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Noncooperative Game Theory:
An Introduction for Engineers and Computer Scientists
João P. Hespanha

Book Description | Endorsements
Chapter 1 [in PDF format]

TABLE OF CONTENTS:

Preamble xi
I INTRODUCTION
1 Noncooperative Games
1.1 Elements of a Game 3
1.2 Cooperative vs. Noncooperative Games: Rope-Pulling 4
1.3 Robust Designs: Resistive Circuit 8
1.4 Mixed Policies: Network Routing 9
1.5 Nash Equilibrium 11
1.6 Practice Exercise 11
2 Policies
2.1 Actions vs. Policies: Advertising Campaign 13
2.2 Multi-Stage Games:War of Attrition 16
2.3 Open vs. Closed-Loop: Zebra in the Lake 18
2.4 Practice Exercises 19
II ZERO-SUM GAMES
3 Zero-Sum Matrix Games
3.1 Zero-Sum Matrix Games 25
3.2 Security Levels and Policies 26
3.3 Computing Security Levels and Policies with MATLAB® 27
3.4 Security vs. Regret: Alternate Play 28
3.5 Security vs. Regret: Simultaneous Plays 28
3.6 Saddle-Point Equilibrium 29
3.7 Saddle-Point Equilibrium vs. Security Levels 30
3.8 Order Interchangeability 32
3.9 Computational Complexity 32
3.10 Practice Exercise 34
3.11 Additional Exercise 34
4 Mixed Policies
4.1 Mixed Policies: Rock-Paper-Scissor 35
4.2 Mixed Action Spaces 37
4.3 Mixed Security Policies and Saddle-Point Equilibrium 38
4.4 Mixed Saddle-Point Equilibrium vs. Average Security Levels 41
4.5 General Zero-Sum Games 43
4.6 Practice Exercises 47
4.7 Additional Exercise 50
5 Minimax Theorem
5.1 Theorem Statement 52
5.2 Convex Hull 53
5.3 Separating Hyperplane Theorem 54
5.4 On theWay to Prove the Minimax Theorem 55
5.5 Proof of the Minimax Theorem 57
5.6 Consequences of the Minimax Theorem 58
5.7 Practice Exercise 58
6 Computation of Mixed Saddle-Point Equilibrium Policies
6.1 Graphical Method 60
6.2 Linear Program Solution 61
6.3 Linear Programs with MATLAB® 63
6.4 Strictly Dominating Policies 64
6.5 "Weakly" Dominating Policies 66
6.6 Practice Exercises 67
6.7 Additional Exercise 70
7 Games in Extensive Form
7.1 Motivation 71
7.2 Extensive Form Representation 72
7.3 Multi-Stage Games 72
7.4 Pure Policies and Saddle-Point Equilibria 74
7.5 Matrix Form for Games in Extensive Form 75
7.6 Recursive Computation of Equilibria for Single-Stage Games 77
7.7 Feedback Games 79
7.8 Feedback Saddle-Point for Multi-Stage Games 79
7.9 Recursive Computation of Equilibria for Multi-Stage Games 83
7.10 Practice Exercise 85
7.11 Additional Exercises 86
8 Stochastic Policies for Games in Extensive Form
8.1 Mixed Policies and Saddle-Point Equilibria 87
8.2 Behavioral Policies for Games in Extensive Form 90
8.3 Behavioral Saddle-Point Equilibria 91
8.4 Behavioral vs. Mixed Policies 92
8.5 Recursive Computation of Equilibria for Feedback Games 93
8.6 Mixed vs. Behavioral Order Interchangeability 95
8.7 Non-Feedback Games 95
8.8 Practice Exercises 96
8.9 Additional Exercises 102
III NON-ZERO-SUM GAMES
9 Two-Player Non-Zero-Sum Games
9.1 Security Policies and Nash Equilibria 105
9.2 Bimatrix Games 107
9.3 Admissible Nash Equilibria 108
9.4 Mixed Policies 110
9.5 Best-Response Equivalent Games and Order Interchangeability 111
9.6 Practice Exercises 114
9.7 Additional Exercises 116
10 Computation of Nash Equilibria for Bimatrix Games
10.1 Completely Mixed Nash Equilibria 118
10.2 Computation of Completely Mixed Nash Equilibria 120
10.3 Numerical Computation of Mixed Nash Equilibria 121
10.4 Practice Exercise 124
10.5 Additional Exercise 126
11 N-Player Games
11.1 N-Player Games 127
11.2 Pure N-Player Games in Normal Form 129
11.3 Mixed Policies for N-Player Games in Normal Form 130
11.4 Completely Mixed Policies 131
12 Potential Games
12.1 Identical Interests Games 133
12.2 Potential Games 135
12.3 Characterization of Potential Games 138
12.4 Potential Games with Interval Action Spaces 139
12.5 Practice Exercises 142
12.6 Additional Exercise 144
13 Classes of Potential Games
13.1 Identical Interests Plus Dummy Games 145
13.2 Decoupled Plus Dummy Games 146
13.3 Bilateral Symmetric Games 147
13.4 Congestion Games 148
13.5 Other Potential Games 149
13.6 Distributed Resource Allocation 150
13.7 Computation of Nash Equilibria for Potential Games 153
13.8 Fictitious Play 156
13.9 Practice Exercises 159
13.10 Additional Exercises 167
IV DYNAMIC GAMES
14 Dynamic Games
14.1 Game Dynamics 171
14.2 Information Structures 173
14.3 Continuous-Time Differential Games 175
14.4 Differential Games with Variable Termination Time 177
15 One-Player Dynamic Games
15.1 One-Player Discrete-Time Games 178
15.2 Discrete-Time Cost-To-Go 179
15.3 Discrete-Time Dynamic Programming 179
15.4 Computational Complexity 184
15.5 Solving Finite One-Player Games with MATLAB® 186
15.6 Linear Quadratic Dynamic Games 187
15.7 Practice Exercise 187
15.8 Additional Exercise 189
16 One-Player Differential Games
16.1 One-Player Continuous-Time Differential Games 190
16.2 Continuous-Time Cost-To-Go 191
16.3 Continuous-Time Dynamic Programming 191
16.4 Linear Quadratic Dynamic Games 195
16.5 Differential Games with Variable Termination Time 196
16.6 Practice Exercise 198
17 State-Feedback Zero-Sum Dynamic Games
17.1 Zero-Sum Dynamic Games in Discrete Time 201
17.2 Discrete-Time Dynamic Programming 203
17.3 Solving Finite Zero-Sum Games with MATLAB® 205
17.4 Linear Quadratic Dynamic Games 206
17.5 Practice Exercise 209
18 State-Feedback Zero-Sum Differential Games
18.1 Zero-Sum Dynamic Games in Continuous Time 214
18.2 Linear Quadratic Dynamic Games 216
18.3 Differential Games with Variable Termination Time 219
18.4 Pursuit-Evasion 220
18.5 Practice Exercise 222
References 223
Index 225

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File created: 5/15/2017

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