Applied Differential Games

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Springer Science & Business Media, Jun 30, 1988 - Business & Economics - 208 pages
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This book grew out of a set of lecture notes for a one semester course on dynamic game theory held at the University of Technology, Vienna. It is intended primarily at the graduate level for students in operations research, management science, applied mathematics, and eco nomics. I hope that I have been able to give the reader an accessible introduction to the subject of nonzero-sum dif ferential games with particular emphasis on applications. It would be irrational to try to re ach total com prehensiveness in a single volume. Therefore, I have resisted the temptation to "over-cannibalize" previous textbooks and monographs on the subject. It has rather been my desire to cover material that (I think) is impor tant and interesting, but gets left out of these publications. Writing a book is quite a game. In the beginning -before c10sing the binding agreement* with Plenum-I believed this to be a fi·nite horizon game. Time, however, * Key words will be explained in the text. 7 PREFACE 8 was a merciless arbiter. I am grateful to the Senior Editor, Dr. Ken Derharn, for allowing manuscript delivery to become a (restricted) free terminal time problem. Most of all, I thank my wife Grace for offering me the needed spiritual support, and my two-year-old daughter Sabrina for ignoring the paradoxical situation that there are games which prevent Dad from playing with her.
 

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Contents

11 The Glass Bead Game
15
111 Isaacss Decade
16
112 The Aftermath
17
12 Dynamic Models of Conflict
18
122 A Game of Capitalism
21
123 Strike Negotiation
23
124 A Model of Duopolistic Competition
24
125 The Competitive LimitedAccess Fishery
25
41 LinearQuadratic Games
114
412 Stackelberg Solutions
121
42 Perfect Games
129
422 Identifying Perfect Games
136
43 Qualitatively Solvable Games
139
431 Phase Diagram Analysis of Perfect Games Under the additional assumption
141
432 Symmetric Games with a Single State Variable
147
Exercises
150

13 Symbols and Terminology
26
132 Related Terms
29
Playing the Game
35
21 Rules of the Game
37
212 The Loop Model
40
213 Generalized Concepts
44
22 The Noncooperative Approach
49
222 Strategic Features
64
Exercises
71
Methods of Solution
73
31 Simultaneous Play
75
311 Sufficiency under Generalized Constraints
77
312 Necessary Conditions under Generalized Constraints
82
32 Hierarchical Play
96
322 The Stackelberg Solution
102
Exercises
109
Typologies of Differential Games
111
Selected Applications
153
51 FaustThe Game
155
511 First ScenarioGoethes Play
156
512 Second ScenarioThe Original Source
160
52 The Dynamics of Oligopoly
162
521 The Finite Horizon Oligopoly
164
522 The Infinite Horizon Oligopoly
170
53 R D Games
173
532 Market Structure and Research Intensity
178
54 Fishery Games
179
542 Extinction Conservation and Economic Regulation
183
Exercises
186
References
189
Selected Bibliography
197
Index
201
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