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Index
Title
Copyright
Contents
Preface
1. Definition of a Game
1.1. General Notions
1.2. Games in Extensive Form
1.3. Strategies: The Normal Form
1.4. Equilibrium n-Tuples
1.5. The Monty Hall Game
Problems
2. Two-Person Zero-Sum Games
2.1. Zero-Sum Games
2.2. The Normal Form
2.3. Mixed Strategies
2.4. The Minimax Theorem
2.5. Computation of Optimal Strategies
2.6. Symmetric Games
Problems
3. Linear Programming
3.1. Introduction
3.2. Duality
3.3. Solution of Linear Programs
3.4. The Simplex Algorithm
3.5. The Simplex Algorithm (Continued)
3.5.1. Rules for Choosing a Pivot
3.6. Examples
3.7. Constrained Games
Problems
4. Infinite Games
4.1. Games with Countably many Strategies
4.2. Games on the Square
4.3. Games with Continuous Kernel
4.4. Concave–Convex Games
4.5. Games of Timing
4.6. Higher Dimensions
Problems
5. Multistage Games
5.1. Behavioral Strategies
5.2. Games of Exhaustion
5.3. Stochastic Games
5.4. Recursive Games
5.5. Differential Games
Problems
6. Games with Incomplete Information
6.1. Introduction: The One-Stage Signaling Model
6.2. The Multistage Model
Problems
7. Utility Theory
7.1. Ordinal Utility
7.2. Lotteries
7.3. Commodity Bundles
7.4. Absolute Utility
Problems
8. Two-Person General-Sum Games
8.1. Bimatrix Games (Noncooperative)
8.2. Perfect Equilibrium Points
Subgame-Perfect Equilibria
8.3. Evolutionary Stable Systems
and Larger Systems
8.4. Correlated Equilibria
Problems
9. Two-Person Cooperative Games
9.1. The Bargaining Problem
9.2. Threats
9.3. Time-Restricted Bargaining
Problems
10. n-Person Games
10.1. Noncooperative Games
10.2. Cooperative Games
10.3. Domination, Strategic Equivalence, and Normalization
10.4. The Core
10.5. Balanced Collections
Problems
11. Stable Sets
11.1. Introduction
11.2. Properties of Stable Sets
11.3. Edgeworth Market Games—An Example
11.4. A Game with No Solutions
Problems
12. Indices of Power
12.1. The Shapley Value
12.2. Multilinear Extensions
12.3. The Banzhaf–Coleman Index of Power
12.4. The Presidential Election “Game”
12.5. The Coalition Value
Problems
13. The Bargaining Set and Related Concepts
13.1. The Bargaining Set
13.2. The Kernel
13.3. The Nucleolus
13.4. The Airport Game
Problems
14. Nonatomic Games
14.1. Games with a Continuum of Players
14.2. Values of Nonatomic Games
14.3. Internal Telephone Billing Rates — An Example
Problems
15. Games without Side Payments
15.1. Introduction
15.2. The Core
15.3. Market Games
15.4. Approaches to the Value
15.5. The Bargaining Sets
Problems
16. Spatial Games
16.1. The Core and Near-Core Solution Concepts
16.2. The Modified Power Index
Problems
17. Other Applications
17.1. Introduction
17.2. Single-Item Auctions
17.2.1. First-Price Sealed-Bid Auctions
17.2.4. Second-Price Auctions
17.3. Mechanisms
17.3.1. Description of Mechanisms
17.4. Public Goods
17.5. Two-sided Matching
Problems
Appendix
A.1. Convexity
A.2. Fixed Point Theorems
Bibliography
Index
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