Game Theory: Mathematical Models of Conflict (Horwood Series in Mathematics & Applications)

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. 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.

• 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

"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."--Jacket. Content: Dedication, Page i ABOUT OUR AUTHOR, Page ii Front Matter, Page iii Copyright, Page iv LIST OF FIGURES, Pages vii-viii Author's Preface, Pages ix-xi Glossary of Symbols, Pages xii-xiv 1 - The name of the game, Pages 1-46 2 - Non-cooperative Games, Pages 47-99 3 - Linear Programming and Matrix Games, Pages 100-160 4 - Cooperative games, Pages 161-209 5 - Bargaining Models, Pages 210-236 Appendix 1 - Fixed Point Theorems, Pages 237-238 Appendix II - Some Poker Terminology, Pages 239-241 Solutions to problems, Pages 242-280 INDEX, Pages 281-286 MATHEMATICS TEACHING PRACTICE, Pages ibc1-ibc3