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Student Mathematical Library
2001; 368 pp; softcover
List Price: US$45
Member Price: US$36
Order Code: STML/11
Modelling in Healthcare
A Primer on the Calculus of Variations and Optimal Control Theory - Mike Mesterton-Gibbons
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
This book is about using game theory in mathematical modelling. It is an introductory text, covering the basic ideas and methods of game theory as well as the necessary ideas from the vast spectrum of scientific study where the methods are applied.
It has by now become generally apparent that game theory is a fascinating branch of mathematics with both serious and recreational applications. Strategic behavior arises whenever the outcome of an individual's action depends on actions to be taken by other individuals--whether human, as in the Prisoners' Dilemma, or otherwise, as in the "duels of damselflies". As a result, game-theoretic mathematical models are applicable in both the social and natural sciences. In reading this book, you can learn not just about game theory, but also about how to model real situations so that they can be analyzed mathematically.
Mesterton-Gibbons includes the familiar game theory examples where they are needed for explaining the mathematics or when they provide a valuable application. There are also plenty of new examples, in particular from biology, such as competitions for territory or mates, games among kin versus games between kin, and cooperative wildlife management.
Prerequisites are modest. Students should have some mathematical maturity and a familiarity with basic calculus, matrix algebra, probability, and some differential equations. As Mesterton-Gibbons writes, "The recurring theme is that game theory is fun to learn, doesn't require a large amount of mathematical rigor, and has great potential for application."
This new edition contains a significant amount of updates and new material, particularly on biological games. An important chapter on population games now has virtually all new material. The book is absolutely up-to-date with numerous references to the literature. Each chapter ends with a commentary which surveys current developments.
Advanced undergraduates, graduate students, and research mathematicians interested in mathematical modelling; applied mathematicians; biologists, social scientists, and management scientists.
"This book helps not only to make game theory accessible, but also to convey both its power and scope in a variety of applications. The books deals in a unified manner with the central ideas of both classical and evolutionary game theory. The key ideas are illustrated by a variety of well-chosen examples."
-- Zentralblatt MATH
"Mesterton-Gibbons' book deals with mathematical modelling, not by an abstract discussion of how modelling should be done, but rather by presenting many concrete examples ... The mathematics described [in the book] is fascinating and well worth studying ... The examples are great, and the author has clearly put enormous effort into building this collection ... a perfect source of problems for a Moore method course ... a valuable contribution to the literature ... Everyone interested in game theory or mathematical modelling should take a look at it."
-- MAA Online
From reviews for the First Edition:
"Readers will be hard-pressed to find a general introduction to game theory that blends biological and mathematical approaches more expertly. It is both a well-rounded survey and a reference work of lasting value."
-- Behavioral Ecology
"This book is an introduction to game theory with two specific features: it is written by a mathematician ... and it is written from the perspective of a mathematical modeller. This last characteristic implies that all chapters start with examples and the general concepts are only presented once the specific examples have been carefully developed ... I find this book excellent and ... worth considering when teaching an undergraduate course in game theory to students having some mathematical maturity (some calculus, some knowledge of matrix analysis and probability)."
-- Zentralblatt MATH
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