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Student Mathematical Library
2000; 159 pp; softcover
List Price: US$29
Member Price: US$23.20
Order Code: STML/5
Models of Conflict and Cooperation - Rick Gillman and David Housman
An Introductory Course on Mathematical Game Theory - Julio Gonzalez-Diaz, Ignacio Garcia-Jurado and M Gloria Fiestras-Janeiro
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.
"Fascinating, entertaining and enlightening reading."
-- European Mathematical Society Newsletter
From reviews of the German edition:
"The author, well known for various imaginative, entertaining and instructive writings in the area of game theory, and for his game-theoretic excursions into classical literature, has now brought out this delightful little book on the basics of noncooperative games ... [The book is] rewarding reading for a rather wide variety of reasonably well-educated persons. The reader will gain an appreciation for the mathematical modelling of conflict in economics, the social sciences and biology, and get a glimpse of game-theoretic analysis of conflict in some of the classical literature."
-- Zentralblatt MATH
"Through the amusing exposition of the material, overflowing with jokes and general culture, the new book by Alexander Mehlmann has become bedtime reading for me ... It is a pleasure to see such things as the Dilemma of the Arms Race, Goethe's Mephisto, the Chain-Store Paradox, and the Madness of Odysseus brought under one game-theoretic roof."
-- Eric Lessing (from a translation of "What I am reading" in Die Presse)
"The book is an erudite and entertaining account of noncooperative games and is designed for a broad audience. Newcomers to game theory are likely to find this book to be a playful introduction to the topic; whereas experts are likely to discover delightful new games to contemplate."
-- Journal of Mathematical Psychology
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