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NONCOOPERATIVE GAME THEORY. AN INTRODUCTION FOR ENGINEERS AND COMPUTER SCIENTISTS
Título:
NONCOOPERATIVE GAME THEORY. AN INTRODUCTION FOR ENGINEERS AND COMPUTER SCIENTISTS
Subtítulo:
Autor:
HESPANHA, J
Editorial:
PRINCETON UNIVERSITY PRESS
Año de edición:
2017
ISBN:
978-0-691-17521-8
Páginas:
248
66,50 € -10,0% 59,85 €

 

Sinopsis

Noncooperative Game Theory is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. João Hespanha shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem´s essence: Who are the players? What are their goals? Will the solution to ´the game´ solve the original design problem? Using the fundamentals of game theory, Hespanha explores these issues and more.

The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria-such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, Hespanha examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty-the unforgiving variable that can wreck engineering designs. Hespanha looks at such standard topics as zero-sum, non-zero-sum, and dynamics games and includes a MATLAB guide to coding.

Noncooperative Game Theory offers students a fresh way of approaching engineering and computer science applications.

An introduction to game theory applications for students of engineering and computer science
Materials presented sequentially and in an easy-to-understand fashion
Topics explore zero-sum, non-zero-sum, and dynamics games
MATLAB commands are included
João P. Hespanha is a professor in the Department of Electrical and Computer Engineering at the University of California, Santa Barbara. He is the author of Linear Systems Theory (Princeton).



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 "Weaklyö 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