Summer Reading Sale
 
 

Recently Viewed clear list


Original Essays | June 20, 2014

Lauren Owen: IMG The Other Vampire



It's a wild and thundery night. Inside a ramshackle old manor house, a beautiful young girl lies asleep in bed. At the window, a figure watches... Continue »

spacer
Qualifying orders ship free.
$17.95
New Trade Paper
Ships in 1 to 3 days
Add to Wishlist
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
6 Remote Warehouse Mathematics- Modeling

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

by

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

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

A reprint of a 1965 volume which looks at game theory methods for obtaining solutions in conflict situations. Combining principles of game theory, the calculus of variation, and control theory, the author considers an array of problems from military situations and pursuit and evasion tactics to athletic contests and games of firing and maneuver.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

Synopsis:

Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, games of firing and maneuver, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

Synopsis:

One of the definitive works in game theory, this volume takes an original and expert look at conflict solutions. Drawing on game theory, the calculus of variations, and control theory, the author solves an amazing array of problems relating to military situations, pursuit and evasion tactics, athletic contests, and many more. Clearly detailed examples; numerous calculations. 1965 edition.

Description:

Includes bibliographical references (p. 379-380) and index.

Table of Contents

CHAPTER 1 An Introduction

  1.1 The Theory of Games

  1.2 The State of Control Variables

  1.3 Battle Games

  1.4 Games with Moving Craft

  1.5 Pursuit Games

  1.6 Games of Kind and Games of Degrees

  1.7 Strategies

  1.8 "Dogfights, Firing Games, Programming, and Athletics"

  1.9 Two Examples

  1.10 A Perspective on Precision

  1.11 A Perspective on Progress

  1.12 On Reading This Book

"CHAPTER 2 Definitions, Formulation, and Assumptions"

  2.1 The Kinematic Situation

  2.2 The Realistic and Reduced Space

  2.3 Termination of the Game

  2.4 The Payoff

  2.5 Games of Kind and Games of Degree

  2.6 Strategies

  2.7 Canonization of the Vectograms

  2.8 A Lemma on Circular Vectograms

CHAPTER 3 Discrete Differential Games

  3.1 Introduction

  3.2 The General Discrete Game

  3.3 Battles of Extinction

  3.4 Two Discrete Pursuit Games

  3.5 Quasi-Discrete Games

CHAPTER 4 The Basic Mathematics and the Solution Technique in the Small

  4.1 The Nature of a Solution

  4.2 The Main Equation

  4.3 Semipermeable Surfaces and a Second Derivation of the Main Equation

  4.4 The Verification Theorem

  4.5 The Path Equations

  4.6 The Retrogression Principle

  4.7 The Initial Conditions

CHAPTER 5 Mainly Examples: Transition Surfaces: Integral Constraints

  5.1 Transition Surfaces

  5.2 The Dolichobrachistochrone

  5.3 The Relationship to the Euler Equation

  5.4 The War of Attrition and Attack

  5.5 The Isotropic Rocket Pursuit Game

  5.6 An Optimal Program of Steel Production

  5.7 Integral Constraints

CHAPTER 6 Efferent of Dispersal Surfaces

  6.1 Singular Surfaces

  6.2 Dispersal Surfaces

  6.3 The Nature of Dispersal Surfaces

  6.4 The Question of the Perpetuated Dilemma

  6.5 The Construction of Dispersal Surfaces

  6.6 Further Examples

  6.7 The Geometric Method for Simple Pursuit Games of Kind

  6.8 Further Examples: The Football Players and the Cooperative Cutters

  6.9 The Existence of the Perpetuated Dilemma

  6.10 Various Problems

CHAPTER 7 Afferent or Universal Surfaces

  7.1 Introduction

  7.2 Universal Surfaces with Null Integrand

  7.3 "Universal Surfaces with Linear Vectograms, An Intuitive Purview"

  7.4 The Analytic Necessary Condition for a Linear Vectogram Type Universal Service

  7.5 The Workable Condition when n = 3

  7.6 Why the Name Universal Surface?

  7.7 The Calculus of Variations Viewpoint

  7.8 All Strategies Optimal

  7.9 The Workable Criterion when n = 4

  7.10 A Test for a Void and a Further Necessary Condition for a Universal Service

  7.11 Test for a Transition Surface

  7.12 Further Discussion fo the Basic Nature of Universal Surfaces and Their Relation to the Euler Equation

  7.13 Restoration of the Totality of Control Variables

  7.14 Semiuniversal Surfaces

CHAPTER 8 Games of Kind

  8.1 Introduction

  8.2 The Barrier Concept

  8.3 The Construction of Semipermeable Surfaces

  8.4 Termination of Barriers

  8.5 Construction of the Barrier

  8.6 Some Brief Examples

  8.7 Possible Other Species of Barriers

  8.8 Fusion of Games of Kind and Degree

CHAPTER 9 Examples of Games of Kind

  9.1 The Homicidal Chauffeur Game

  9.1A Dogfighting a Highly Mobile Target

  9.2 The Game of Two Cars

  9.3 The Isotropic Rocket

  9.4 The Isotropic Rocket: The Envelope Barrier

  9.5 Two Remarkably Dissimilar Games in the Same Setting

  9.6 Extensions and Applications of the Deadline Game

  9.7 Further Games

  9.8 Application to Stability and Control

CHAPTER 10 Equivocal Surfaces and the Homicidal Chauffeur Game

  10.1 Introduction

  10.2 The Homicidal Chauffeur: Geometric Solution of the Game of Kind

  10.3 The Primary Solution of the Homicidal Chauffeur Game of Degree

  10.4 The Universal Curve and Its Tributaries

  10.5 Equivocal Surfaces

  10.6 An Example with an Equivocal Surface: Preliminaries

  10.7 An Example with an Equivocal Surface: Solution

  10.8 Discussion of Equivocal Surfaces

  10.9 The Equivocal Phenomenon in the Homicidal Chauffeur Game

  10.10 Appendix

CHAPTER 11 The Application to Warfare

  11.1 Game Theory and War

  11.2 The Available Techniques

  11.3 Types of Applications

  11.4 The Broader Problems of Combat

  11.5 Problems of Formulation

  11.6 The War of Attrition and Attack: A Study

  11.7 The Battle of Bunker Hill

  11.8 Some Pitfalls in Adapting Game Theory to Warfare

  11.9 War of Attrition and Attack: Second Version

CHAPTER 12 Toward a Theory with Incomplete Information

  12.1 Introduction

  12.2 A Speculative Purview

  12.3 Search Games with Immobile Hiders

  12.4 Search Games with Mobile Hiders

  12.5 The Importance of Approximations

  12.6 The Chancifying Method

APPENDIX

  A1. A Hit Probability Payoff

  A2. The Fixed Battery Pursuit Game

  A3. Optimal Trajectories of Guided Missiles

  A4. An Illustration from Control Theory

  A5. The Bomber and Battery Game

REFERENCES

INDEX

Product Details

ISBN:
9780486406824
Author:
Isaacs, Rufus
Publisher:
Dover Publications
Author:
Isaacs
Author:
Isaacs, Nathan
Author:
Mathematics
Location:
Mineola, N.Y. :
Subject:
Applied
Subject:
Game Theory
Subject:
Mathematical optimization
Subject:
Differential games
Subject:
General Mathematics
Subject:
Mathematics-Modeling
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19990131
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
416
Dimensions:
8.5 x 5.38 in 1 lb

Other books you might like

  1. Quick Calculus 2ND Edition a Self... Used Trade Paper $11.00
  2. Matrix Theory New Trade Paper $16.95
  3. Mathographics Used Trade Paper $9.95
  4. Geometry, Relativity and the Fourth... Used Trade Paper $3.95
  5. Introduction To Numerical Analysis... Used Trade Paper $15.00
  6. An Introduction to Mathematical Modeling
    Used Trade Paper $7.95

Related Subjects

Arts and Entertainment » Architecture » Buildings » Religious
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Modeling

Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization New Trade Paper
0 stars - 0 reviews
$17.95 In Stock
Product details 416 pages Dover Publications - English 9780486406824 Reviews:
"Synopsis" by ,
Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.
"Synopsis" by , Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, games of firing and maneuver, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

"Synopsis" by ,
One of the definitive works in game theory, this volume takes an original and expert look at conflict solutions. Drawing on game theory, the calculus of variations, and control theory, the author solves an amazing array of problems relating to military situations, pursuit and evasion tactics, athletic contests, and many more. Clearly detailed examples; numerous calculations. 1965 edition.
spacer
spacer
  • back to top
Follow us on...




Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.