Game Theory for Economic Analysis

Preface


0. Preliminary Discussion


0.1. Basic Notation


0.2. Pure Exchange Economy


1. Introduction to Convex Analysis


1.1. Convex Set


1.2. Affine Subspace


1.3. Hyperplane


1.4. Algebraic Interior, Algebraic Relative Interior


1.5. Separation Principle


1.6. Extreme Points

Appendix

Exercises


2. Introduction to Continuity of a Correspondence


2.1. Upper and Lower Semicontinuities


2.2. Closedness


2.3. Maximum Theorem

Exercises


3. Introduction to Fixed-Point Theorems in Rn


3.1. Sperner's Lemma, K-K-M Theorem


3.2. Fixed-Point Theorems


3.3. Fixed-Point Theorem and Separation Principle: Coincidence Theorem

Exercises


4. Noncooperative Behavior and Equilibrium


4.1. Nash Equilibrium of a Game in Normal Form


4.2. Optimality


4.3. Social Equilibrium of an Abstract Economy


4.4. Competitive Equilibrium of a Pure Exchange Economy


4.5. Fundamental Theorems of Welfare Economics


4.6. Game-Theoretical Interpretation of the Competitive Equilibrium


4.7. Notes

Exercises


5. Cooperative Behavior and Stability


5.1. Linear Inequalities


5.2. Core of a Side-Payment Game


5.3. K-K-M-S Theorem


5.4. Core of a Non-Side-Payment Game


5.5. Core Allocation of a Pure Exchange Economy


5.6. A Limit Theorem of Cores


5.7. Social Coalitional Equilibrium of a Society


5.8. Optimality of the Nash Equilibrium: Strong Equilibrium


5.9. Notes

Exercises


6. Cooperative Behavior and Fairness


6.1. Shapley Value of a Side-Payment Game


6.2. Convex Game


6.3. X-Transfer Value of a Non-Side-Payment Game


6.4. Value Allocation of a Pure Exchange Economy


6.5. A Limit Theorem of Value Allocations of Replica Economies


6.6. Notes

Exercises

References

Author Index

Subject Index