An Introduction to Game-Theoretic Modelling

(The following review is for the third edition of An Introduction to Game-Theoretic Modelling.  To read the 2002 review of the first edition please see An Introduction to Game-Theoretic Modelling.)

 

This text is an undergraduate-level introduction to the subject. The emphasis is clearly on concrete examples, often from population biology or social sciences, and not on theory. Accordingly, the games discussed have a finite number of participants.  The ideal student learning from the book is a college junior or senior who completed the Calculus sequence, had a class in Differential Equations and Linear Algebra, knows at least the basic notions of probability, and has access to a mathematical software package. That said, the author's intention was to make the book readable at different level so that readers who come from population biology or sociology could still get the big picture if not all the mathematical details. 

 

The raw data that the book has 395 pages is misleading. This reviewer found that the book has significantly more text than most mathematics books of that length. This is because of the focus on real-life examples mentioned above. The usual proposition-proof-lemma-proof-theorem-proof-corollary-proof structure is not present. 

 

There are plenty of exercises at the end of each chapter, and about every third one has an answer or hint included in the book. A solution manual is available for instructors. The book can be a good choice for a textbook IF the audience is right, that is, if the audience consists of students who know enough mathematics to fully appreciate it, but do not mind the lack of the usual theorem-proof style. Perhaps students of applied mathematics are the best market for this book. 

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Miklós Bóna (bona@ufl.edu) is a Professor and Distinguished Teaching Scholar at the University of Florida, and the author and editor of several books. His main research interest is Enumerative Combinatorics.