Mathematical Foundations of Game Theory

The book under review is a solid mathematical introduction to strategic games. A good thing about the book is that almost all important results required in such a book are proved here and is for the most part self-contained. The book is based on a series of lectures and as such the tone may be slightly different at least in the first few chapters then what one would expect. Although it is a relatively short book, the exposition is not terse and is quite well-written.

 

The preface already contains a very well written summary of the chapters in the book, which we will not repeat. We just mention some of the sequence of topics discussed: a general introduction to strategic games, zero-sum games in normal forms as well as general-sum games, games in extended form and repeated games, etc. There are enough examples in each chapter with easy to understand tables and figures. The exercises also cover extensions of the material in the text and hints to solutions are generously provided at the end.

 

At places the book also has some nice historical remarks, and each chapter ends with comments which direct to other resources or give new information on the subject matter. The bibliography is also adequate. Given the length of the book, there is not much scope for discussing detailed applications of several topics which doesn’t really feel like a drawback. This book can be recommended to graduate students as undergraduate knowledge of analysis, linear algebra and probability theory is assumed. Researchers in the area might also find the book handy for teaching a graduate course based on this.

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Manjil Saikia (manjil@saikia.in) is presently at Cardiff University, UK. He studied mathematics at Tezpur (India), Trieste (Italy) and Vienna (Austria), and manages the bilingual (Assamese and English) website Gonit Sora (https://gonitsora.com).