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• GAME THEORY
• Title
• Copyright
• Contents
• Preface
• PART I Rational Decision Making
• Chapter 1 The Single-Person Decision Problem
• 1.1 Actions, Outcomes, and Preferences
• 1.1.1 Preference Relations
• 1.1.2 Payoff Functions
• 1.2 The Rational Choice Paradigm
• 1.4 Exercises
• 1.3 Summary
• Chapter 2 Introducing Uncertainty and Time
• 2.1 Risk, Nature, and Random Outcomes
• 2.1.1 Finite Outcomes and Simple Lotteries
• 2.1.2 Simple versus Compound Lotteries
• 2.1.3 Lotteries over Continuous Outcomes
• 2.2 Evaluating Random Outcomes
• 2.2.1 Expected Payoff: The Finite Case
• 2.2.2 Expected Payoff: The Continuous Case
• 2.2.3 Caveat: It’s Not Just the Order Anymore
• 2.2.4 Risk Attitudes
• 2.2.5 The St. Petersburg Paradox
• 2.3 Rational Decision Making with Uncertainty
• 2.3.1 Rationality Revisited
• 2.3.2 Maximizing Expected Payoffs
• 2.4 Decisions over Time
• 2.4.1 Backward Induction
• 2.4.2 Discounting Future Payoffs
• 2.5 Applications
• 2.5.1 The Value of Information
• 2.5.2 Discounted Future Consumption
• 2.6 Theory versus Practice
• 2.7 Summary
• 2.8 Exercises
• PART II Static Games of Complete Information
• Chapter 3 Preliminaries
• 3.1 Normal-Form Games with Pure Strategies
• 3.1.1 Example: The Prisoner’s Dilemma
• 3.1.2 Example: Cournot Duopoly
• 3.1.3 Example: Voting on a New Agenda
• 3.2 Matrix Representation: Two-Player Finite Game
• 3.2.1 Example: The Prisoner’s Dilemma
• 3.2.2 Example: Rock-Paper-Scissors
• 3.3 Solution Concepts
• 3.3.1 Assumptions and Setup
• 3.3.2 Evaluating Solution Concepts
• 3.3.3 Evaluating Outcomes
• 3.4 Summary
• 3.5 Exercises
• Chapter 4 Rationality and Common Knowledge
• 4.1 Dominance in Pure Strategies
• 4.1.1 Dominated Strategies
• 4.1.2 Dominant Strategy Equilibrium
• 4.1.3 Evaluating Dominant Strategy Equilibrium
• 4.2 Iterated Elimination of Strictly Dominated Pure Strategies
• 4.2.1 Iterated Elimination and Common Knowledge of Rationality
• 4.2.2 Example: Cournot Duopoly
• 4.2.3 Evaluating IESDS
• 4.3 Beliefs, Best Response, and Rationalizability
• 4.3.1 The Best Response
• 4.3.2 Beliefs and Best-Response Correspondences
• 4.3.3 Rationalizability
• 4.3.4 The Cournot Duopoly Revisited
• 4.3.5 The “p-Beauty Contest”
• 4.3.6 Evaluating Rationalizability
• 4.4 Summary
• 4.5 Exercises
• Chapter 5 Pinning Down Beliefs: Nash Equilibrium
• 5.1 Nash Equilibrium in Pure Strategies
• 5.1.1 Pure-Strategy Nash Equilibrium in a Matrix
• 5.1.2 Evaluating the Nash Equilibria Solution
• 5.2 Nash Equilibrium: Some Classic Applications
• 5.2.1 Two Kinds of Societies
• 5.2.2 The Tragedy of the Commons
• 5.2.3 Cournot Duopoly
• 5.2.4 Bertrand Duopoly
• 5.2.5 Political Ideology and Electoral Competition
• 5.3 Summary
• 5.4 Exercises
• Chapter 6 Mixed Strategies
• 6.1 Strategies, Beliefs, and Expected Payoffs
• 6.1.1 Finite Strategy Sets
• 6.1.2 Continuous Strategy Sets
• 6.1.3 Beliefs and Mixed Strategies
• 6.1.4 Expected Payoffs
• 6.2 Mixed-Strategy Nash Equilibrium
• 6.2.1 Example: Matching Pennies
• 6.2.2 Example: Rock-Paper-Scissors
• 6.2.3 Multiple Equilibria: Pure and Mixed
• 6.3 IESDS and Rationalizability Revisited
• 6.4 Nash’s Existence Theorem
• 6.5 Summary
• 6.6 Exercises
• PART III Dynamic Games of Complete Information
• Chapter 7 Preliminaries
• 7.1 The Extensive-Form Game
• 7.1.1 Game Trees
• 7.1.2 Imperfect versus Perfect Information
• 7.2 Strategies and Nash Equilibrium
• 7.2.1 Pure Strategies
• 7.2.2 Mixed versus Behavioral Strategies
• 7.2.3 Normal-Form Representation of Extensive-Form Games
• 7.3 Nash Equilibrium and Paths of Play
• 7.4 Summary
• 7.5 Exercises
• Chapter 8 Credibility and Sequential Rationality
• 8.1 Sequential Rationality and Backward Induction
• 8.2 Subgame-Perfect Nash Equilibrium: Concept
• 8.3 Subgame-Perfect Nash Equilibrium: Examples
• 8.3.1 The Centipede Game
• 8.3.2 Stackelberg Competition
• 8.3.3 Mutually Assured Destruction
• 8.3.4 Time-Inconsistent Preferences
• 8.4 Summary
• 8.5 Exercises
• Chapter 9 Multistage Games
• 9.1 Preliminaries
• 9.2 Payoffs
• 9.3 Strategies and Conditional Play
• 9.4 Subgame-Perfect Equilibria
• 9.5 The One-Stage Deviation Principle
• 9.6 Summary
• 9.7 Exercises
• Chapter 10 Repeated Games
• 10.1 Finitely Repeated Games
• 10.2 Infinitely Repeated Games
• 10.2.1 Payoffs
• 10.2.2 Strategies
• 10.3 Subgame-Perfect Equilibria
• 10.4 Application: Tacit Collusion
• 10.5 Sequential Interaction and Reputation
• 10.5.1 Cooperation as Reputation
• 10.5.2 Third-Party Institutions as Reputation Mechanisms
• 10.5.3 Reputation Transfers without Third Parties
• 10.6 The Folk Theorem: Almost Anything Goes
• 10.7 Summary
• 10.8 Exercises
• Chapter 11 Strategic Bargaining
• 11.1 One Round of Bargaining: The Ultimatum Game
• 11.2 Finitely Many Rounds of Bargaining
• 11.3 The Infinite-Horizon Game
• 11.4 Application: Legislative Bargaining
• 11.4.1 Closed-Rule Bargaining
• 11.4.2 Open-Rule Bargaining
• 11.5 Summary
• 11.6 Exercises
• PART IV Static Games of Incomplete Information
• Chapter 12 Bayesian Games
• 12.1 Strategic Representation of Bayesian Games
• 12.1.1 Players, Actions, Information, and Preferences
• 12.1.2 Deriving Posteriors from a Common Prior: A Player’s Beliefs
• 12.1.3 Strategies and Bayesian Nash Equilibrium
• 12.2 Examples
• 12.2.1 Teenagers and the Game of Chicken
• 12.2.2 Study Groups
• 12.3 Inefficient Trade and Adverse Selection
• 12.4 Committee Voting
• 12.5 Mixed Strategies Revisited: Harsanyi’s Interpretation
• 12.6 Summary
• 12.7 Exercises
• Chapter 13 Auctions and Competitive Bidding
• 13.1 Independent Private Values
• 13.1.1 Second-Price Sealed-Bid Auctions
• 13.1.2 English Auctions
• 13.1.3 First-Price Sealed-Bid and Dutch Auctions
• 13.1.4 Revenue Equivalence
• 13.2 Common Values and the Winner’s Curse
• 13.3 Summary
• 13.4 Exercises
• Chapter 14 Mechanism Design
• 14.1 Setup: Mechanisms as Bayesian Games
• 14.1.1 The Players
• 14.1.2 The Mechanism Designer
• 14.1.3 The Mechanism Game
• 14.2 The Revelation Principle
• 14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms
• 14.3.1 Dominant Strategy Implementation
• 14.3.2 Vickrey-Clarke-Groves Mechanisms
• 14.4 Summary
• 14.5 Exercises
• PART V Dynamic Games of Incomplete Information
• Chapter 15 Sequential Rationality with Incomplete Information
• 15.1 The Problem with Subgame Perfection
• 15.2 Perfect Bayesian Equilibrium
• 15.3 Sequential Equilibrium
• 15.4 Summary
• 15.5 Exercises
• Chapter 16 Signaling Games
• 16.1 Education Signaling: The MBA Game
• 16.2 Limit Pricing and Entry Deterrence
• 16.2.1 Separating Equilibria
• 16.2.2 Pooling Equilibria
• 16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games
• 16.4 Summary
• 16.5 Exercises
• Chapter 17 Building a Reputation
• 17.1 Cooperation in a Finitely Repeated Prisoner’s Dilemma
• 17.2 Driving a Tough Bargain
• 17.3 A Reputation for Being “Nice”
• 17.4 Summary
• 17.5 Exercises
• Chapter 18 Information Transmission and Cheap Talk
• 18.1 Information Transmission: A Finite Example
• 18.2 Information Transmission: The Continuous Case
• 18.3 Application: Information and Legislative Organization
• 18.4 Summary
• 18.5 Exercises
• Chapter 19 Mathematical Appendix
• 19.1 Sets and Sequences
• 19.1.1 Basic Definitions
• 19.1.2 Basic Set Operations
• 19.2 Functions
• 19.2.1 Basic Definitions
• 19.2.2 Continuity
• 19.3 Calculus and Optimization
• 19.3.1 Basic Definitions
• 19.3.2 Differentiation and Optimization
• 19.3.3 Integration
• 19.4 Probability and Random Variables
• 19.4.1 Basic Definitions
• 19.4.2 Cumulative Distribution and Density Functions
• 19.4.3 Independence, Conditional Probability, and Bayes’ Rule
• 19.4.4 Expected Values
• References
• Index