Geometry, Language and Strategy is a way of looking at game theory or strategic decision-making from a scientific perspective, using standard equations from the fields of engineering and physics. To better approximate reality, it extends game theory beyond the two-player set piece.
The book begins where former game theory literature ends — with multi-person games on a world stage. It encompasses many of the variables encountered in strategic planning, using mathematics borrowed from physics and engineering, rather than the economic models which have not proven to be good in predicting reality.
Readership: Mathematicians and scientists who wish to broaden their understanding of economic possibilities using game theory.
Author(s): Gerald H. Thomas
Series: K & E Series on Knots and Everything 37
Publisher: World Scientific Publishing Company
Year: 2006
Language: English
Pages: xi+240
Foreword v
Preface vii
1. Introduction I
1.1 Geometry of Economic Games 3
1.2 Market Fluid 8
1.3 Thermodynamics of Games 12
1.4 Rules of the Game 14
1.5 Economic Justification 19
1.6 Dynamic Games 26
1.7 Nature of Time 30
1.8 Outline 31
2. Rules-of-the-Game 33
2.1 Games are Covariant 34
2.2 General Attributes of the Game Matrix 36
2.3 Geodesics 38
2.4 Games are Locally Flat 42
2.5 Dynamic Game Theory Hypothesis 45
3. Flow of Strategic-Mass 47
3.1 Local versus Global 47
3.2 The Connection 52
3.3 Curvature 56
3.4 Geometry Specified by Sources 58
4. Game Symmetries 65
4.1 Earth's Symmetries 65
4.2 Active and Inactive Choices 69
4.3 Covariance or Isometry 70
4.4 Dynamic Theory of Games 71
4.5 Time Isometry 74
5. Analysis 77
5.1 Reference Frames 78
5.2 Two-Person Zero-Sum Fair Game 81
5.3 Central Frame Models 85
5.4 Basic Behavior 89
6. Graphical Presentation 96
6.1 Fair Games 99
6.1.1 No gravity or pressure 99
6.1.2 Gravity . 102
6.1.3 Pressure 109
6.1.4 Single strategy model 112
6.2 Value Games 117
6.2.1 No gravity or pressure 118
6.2.2 Gravity 122
6.2.3 Pressure 131
6.3 Three-Person Game 136
6.4 Observations 140
7. Applications and Open Problems 143
7.1 Organizational Dynamics 143
7.2 Reorganization Cycles 146
7.3 What is a Player? 149
7.4 Flat Games 151
7.5 Three-Person and Higher Games 152
7.6 Non-Zero Sum Games 153
7.7 Viscous Games 153
7.8 Quantum Games 154
7.9 Complete Solutions 155
Appendix A Thermodynamics 157
Appendix B Symmetry in Differential Geometry 165
B. I Metric Symmetry Group 167
B.2 Active and Inactive Geometries 168
Appendix C Central Strategies 171
Appendix D Single Strategy Model 177
D.1 Solution 178
D.2 Scalar Properties 186
D.3 Thermal Properties 188
D.4 Extensions to Perfect Fluid 192
Appendix E Single Strategy Numerical Solutions 202
E.1 Fair Game Initial Conditions 203
E.2 Fair Game Single Strategy Model 208
Appendix F Streamlines 215
F.1 General Treatment 216
F.2 Fermi Derivative 219
F.3 Deviation using Fermi Derivatives 220
F.4 Evolution Matrix 221
F.5 Expansion Compression and Vorticity 223
Appendix G Player Fluid 226
Bibliography 233
Index 237
