Game Theory for Economic Analysis
- 1st Edition - January 28, 1983
- Latest edition
- Author: Tatsuro Ichiishi
- Editor: Karl Shell
- Language: English
Game Theory for Economic Analysis provides information pertinent to the more general game-theoretical concept. This book discusses fundamental aspects of a social coalitional… Read more
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Description
Description
Game Theory for Economic Analysis provides information pertinent to the more general game-theoretical concept. This book discusses fundamental aspects of a social coalitional equilibrium. Organized into six chapters, this book begins with an overview of the mathematical tools and theorems that play critical roles in n-person game theory. This text then provides a systematic account for the first strand of n-person game theory and presents the mathematical foundation for economic analysis. Other chapters consider the concept of Nash equilibrium of a game in normal form, wherein a solution of a game is based on the postulate that each player behaves individualistically and passively. This book discusses as well the central concept of the core of a game in characteristic function form, with or without side-payments. The final chapter deals with the Shapley value of a side-payment game. This book is a valuable resource for economists, economic theorists, and research workers.
Table of contents
Table of contents
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
Product details
Product details
- Edition: 1
- Latest edition
- Published: December 5, 2014
- Language: English
About the editor
About the editor
KS
Karl Shell
Affiliations and expertise
Cornell UniversityAbout the author
About the author
TI
Tatsuro Ichiishi
Affiliations and expertise
The Ohio State University, Columbus, U.S.A.View book on ScienceDirect
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