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Game Theory for Economic Analysis - 1st Edition - ISBN: 9780123701800, 9781483295060

Game Theory for Economic Analysis

1st Edition

Author: Tatsuro Ichiishi
Series Editor: Karl Shell
eBook ISBN: 9781483295060
Imprint: Academic Press
Published Date: 28th January 1983
Page Count: 164
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Table of Contents


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



2. Introduction to Continuity of a Correspondence

2.1. Upper and Lower Semicontinuities

2.2. Closedness

2.3. Maximum Theorem


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


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


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


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



Author Index

Subject Index


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.


No. of pages:
© Academic Press 1983
28th January 1983
Academic Press
eBook ISBN:

Ratings and Reviews

About the Author

Tatsuro Ichiishi

Affiliations and Expertise

The Ohio State University, Columbus, U.S.A.

About the Series Editor

Karl Shell

Affiliations and Expertise

Cornell University