Title Two-Person Zero-Sum Game English 1.8 MB 207
```                            Foreword
Preface to the Fourth Edition
Prerequisites, Conventions, and Notation
Contents
Chapter 1: Single Person Background
1.1 Utility
1.2 The Maxmin Method
Chapter 2: Maxmin Versus Minmax
2.1 Strategies
2.2 MaxminMinmax
2.3 Action and Reaction
2.4 Defense of a Convoy
2.5 Methodology for Large Maxmin Problems
2.5.1 The Theory of Maxmin
2.5.2 Column Generation
2.5.3 The Dual Trick
2.6 Exercises
Chapter 3: Matrix Games
3.1 Holmes Versus Moriarty
3.2 von Neumann´s Theorem
3.4 Solving 2-by-2 Games
3.5 Sensor Selection
3.6 Graphical Solution of 2-by-n and m-by-2 Games
3.7 Dominance
3.8 Poker, Extensive Forms, and the PEG
3.9 Bare Hands and the Principle of Equality
3.10 Linear Programming
3.11 Methods for Large Games
3.11.1 The Brown-Robinson Method
3.11.2 Strategy Generation
3.12 Experiments with TPZS Games
3.13 Exercises
Chapter 4: Markov (Multistage) Games
4.1 Introduction, Inspection Game
4.2 Definition of Markov Games, Sufficiency Theorems
4.3 Tree Games
4.3.1 Combinatorial Games, Nim
4.4 Exhaustive Games
4.4.1 Women and Cats Versus Mice and Men
4.4.2 Attrition Battles
4.5 Graphical and Recursive Games
4.6 Stochastic Games
4.7 Football as a Markov Game
4.8 Tactical Air War
4.9 The Hamstrung Squad Car and Differential Games
4.10 Non-Terminating Markov Games
4.11 Exercises
Chapter 5: Games with a Continuum of Strategies
5.1 Games on the Unit Square, Continuous Poker
5.2 Concave-Convex Games
5.3 Logistics Games and Extensions
5.4 Single-Shot Duels
5.5 Bilinear Games
5.6 Submarines and Machine Guns
5.7 Exercises
Chapter 6: Blotto Games
6.1 The Symmetric Case
6.2 Playability
6.3 The Asymmetric Case
6.4 Continuous Actions
6.5 Attack and Defense of a Group of Targets
6.6 Concave-Convex Blotto Games
6.7 Exercises
Chapter 7: Network Interdiction
7.1 Maxmin Network Problems
7.1.1 Maximizing the Length of the Shortest Path
7.1.2 Minimizing the Maximum Flow
7.1.3 Minimizing the Maximum Survival Probability
7.2 Network Detection Games
7.2.1 Surveillance of a Region
7.2.2 Survival Probability Payoff
7.3 Exercises
Chapter 8: Search Games
8.1 Search Games in Discrete Space
8.1.1 Searcher Has a Single Look
8.1.2 Searcher Has Multiple Looks, No Overlook Probability
8.1.3 Searcher Has Multiple Looks, Nonzero Overlook Probability
8.1.4 Searcher Has Continuous ``Looks´´
8.2 Search Games in Continuous Space
8.2.1 One Dimension, Including Certain Networks
8.2.2 Stationary Search in Two Dimensions, HDG
8.2.3 Moving Search in Two Dimensions, PandM
8.3 Exercises
Chapter 9: Miscellaneous Games
9.1 Ratio Games
9.2 Racetime Games
9.3 Lopside Games and Signaling Games
9.3.1 Lopside Games
9.3.2 Signaling Games
9.4 The Bomber Versus Battleship Game
9.5 Exercises
Appendix A: Math Programming
Appendix B: Convexity
B.1 Convex Sets and Convex Hulls
B.2 Convex Functions and Jensen´s Inequality
Appendix C: Exercise Solutions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
References
Index
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