This text presents an easy-to-read introduction to the basic ideas and techniques of game theory. It begins by discussing combinatorial games-a topic often neglected in other texts-and then moves to two-person zero-sum games. The final chapter explores the concepts and tools of non-zero-sum games and games with more than two players. Suitable as a textbook, for self-study, and as a reference, this introduction prepares readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.
This text presents an easy-to-read introduction to the basic ideas and techniques of game theory. It begins by discussing combinatorial games-a topic often neglected in other texts-and then moves to two-person zero-sum games. The final chapter explores the concepts and tools of non-zero-sum games and games with more than two players. Suitable as a textbook, for self-study, and as a reference, this introduction prepares readers for more advanced study of game theory's applications in economics, business, and the physical, biological, and social sciences.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Introduction. Combinatorial Games. Two Person Zero Sum Games. The Simplex Method. The Fundamental Theorem of Duality. Solution of Two Person Zero Sum Games. Non Zero Sum Games and k Person Games. Appendices: Finite Probability Theory. Utility Theory. Nash's Theorem. Answers to Selected Exercises. Bibliography.
Preface
Introduction
1 Combinatorial games
1.1 Definition of combinatorial games
1.2 Fundamental theorem of combinatorial games
1.3 Nim
1.4 Hex and other games
1.5 Tree games
1.6 Grundy functions
1.7 Bogus Nim-sums
1.8 Chapter summary
2 Two-person zero-sum games
2.1 Games in normal form
2.2 Saddle points and equilibrium pairs
2.3 Maximin and minimax
2.4 Mixed strategies
2.5 2-by-2 matrix games
2.6 2-by-n, m-by-2 and 3-by-3 matrix games
2.7 Linear programming
2.8 Chapter summary
3 Solving two-person zero-sum games using LP
3.1 Perfect canonical linear programming problems
3.2 The simplex method
3.3 Pivoting
3.4 The perfect phase of the simplex method
3.5 The Big M method
3.6 Bland's rules to prevent cycling
3.7 Duality and the simplex method
3.8 Solution of game matrices
3.9 Chapter summary
4 Non-zero-sum games and k-person games
4.1 The general setting
4.2 Nash equilibria
4.3 Graphical method for 2 Ã- 2 matrix games
4.4 Inadequacies of Nash equilibria & cooperative games
4.5 The Nash arbitration procedure
4.6 Games with two or more players
4.7 Coalitions
4.8 Games in coalition form
4.9 The Shapley value
4.10 The Banzhaf power index
4.11 Imputations
4.12 Strategic equivalence
4.13 Stable sets
4.14 Chapter summary
5 Imperfect Information Games
5.1 The general setting
5.2 Complete information games in extensive form
5.3 Imperfect information games in extensive form
5.4 Games with random effects
5.5 Chapter summary
6 Computer solutions to games
6.1 Zero-sum games - invertible matrices
6.2 Zero sum games - linear program problem (LP)
6.3 Special Linear Programming Capabilities
6.4 Non-zero sum games - linear complementarity problem (LCP)
Introduction. Combinatorial Games. Two Person Zero Sum Games. The Simplex Method. The Fundamental Theorem of Duality. Solution of Two Person Zero Sum Games. Non Zero Sum Games and k Person Games. Appendices: Finite Probability Theory. Utility Theory. Nash's Theorem. Answers to Selected Exercises. Bibliography.
Preface
Introduction
1 Combinatorial games
1.1 Definition of combinatorial games
1.2 Fundamental theorem of combinatorial games
1.3 Nim
1.4 Hex and other games
1.5 Tree games
1.6 Grundy functions
1.7 Bogus Nim-sums
1.8 Chapter summary
2 Two-person zero-sum games
2.1 Games in normal form
2.2 Saddle points and equilibrium pairs
2.3 Maximin and minimax
2.4 Mixed strategies
2.5 2-by-2 matrix games
2.6 2-by-n, m-by-2 and 3-by-3 matrix games
2.7 Linear programming
2.8 Chapter summary
3 Solving two-person zero-sum games using LP
3.1 Perfect canonical linear programming problems
3.2 The simplex method
3.3 Pivoting
3.4 The perfect phase of the simplex method
3.5 The Big M method
3.6 Bland's rules to prevent cycling
3.7 Duality and the simplex method
3.8 Solution of game matrices
3.9 Chapter summary
4 Non-zero-sum games and k-person games
4.1 The general setting
4.2 Nash equilibria
4.3 Graphical method for 2 Ã- 2 matrix games
4.4 Inadequacies of Nash equilibria & cooperative games
4.5 The Nash arbitration procedure
4.6 Games with two or more players
4.7 Coalitions
4.8 Games in coalition form
4.9 The Shapley value
4.10 The Banzhaf power index
4.11 Imputations
4.12 Strategic equivalence
4.13 Stable sets
4.14 Chapter summary
5 Imperfect Information Games
5.1 The general setting
5.2 Complete information games in extensive form
5.3 Imperfect information games in extensive form
5.4 Games with random effects
5.5 Chapter summary
6 Computer solutions to games
6.1 Zero-sum games - invertible matrices
6.2 Zero sum games - linear program problem (LP)
6.3 Special Linear Programming Capabilities
6.4 Non-zero sum games - linear complementarity problem (LCP)
6.5 Special game packages
6.6 Chapter summary
Appendices
Appendix A Utility theory
Appendix B Nash's theorem
Appendix C Finite probability theory
Appendix D Calculus & Differentiation
Appendix E Linear Algebra
Appendix F Linear Programming
Appendix G Named Games and Game Data
Answers to selected exercises
Bibliography
Index
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