Game Theory and Politics

by Steven J. Brams

Overview

In this illuminating and instructive survey, author Steven J. Brams demonstrates both the insights and the pitfalls that can result from applying game theoretic models to the analysis of problems in political science. Using plenty of real-life examples, Brams shows how game theory can explain and elucidate complex political situations, from warfare to presidential vetoes. In these cases and others, game theory's mathematical structure provides a rigorous, consistent method for formulating, analyzing, and solving strategic problems. Minimal mathematical background is necessary, making the book accessible to a wide audience of students and teachers of politics and social science, as well as other readers with a serious interest in politics. New preface to the Dover edition. 1975 edition.

Product Details

ISBN-13:	9780486434971
Publisher:	Dover Publications
Publication date:	11/24/2011
Series:	Dover Books on Mathematics
Pages:	336
Product dimensions:	6.14(w) x 9.21(h) x (d)

Table of Contents

CONTENTS

Preface to the Dover Edition
Preface
Introductory Note
List of Tables
List of Figures

1. INTERNATIONAL RELATIONS GAMES

1.1. Introduction

1.2. Two-Person Zero-Sum Games with Saddle points

1.3. Information in Games

1.4. Two-Person Zero-Sum Games without Saddle points
1.5. Pure and Mixed Strategies

1.6. Interpretation of Mixed Strategies

1.7. Two-Person Nonzero-Sum Games
1.8. Prisoner's Dilemma and the Theory of Metagames

1.9. Chicken and the Cuban Missile Crisis

1.10. Summary and Conclusion
2. QUALITATIVE VOTING GAMES

2.1. Introduction

2.2. Voting Procedures

2.3. Sincere Voting

2.4. Straightforward Strategies and Voting Procedures
2.5. Equilibrium Choices and Vulnerability

2.6. Desirable Strategies and Equilibria

2.7. The Relationship between Desirable and Admissible Strategies

2.8. Sophisticated Voting

2.9. Coalitions and Information
2.10. Voting on Voting Procedures
2.11. The Paradox of Voting
2.12. Empirical Examples

2.13. Summary and Conclusion
3. QUANTITATIVE VOTING GAMES

3.1. Introduction
3.2. Requirements for a Voting System of Proportional Representation

3.3. Rules that Meet the Requirements

3.4. Interdependence of the Requirements
3.5. The Effects of Size
3.6. Information and the Choice of Strategies
3.7. Empirical Examples
3.8. Summary and Conclusion
4. VOTE-TRADING GAMES

4.1. Introduction
4.2. What the General Possibility Theorem Precludes
4.3. Judgments about Vote Trading
4.4. Definitions and Assumptions
4.5. Sincere and Insincere Voting
4.6. Initial Trades and the Paradox of Vote Trading
4.7. Subsequent Trades and the Instability of Vote Trading
4.8. The Consequences of Refusing to Trade
4.9 The Consequences of Forming Coalitions
4.10. Conditions Limiting Vote Trading
4.11. Empirical Examples ofthe Paradox of Vote Trading
4.12. Summary and Conclusion
5. VOTING POWER

5.1. Introduction
5.2. The Shapley-Shubik Index of Voting Power
5.3. The Banzhaf Index of Voting Power
5.4. Coalition Models ofthe Two Power Indices
5.5. Calculation ofthe Power Indices
5.6. Three Paradoxes of Voting Power
5.7. Empirical Applications ofthe Power Indices
5.8. Summary and Conclusion
6. COALITION GAMES
6.1. Introduction
6.2. Power and Coalitions
6.3. Restrictions on Coalition Alignments
6.4. The Stability ofAlignments
6.5. Empirical Conclusions of the Luce-Rogow Model
6.6. The Concept of Winning
6.7. The Size Principle
6.8. The Information Effect
6.9. Empirical Evidence for the Size Principle
6.10. Criticisms ofthe Size Principle
6.11. An Alternative Goal: Maximizing One's Share of Spoils
6.12. Summary and Conclusion
7. ELECTION GAMES 7.1. Introduction
7.2. The Need for Models to Assess the Consequences of Electoral Reform
7.3. Presidential Campaigns and Voting Behavior
7.4 The Goals of Candidates
7.5. The Popular-Vote Model
7.6. The Electoral-Vote Model
7.7. The 3/2's Allocation Rule
7.8. Why the Large States Are Favored
7.9. Testing the Models
7.10. Campaign Allocations and Biases through 1980
7.11. Limitations and Extensions of the Models
7.12. Summary and Conclusion
Glossary
Annotated Bibliography
Index