Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization

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Courier Corporation, 1999 - Mathematics - 384 pages
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One of the definitive works in game theory, this fascinating volume offers an original look at methods of obtaining solutions for conflict situations. Combining the principles of game theory, the calculus of variations, and control theory, the author considers and solves an amazing array of problems: military, pursuit and evasion, games of firing and maneuver, athletic contests, and many other problems of conflict.
Beginning with general definitions and the basic mathematics behind differential game theory, the author proceeds to examinations of increasingly specific techniques and applications: dispersal, universal, and equivocal surfaces; the role of game theory in warfare; development of an effective theory despite incomplete information; and more. All problems and solutions receive clearly worded, illuminating discussions, including detailed examples and numerous formal calculations.
The product of fifteen years of research by a highly experienced mathematician and engineer, this volume will acquaint students of game theory with practical solutions to an extraordinary range of intriguing problems.
  

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Contents

An Introduction
1
Definitions Formulation and Assumptions
25
Discrete Differential Games
44
The Basic Mathematics and the Solution Technique in the Small
64
Mainly Examples Transition Surfaces Integral Constraints
86
Efferent or Dispersal Surfaces
132
Afferent or Universal Surfaces
156
Games of Kind
200
Examples of Games of Kind
231
Equivocal Surfaces and the Homicidal Chauffeur Game
273
The Application to Warfare
305
Toward a Theory with Incomplete Information
336
Copyright

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