This item is in: Mathematics > Applied mathematics

Game theory: Mathematical models of conflict

A J Jones, University of Cardiff, UK

Begins with saddle points and maximax theorem results. Readers should be able to solve simple two-person zero-sum games. It analyses non-cooperative games (Nash equilibrium), linear programming and matrix games, and co-operative games (Edgeworth trading model). Detailed solutions are provided to all problems.
Choice

 - balances a light touch with a rigorous yet economical account of the theory of games and bargaining models
 - shows basic ideas of extensive form, pure and mixed strategies, the minimax theorem, non-cooperative and co-operative games, and a ‘‘first class’’ account of linear programming, theory and practice
 - based on a series of lectures given by the author in the theory of games at Royal Holloway College

Written engagingly and with agreeable humour, this book balances a light touch with a rigorous yet economical account of the theory of games and bargaining models. It provides a precise interpretation, discussion and mathematical analysis for a wide range of “game-like” problems in economics, sociology, strategic studies and war.

There is first an informal introduction to game theory, which can be understood by non-mathematicians, which covers the basic ideas of extensive form, pure and mixed strategies and the minimax theorem. The general theory of non-cooperative games is then given a detailed mathematical treatment in the second chapter. Next follows a “first class” account of linear programming, theory and practice, terse, rigorous and readable, which is applied as a tool to matrix games and economics from duality theory via the equilibrium theorem, with detailed explanations of computational aspects of the simplex algorithm.

The remaining chapters give an unusually comprehensive but concise treatment of cooperative games, an original account of bargaining models, with a skillfully guided tour through the Shapley and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.

ISBN 1 898563 14 4
ISBN-13: 978 1 898563 14 3
December 2000
300 pages  242 x 169mm  paperback  
£55.00 / US$95.00 / €65.00

Usually dispatched within 24 hours

An e-book version of this title is available to purchase as part of a Collection or Pick n Mix or by Chapter. Visit Woodhead Publishing Online

Titles which may also be of interest:
Ordinary differential equations and applications
Delta functions

Contents

The name of the game

Non-co-operative games

Linear programming and matrix games

Co-operative games

Bargaining models

Appendix 1. Fixed Point Theorems

Appendix II. Some Poker Terminology

Solutions to problems