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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.
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.
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
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