Description
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.
Chapter
3.1 Zero-Sum Matrix Games
3.2 Security Levels and Policies
3.3 Computing Security Levels and Policies with MATLAB®
3.4 Security vs. Regret: Alternate Play
3.5 Security vs. Regret: Simultaneous Plays
3.6 Saddle-Point Equilibrium
3.7 Saddle-Point Equilibrium vs. Security Levels
3.8 Order Interchangeability
3.9 Computational Complexity
4.1 Mixed Policies: Rock-Paper-Scissor
4.3 Mixed Security Policies and Saddle-Point Equilibrium
4.4 Mixed Saddle-Point Equilibrium vs. Average Security Levels
4.5 General Zero-Sum Games
5.3 Separating Hyperplane Theorem
5.4 On theWay to Prove the Minimax Theorem
5.5 Proof of the Minimax Theorem
5.6 Consequences of the Minimax Theorem
6 Computation of Mixed Saddle-Point Equilibrium Policies
6.2 Linear Program Solution
6.3 Linear Programs with MATLAB®
6.4 Strictly Dominating Policies
6.5 “Weakly” Dominating Policies
7 Games in Extensive Form
7.2 Extensive Form Representation
7.4 Pure Policies and Saddle-Point Equilibria
7.5 Matrix Form for Games in Extensive Form
7.6 Recursive Computation of Equilibria for Single-Stage Games
7.8 Feedback Saddle-Point for Multi-Stage Games
7.9 Recursive Computation of Equilibria for Multi-Stage Games
7.11 Additional Exercises
8 Stochastic Policies for Games in Extensive Form
8.1 Mixed Policies and Saddle-Point Equilibria
8.2 Behavioral Policies for Games in Extensive Form
8.3 Behavioral Saddle-Point Equilibria
8.4 Behavioral vs. Mixed Policies
8.5 Recursive Computation of Equilibria for Feedback Games
8.6 Mixed vs. Behavioral Order Interchangeability
9 Two-Player Non-Zero-Sum Games
9.1 Security Policies and Nash Equilibria
9.3 Admissible Nash Equilibria
9.5 Best-Response Equivalent Games and Order Interchangeability
10 Computation of Nash Equilibria for Bimatrix Games
10.1 Completely Mixed Nash Equilibria
10.2 Computation of Completely Mixed Nash Equilibria
10.3 Numerical Computation of Mixed Nash Equilibria
11.2 Pure N-Player Games in Normal Form
11.3 Mixed Policies for N-Player Games in Normal Form
11.4 Completely Mixed Policies
12.1 Identical Interests Games
12.3 Characterization of Potential Games
12.4 Potential Games with Interval Action Spaces
13 Classes of Potential Games
13.1 Identical Interests Plus Dummy Games
13.2 Decoupled Plus Dummy Games
13.3 Bilateral Symmetric Games
13.5 Other Potential Games
13.6 Distributed Resource Allocation
13.7 Computation of Nash Equilibria for Potential Games
13.10 Additional Exercises
14.2 Information Structures
14.3 Continuous-Time Differential Games
14.4 Differential Games with Variable Termination Time
15 One-Player Dynamic Games
15.1 One-Player Discrete-Time Games
15.2 Discrete-Time Cost-To-Go
15.3 Discrete-Time Dynamic Programming
15.4 Computational Complexity
15.5 Solving Finite One-Player Games with MATLAB®
15.6 Linear Quadratic Dynamic Games
16 One-Player Differential Games
16.1 One-Player Continuous-Time Differential Games
16.2 Continuous-Time Cost-To-Go
16.3 Continuous-Time Dynamic Programming
16.4 Linear Quadratic Dynamic Games
16.5 Differential Games with Variable Termination Time
17 State-Feedback Zero-Sum Dynamic Games
17.1 Zero-Sum Dynamic Games in Discrete Time
17.2 Discrete-Time Dynamic Programming
17.3 Solving Finite Zero-Sum Games with MATLAB®
17.4 Linear Quadratic Dynamic Games
18 State-Feedback Zero-Sum Differential Games
18.1 Zero-Sum Dynamic Games in Continuous Time
18.2 Linear Quadratic Dynamic Games
18.3 Differential Games with Variable Termination Time
Noncooperative Game Theory
：An Introduction for Engineers and Computer Scientists
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