Insights into Game Theory: An Alternative Mathematical Experience

Citation

Hutton, D.M. (2009), "Insights into Game Theory: An Alternative Mathematical Experience", Kybernetes, Vol. 38 No. 6, pp. 1036-1037. https://doi.org/10.1108/03684920910973270

Understanding game theory through reading through interesting examples is an innovative way of being introduced to its mathematical basis. This book was written by Michael B. Maschler and his student Ein‐Ya Gura after a successful project that was designed to teach US high school students about the mathematics of game theory. Like all involved in teaching at that level, the idea was to “sweeten the pill” of learning about some difficult concepts. The ideas behind the project were transferred to this book so that they are presented through a structured set of examples followed by exercise sets that were carefully planned to cover the content of each chapter. An idea of the books structure is given by perusing the contents pages which outline the books four chief chapters. They are:

1. 1.

   Presented as the “stable marriage problem” which in essence is used by the authors to explain the Ga1e‐Shapley matching algorithm.

2. 2.

   By introducing and discussing the typical voting system, Arrow's impossibility theorem is covered.

3. 3.

   Concerns the cooperative, game theory and, covering Shapley value applied to cooperative games and also voting games. It gives an overview of the use of game theory which helps to analyse political organisations.

4. 4.

   Uses the Bankruptcy problem (Aumann and Maschler) for the particular case of a difficult inheritance rule.

Using these chapters with their well‐thought‐out examples, the reader is gently introduced to the insights of game theory in the least demanding way.

This is a book which is essentially an introduction to mathematical concepts and will appeal to anyone who wants to learn about a theory which has had application in a multitude of differing areas that directly affect so many of our ordinary activities as well as our more formal studies.

The authors' insights do indeed provide readers with “an alternative Mathematical Experience” as the title of this book promises and at the same time provides such an excellent guide to what game theory is about and how it is and has been applied.