Invitation to Linear Programming and Game Theory

Cover
Contents
Preface
1 Preliminaries
	1.1 Mathematical Models
	1.2 Systems of Linear Equations
	1.3 Elimination and Matrices
	1.4 Vectors, Linear Combinations, and Bases
	1.5 Three Points of View
	1.6 Some Nonlinear Models
2 Matrix Algebra
	2.1 Matrices
	2.2 Operations on Matrices I
	2.3 Operations on Matrices II: Matrix Inversion
	2.4 Solving Linear Systems by Matrix Inversion
	2.5 Some Applications to Cryptography and Economics
3 Graphical Linear Programming
	3.1 Introduction and Graphical Solutions
	3.2 The Decision Space: m × 2 Problems
	3.3 Convex Sets and the Corner Point Theorem
	3.4 Problems with No Solution or Infinitely Many Solutions
	3.5 The Constraint Space: 2 × n Problems
4 Sensitivity Analysis and Duality
	4.1 Introduction to Sensitivity Analysis
	4.2 Changes in the Objective Coefficients
	4.3 Marginal Values Associated with Constraints
	4.4 Other Changes: Drawbacks of the Graphical Methods
	4.5 Duality
5 The Simplex Algorithm
	5.1 Standard Form Maximization Problems
	5.2 Phase II Pivoting
	5.3 Standard Form Minimization Problems
	5.4 Solving Linear Programming Problems with a Computer
6 Game Theory
	6.1 Introduction
	6.2 Dominant Strategies and Nash Equilibrium Points
	6.3 Mixed-Strategy Constant-Sum Games
	6.4 Solving Mixed-Strategy Games: The Minimax Theorem in the 2 × 2 Case
7 More Game Theory
	7.1 Solving Larger Constant-Sum Games
	7.2 Solving Constant Sum-Games with Linear Programming
	7.3 Using a Computer to Solve Constant-Sum Games
	7.4 Variable-Sum Games
8 Sensitivity Analysis, Ordinal Games, and n-Person Games
	8.1 Sensitivity Analysis in Game Theory
	8.2 Ordinal Games
	8.3 Sequential Games: The Theory of Moves
	8.4 A Brief Introduction to n-Player Games
	8.5 Legislative Voting and Political Power
9 More Linear Programming
	9.1 Phase I Pivoting
	9.2 Alternate Approach to Minimization Problems
	9.3 Sensitivity Analysis and the Simplex Algorithm
Appendix: A Rapid Review of Sets and Probability
	A.1 A Review of Sets
	A.2 Enumeration
	A.3 Experiments, Sample Spaces, and Probability Models
	A.4 Uniform Sample Spaces
	A.5 Conditional Probability and Independent Events
	A.6 Bayes’s Theorem
References
Index