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Cover type: Hardback

Edition: 94

Copyright: 1994

Publisher: Princeton University Press

Published: 1994

International: No

Edition: 94

Copyright: 1994

Publisher: Princeton University Press

Published: 1994

International: No

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Game theory is the mathematical analysis of strategic interaction. In the fifty years since the appearance of von Neumann and Morgenstern's classic Theory of Games and Economic Behavior (Princeton, 1944), game theory has been widely applied to problems in economics. Until recently, however, its usefulness in political science has been underappreciated, in part because of the technical difficulty of the methods developed by economists. James Morrow's book is the first to provide a standard text adapting contemporary game theory to political analysis. It uses a minimum of mathematics to teach the essentials of game theory and contains problems and their solutions suitable for advanced undergraduate and graduate students in all branches of political science.

Morrow begins with classical utility and game theory and ends with current research on repeated games and games of incomplete information. The book focuses on noncooperative game theory and its application to international relations, political economy, and American and comparative politics. Special attention is given to models of four topics: bargaining, legislative voting rules, voting in mass elections, and deterrence. An appendix reviews relevant mathematical techniques. Brief bibliographic essays at the end of each chapter suggest further readings, graded according to difficulty. This rigorous but accessible introduction to game theory will be of use not only to political scientists but also to psychologists, sociologists, and others in the social sciences.

**Morrow, James D. : Stanford University**

James D. Morrow is Senior Research Fellow at the Hoover Institution on War, Revolution and Peace at Stanford University.

List of Figures and Tables

Preface and Acknowledgments

Ch. 1 Overview

What Is Game Theory?

What Can You Do with Game Theory?

Four Problems in Political Science

Why Model?

The Rational Choice Approach to Social Modeling

Ch. 2 Utility Theory

The Concept of Rationality

How Do Utility Functions Predict Actions?

An Example: Nixon's Christmas Bombing

Certainty, Risk, and Uncertainty

Utility Theory under the Condition of Risk

Some Common Misconceptions about Utility Theory

Utility Functions and Types of Preferences

A Simple Example: The Calculus of Deterrence

Another Simple Example: The Decision to Vote

Why Might Utility Theory Not Work?

Ch. 3 Specifying a Game

Formalizing a Situation: Deterrence in the Cuban Missile Crisis

Games in Extensive Form

Games in Strategic Form

Ch. 4 Classical Game Theory

Defining the Terms of Classi`cal Game Theory

Domination, Best Replies, and Equilibrium

Mixed Strategies

The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games

Characteristics of Nash Equilibria

Nash Equilibria and Common Conjectures

Rationalizability

Political Reform in Democracies

Candidate Competition in the Spatial Model of Elections

A Very Brief Introduction to Cooperative Game Theory

Ch. 5 Solving Extensive-Form Games: Backwards Induction and Subgame Perfection

Backwards Induction

Subgame Perfection

Sophisticated Voting

Agenda Control

Legislative Rules and Structure-Induced Equilibria

The Rubinstein Bargaining Model

Bargaining in Legislatures

Why Might Backwards Induction Yield Counterintuitive Results?

Ch. 6 Beliefs and Perfect Bayesian Equilibria

Bayes's Theorem

The Preference for Biased Information

Perfect Bayesian Equilibria

Nuclear Deterrence

Ch. 7 More on Noncooperative Equilibrium: Perfect and Sequential Equilibria

Elimination of Weakly Dominated Strategies

Perfect Equilibrium

Sequential Equilibrium

Deterrence and the Signaling of Resolve

''Why Vote?'' Redux

Ch. 8 Games of Limited Information and Restrictions on Beliefs

Signaling Games

The Informational Role of Congressional Committees

Bargaining under Incomplete Information

Deterrence and Out-of-Equilibrium Beliefs

An Introduction to Restrictions on Beliefs

''Cheap Talk'' and Coordination

Ch. 9 Repeated Games

Thinking about Repetition: Iterated Prisoner's Dilemma

Folk Theorems

Finite Repeated Games: The Chain Store Paradox

Stationarity

Retrospective Voting and Electoral Control

Ch. 10 Conclusion: Where Do We Go from Here?

How Do Formal Models Increase Our Knowledge?

The Weaknesses of Game Theory

How Does One Build a Model?

Appendix 1: Basic Mathematical Knowledge

Algebra

Set Theory

Relations and Functions

Probability Theory

Limits

Differential Calculus

Partial Derivatives and Lagrange Multipliers

Integral Calculus

The Idea of a Mathematical Proof

Appendix 2: Answers to Selected Problems

Notes

Glossary of Terms in Game Theory

Bibliography

Index

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Summary

Game theory is the mathematical analysis of strategic interaction. In the fifty years since the appearance of von Neumann and Morgenstern's classic Theory of Games and Economic Behavior (Princeton, 1944), game theory has been widely applied to problems in economics. Until recently, however, its usefulness in political science has been underappreciated, in part because of the technical difficulty of the methods developed by economists. James Morrow's book is the first to provide a standard text adapting contemporary game theory to political analysis. It uses a minimum of mathematics to teach the essentials of game theory and contains problems and their solutions suitable for advanced undergraduate and graduate students in all branches of political science.

Morrow begins with classical utility and game theory and ends with current research on repeated games and games of incomplete information. The book focuses on noncooperative game theory and its application to international relations, political economy, and American and comparative politics. Special attention is given to models of four topics: bargaining, legislative voting rules, voting in mass elections, and deterrence. An appendix reviews relevant mathematical techniques. Brief bibliographic essays at the end of each chapter suggest further readings, graded according to difficulty. This rigorous but accessible introduction to game theory will be of use not only to political scientists but also to psychologists, sociologists, and others in the social sciences.

Author Bio

**Morrow, James D. : Stanford University**

James D. Morrow is Senior Research Fellow at the Hoover Institution on War, Revolution and Peace at Stanford University.

Table of Contents

List of Figures and Tables

Preface and Acknowledgments

Ch. 1 Overview

What Is Game Theory?

What Can You Do with Game Theory?

Four Problems in Political Science

Why Model?

The Rational Choice Approach to Social Modeling

Ch. 2 Utility Theory

The Concept of Rationality

How Do Utility Functions Predict Actions?

An Example: Nixon's Christmas Bombing

Certainty, Risk, and Uncertainty

Utility Theory under the Condition of Risk

Some Common Misconceptions about Utility Theory

Utility Functions and Types of Preferences

A Simple Example: The Calculus of Deterrence

Another Simple Example: The Decision to Vote

Why Might Utility Theory Not Work?

Ch. 3 Specifying a Game

Formalizing a Situation: Deterrence in the Cuban Missile Crisis

Games in Extensive Form

Games in Strategic Form

Ch. 4 Classical Game Theory

Defining the Terms of Classi`cal Game Theory

Domination, Best Replies, and Equilibrium

Mixed Strategies

The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games

Characteristics of Nash Equilibria

Nash Equilibria and Common Conjectures

Rationalizability

Political Reform in Democracies

Candidate Competition in the Spatial Model of Elections

A Very Brief Introduction to Cooperative Game Theory

Ch. 5 Solving Extensive-Form Games: Backwards Induction and Subgame Perfection

Backwards Induction

Subgame Perfection

Sophisticated Voting

Agenda Control

Legislative Rules and Structure-Induced Equilibria

The Rubinstein Bargaining Model

Bargaining in Legislatures

Why Might Backwards Induction Yield Counterintuitive Results?

Ch. 6 Beliefs and Perfect Bayesian Equilibria

Bayes's Theorem

The Preference for Biased Information

Perfect Bayesian Equilibria

Nuclear Deterrence

Ch. 7 More on Noncooperative Equilibrium: Perfect and Sequential Equilibria

Elimination of Weakly Dominated Strategies

Perfect Equilibrium

Sequential Equilibrium

Deterrence and the Signaling of Resolve

''Why Vote?'' Redux

Ch. 8 Games of Limited Information and Restrictions on Beliefs

Signaling Games

The Informational Role of Congressional Committees

Bargaining under Incomplete Information

Deterrence and Out-of-Equilibrium Beliefs

An Introduction to Restrictions on Beliefs

''Cheap Talk'' and Coordination

Ch. 9 Repeated Games

Thinking about Repetition: Iterated Prisoner's Dilemma

Folk Theorems

Finite Repeated Games: The Chain Store Paradox

Stationarity

Retrospective Voting and Electoral Control

Ch. 10 Conclusion: Where Do We Go from Here?

How Do Formal Models Increase Our Knowledge?

The Weaknesses of Game Theory

How Does One Build a Model?

Appendix 1: Basic Mathematical Knowledge

Algebra

Set Theory

Relations and Functions

Probability Theory

Limits

Differential Calculus

Partial Derivatives and Lagrange Multipliers

Integral Calculus

The Idea of a Mathematical Proof

Appendix 2: Answers to Selected Problems

Notes

Glossary of Terms in Game Theory

Bibliography

Index

Publisher Info

Publisher: Princeton University Press

Published: 1994

International: No

Published: 1994

International: No

Morrow begins with classical utility and game theory and ends with current research on repeated games and games of incomplete information. The book focuses on noncooperative game theory and its application to international relations, political economy, and American and comparative politics. Special attention is given to models of four topics: bargaining, legislative voting rules, voting in mass elections, and deterrence. An appendix reviews relevant mathematical techniques. Brief bibliographic essays at the end of each chapter suggest further readings, graded according to difficulty. This rigorous but accessible introduction to game theory will be of use not only to political scientists but also to psychologists, sociologists, and others in the social sciences.

**Morrow, James D. : Stanford University**

James D. Morrow is Senior Research Fellow at the Hoover Institution on War, Revolution and Peace at Stanford University.

List of Figures and Tables

Preface and Acknowledgments

Ch. 1 Overview

What Is Game Theory?

What Can You Do with Game Theory?

Four Problems in Political Science

Why Model?

The Rational Choice Approach to Social Modeling

Ch. 2 Utility Theory

The Concept of Rationality

How Do Utility Functions Predict Actions?

An Example: Nixon's Christmas Bombing

Certainty, Risk, and Uncertainty

Utility Theory under the Condition of Risk

Some Common Misconceptions about Utility Theory

Utility Functions and Types of Preferences

A Simple Example: The Calculus of Deterrence

Another Simple Example: The Decision to Vote

Why Might Utility Theory Not Work?

Ch. 3 Specifying a Game

Formalizing a Situation: Deterrence in the Cuban Missile Crisis

Games in Extensive Form

Games in Strategic Form

Ch. 4 Classical Game Theory

Defining the Terms of Classi`cal Game Theory

Domination, Best Replies, and Equilibrium

Mixed Strategies

The Minmax Theorem and Equilibria of Two-Person, Zero-Sum Games

Characteristics of Nash Equilibria

Nash Equilibria and Common Conjectures

Rationalizability

Political Reform in Democracies

Candidate Competition in the Spatial Model of Elections

A Very Brief Introduction to Cooperative Game Theory

Ch. 5 Solving Extensive-Form Games: Backwards Induction and Subgame Perfection

Backwards Induction

Subgame Perfection

Sophisticated Voting

Agenda Control

Legislative Rules and Structure-Induced Equilibria

The Rubinstein Bargaining Model

Bargaining in Legislatures

Why Might Backwards Induction Yield Counterintuitive Results?

Ch. 6 Beliefs and Perfect Bayesian Equilibria

Bayes's Theorem

The Preference for Biased Information

Perfect Bayesian Equilibria

Nuclear Deterrence

Ch. 7 More on Noncooperative Equilibrium: Perfect and Sequential Equilibria

Elimination of Weakly Dominated Strategies

Perfect Equilibrium

Sequential Equilibrium

Deterrence and the Signaling of Resolve

''Why Vote?'' Redux

Ch. 8 Games of Limited Information and Restrictions on Beliefs

Signaling Games

The Informational Role of Congressional Committees

Bargaining under Incomplete Information

Deterrence and Out-of-Equilibrium Beliefs

An Introduction to Restrictions on Beliefs

''Cheap Talk'' and Coordination

Ch. 9 Repeated Games

Thinking about Repetition: Iterated Prisoner's Dilemma

Folk Theorems

Finite Repeated Games: The Chain Store Paradox

Stationarity

Retrospective Voting and Electoral Control

Ch. 10 Conclusion: Where Do We Go from Here?

How Do Formal Models Increase Our Knowledge?

The Weaknesses of Game Theory

How Does One Build a Model?

Appendix 1: Basic Mathematical Knowledge

Algebra

Set Theory

Relations and Functions

Probability Theory

Limits

Differential Calculus

Partial Derivatives and Lagrange Multipliers

Integral Calculus

The Idea of a Mathematical Proof

Appendix 2: Answers to Selected Problems

Notes

Glossary of Terms in Game Theory

Bibliography

Index