Game Theory: Mathematical Models of Conflict

ISBN-13: 9781898563143 / Angielski / Miękka / 2000 / 300 str.

A. J. Jones

Opis

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

Recenzje

"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

Spis treści

The name of the game; Non-co-operative games; Linear programming and matrix games; Co-operative games; Bargaining models; Appendix I: Fixed point theorems; Appendix II: Some poker terminology; Solutions to problems; Index.