The Game’s Afoot! Game Theory in Myth and Paradox
About this Title
Alexander Mehlmann, Vienna University of Technology, Vienna, Austria. Translated by Professor David Kramer
Publication: The Student Mathematical Library
Publication Year 2000: Volume 5
ISBNs: 978-0-8218-2121-3 (print); 978-1-4704-1820-5 (online)
MathSciNet review: MR1756263
MSC: Primary 00A08; Secondary 91A40
This volume is not part of this online collection, but can be purchased through our online bookstore.
It all started with von Neumann and Morgenstern half a century ago. Their Theory of Games and Economic Behavior gave birth to a whole new area of mathematics concerned with the formal problems of rational decision as experienced by multiple agents. Now, game theory is all around us, making its way even into regular conversations. In the present book, Mehlmann presents mathematical foundations and concepts illustrated via social quandaries, mock political battles, evolutionary confrontations, economic struggles, and literary conflict. Most of the standard models—the prisoners' dilemma, the arms race, evolution, duels, the game of chicken, etc.—are here. Many non-standard examples are also here: the Legend of Faust, shootouts in the movies, the Madness of Odysseus, to name a few.
The author uses familiar formulas, fables, and paradoxes to guide readers through what he calls the “hall of mirrors of strategic decision-making”. His light-hearted excursion into the world of strategic calculation shows that even deep insights into the nature of strategic thought can be elucidated by games, puzzles, and diversions.
Originally written in German and published by Vieweg-Verlag, this AMS edition is a translation tailored for the English-speaking reader. It offers an intriguing look at myths and paradoxes through the lens of game theory, bringing the mathematics into sharper focus at the same time. This book is a must for those who wish to consider game theory from a different perspective: one that embraces science, literature, and real-life conflict.
The Game's Afoot! would make an excellent book for an undergraduate course in game theory. It can also be used for independent study or as supplementary course reading. The connections to literature, films and everyday life also make it highly suitable as a text for a challenging course for non-majors. Its refreshing style and amusing combination of game theoretic analysis and cultural issues even make it appealing as recreational reading.
Mathematicians of any level; educators interested in game theory, economics, and social and behavioral sciences; general readers with an interest in serious mathematics at its most playful.
Table of Contents
Part 1. The glass bead game
- Introduction to Part I
- Chapter 1. Games, form(ula)s, and scholars
- Chapter 2. Equilibrium and game as metaphor
- Chapter 3. In the forest of game trees
- Chapter 4. Games against time
Part 2. The myths of game theory
- Introduction to Part II
- Chapter 5. The prisoner’s dilemma
- Chapter 6. Paradoxes of backward induction
- Chapter 7. Strategic accents of game-theoretic scholasticism
- Chapter 8. Odysseus goes to war
- A postlude in rhyme
- Appendix. Games in the network of networks