For some of the book, differential equations and some advanced calculus would be helpful. The course would be well-suited for students majoring in mathematics or economics, but some students of the behavioral or life sciences will also find it of interest.

The chapter headings are (1) Matrix Two-Person Games, (2) Solution Methods for Matrix Games, (3) Two-Person Nonzero Sum Games, (4) \(N\)-Person Nonzero Sum Games with a Continuum of Strategies, (5) Cooperative Games, and (6) Evolutionary Stable Strategies and Population Games.

A solid one-semester course might include most of the first five chapters. In Chapter 5, the theory of the core, nucleolus and the Shapley value are presented. The book uses Maple to find values and strategies, but to use Maple and the commands to solve any games the student has to know what is going on with the game theory and then use Maple to do the computations. There are appendices on the basics of linear algebra, probability, Maple and Mathematica, and brief biographies of John von Neumann and John Forbes Nash.

The chapter headings are (1) Matrix Two-Person Games, (2) Solution Methods for Matrix Games, (3) Two-Person Nonzero Sum Games, (4) \(N\)-Person Nonzero Sum Games with a Continuum of Strategies, (5) Cooperative Games, and (6) Evolutionary Stable Strategies and Population Games.

A solid one-semester course might include most of the first five chapters. In Chapter 5, the theory of the core, nucleolus and the Shapley value are presented. The book uses Maple to find values and strategies, but to use Maple and the commands to solve any games the student has to know what is going on with the game theory and then use Maple to do the computations. There are appendices on the basics of linear algebra, probability, Maple and Mathematica, and brief biographies of John von Neumann and John Forbes Nash.

Reviewer: Gerald A. Heuer (Moorhead)

##### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91A05 | 2-person games |

91A06 | \(n\)-person games, \(n>2\) |

91A10 | Noncooperative games |

91A12 | Cooperative games |