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

Game Theory for Economic Analysis

1st Edition

Series Editors: Karl Shell
Authors: Tatsuro Ichiishi
eBook ISBN: 9781483295060
Imprint: Academic Press
Published Date: 28th January 1983
Page Count: 164
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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

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.


Details

No. of pages:
164
Language:
English
Copyright:
© Academic Press 1983
Published:
Imprint:
Academic Press
eBook ISBN:
9781483295060

About the Series Editors

Karl Shell Series Editor

Affiliations and Expertise

Cornell University

About the Authors

Tatsuro Ichiishi Author

Affiliations and Expertise

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