Geometry, Language, And Strategy (K & E Series on Knots and Everything)

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