Contents
Part One: Introduction and General Principles
1. Basic Ideas and Examples
2. How to Think about Strategic Games
Part Two: Concepts and Techniques
3. Games with Sequential Moves
4. Simultaneous-Move Games with Pure Strategies
5. Simultaneous-Move Games with Pure Strategies, II
6. Combining Sequential and Simultaneous Moves
7. Simultaneous-Move Games with Mixed Strategies
Part Three: Some Broad Classes of Games and Strategies
8. Uncertainty and Information
9. Strategic Moves
10. The Prisoner’s Dilemma and Repeated Games
11. Collective-Action Games
12. Evolutionary Games
Part Four: Applications to Specific Strategic Situations
13. Mechanism Design
14. Brinkmanship: The Cuban Missile Crisis
15. Strategy and Voting
16. Bidding Strategy and Auction Design
17. Bargaining
Preface
Part One
Introduction and General Principles
1.Basic Ideas and Examples
1. What Is a Game of Strategy?
2. Some Examples and Stories of Strategic Games
A. Which Passing Shot?
B. The GPA Rat Race
C. “We Can’t Take the Exam, Because We Had a Flat Tire”
D. Why Are Professors So Mean?
E. Roommates and Families on the Brink
F. The Dating Game
3. Our Strategy for Studying Games of Strategy
2. How to Think about Strategic Games
1. Decisions versus Games
2. Classifying Games
A. Are the Moves in the Game Sequential or Simultaneous?
B. Are the Players’ Interests in Total Conflict or Is There Some Commonality?
C. Is the Game Played Once or Repeatedly, and with the Same or Changing Opponents?
D. Do the Players Have Full or Equal Information?
E. Are the Rules of the Game Fixed or Manipulable?
F. Are Agreements to Cooperate Enforceable?
3. Some Terminology and Background Assumptions
A. Strategies
B. Payoffs
C. Rationality
D. Common Knowledge of Rules
E. Equilibrium
F. Dynamics and Evolutionary Games
G. Observation and Experiment
4. The Uses of Game Theory
5. The Structure of the Chapters to Follow
Summary
Key Terms
Exercises
Part Two
Concepts and Techniques
3. Games with Sequential Moves
1. Game Trees
A. Nodes, Branches, and Paths of Play
B. Uncertainty and “Nature’s Moves”
C. Outcomes and Payoffs
D. Strategies
E. Tree Construction
2. Solving Games by Using Trees
3. Adding More Players
4. Order Advantages
5. Adding More Moves
A. Tic-Tac-Toe
B. Chess
C. Checkers
6. Evidence Concerning Rollback
7. Strategies in Survivor
Summary
Key Terms
Exercises
4. Simultaneous-Move Games: Discrete Strategies
1. Depicting Simultaneous-Move Games with Discrete Strategies
2. Nash Equilibrium
A. Some Further Explanation of the Concept of Nash Equilibrium
B. Nash Equilibrium as a System of Beliefs and Choices
3. Dominance
A. Both Players Have Dominant Strategies
B. One Player Has a Dominant Strategy
C. Successive Elimination of Dominated Strategies
4. Best-Response Analysis
5. Three Players
6. Multiple Equilibria in Pure Strategies
A. Will Harry Meet Sally? Pure Coordination
B. Will Harry Meet Sally? And Where? Assurance
C. Will Harry Meet Sally? And Where? Battle of the Sexes
D. Will James Meet Dean? Chicken
7. No Equilibrium in Pure Strategies
Summary
Key Terms
Exercises
5. Simultaneous-Move Games: Continuous Strategies, Discussion, and Evidence
1 Pure Strategies that are Continuous Variables
A. Price Competition
B. Some Economics of Oligopoly
C. Political Campaign Advertising
D. General Method for Finding Nash Equilibria
2. Critical Discussion of the Nash Equilibrium Concept
A. The Treatment of Risk in Nash Equilibrium
B. Multiplicity of Nash Equilibria
C. Requirements of Rationality for Nash Equilibrium
3. Rationalizability
A. Applying the Concept of Rationalizability
B. Rationalizability Can Take Us All the Way to Nash Equilibrium
4. Empirical Evidence Concerning Nash Equilibrium
A. Laboratory Experiments
B. Real-World Evidence
Summary
Key Terms
Exercises
Appendix: Finding a Value to Maximize a Function
6. Combining Sequential and Simultaneous Moves
1. Games with Both Simultaneous and Sequential Moves
A. Two-Stage Games and Subgames
B. Configurations of Multistage Games
2. Changing the Order of Moves in a Game
A. Changing Simultaneous-Move Games into Sequential-Move Games
B. Other Changes in the Order of Moves
3. Change in the Method of Analysis
A. Illustrating Simultaneous-Move Games by Using Trees
B. Showing and Analyzing Sequential-Move Games in Strategic Form
4. Three-Player Games
Summary
Key Terms
Exercises
7. Simultaneous-Move Games: Mixed Strategies
1. What Is a Mixed Strategy?
2. Mixing Moves
A. The Benefit of Mixing
B. Best Responses and Equilibrium
3 Nash Equilibrium as a System of Beliefs and Responses
4. Mixing in Non-Zero-Sum Games
A. Will Harry Meet Sally? Assurance, Pure Coordination, and Battle of the Sexes
B. Will James Meet Dean? Chicken
5. General Discussion of Mixed-Strategy Equilibria
A. Weak Sense of Equilibrium
B. Counterintuitive Changes in Mixture Probabilities in Zero-Sum Games
C. Risky and Safe Choices in Zero-Sum Games
6. Mixing When One Player Has Three or More Pure Strategies
A. A General Case
B. Exceptional Cases
7. Mixing When Both Players Have Three Strategies
A. Full Mixure of All Strategies
B. Equilibrium Mixtures with Some Strategies Unused
8. How to Use Mixed Strategies in Practice
9. Evidence on Mixing
A. Zero-Sum Games
B. Non-Zero-Sum Games
Summary
Key Terms
Exercises
Appendix: The Basic Algebra of Probablilities
A. The Addition Rule
B. The Multiplication rule
C. Expected values
Summary
Key terms
Part Three
Some Broad Classes of Games and Strategies
8. Uncertainty and Information
1 Imperfect Information: Dealing with Risk
A. Sharing of Risk
B. Paying to Reduce Risk
C. Manipulating Risk in Contests
2. Asymmetric Information: Basic Ideas
3. Direct Communication, or “Cheap Talk”
A. Perfectly Aligned Interests
B. Totally Conflicting Interests
C. Partially Aligned Interests
D. Formal Analysis of Cheap Talk Games
4. Adverse Selection, Signaling, and Screening
A. Adverse Selection and Market Failure
B. The Market for “Lemons”
C. Signaling and Screening: Sample Situations
D. Experimental Evidence
5. Signaling in the Labor Market
A. Screening to Separate Types
B. Pooling of Types
C. Many Types
6. Equilibria in Two-Player Signaling Games
A. Basic Model and Payoff Structure
B. Separating Equilibrium
C. Pooling Equilibrium
D. Semiseparating Equilibrium
Summary
Key Terms
Exercises
Appendix: Risk Attitudes and Bayes’ Theorem
1. Attitudes Toward Risk and Expected Utility
2. Inferring Probabilities from Observing Consequences
Summary
Key terms
9. Strategic Moves
1. A Classification of Strategic Moves
A. Unconditional Strategic Moves
B. Conditional Strategic Moves
2. Credibility of Strategic Moves
3. Commitments
4. Threats and Promises
A. Example of a Threat: U.S.–Japan Trade Relations
B. Example of a Promise: The Restaurant Pricing Game
C. Example Combining Threat and Promise: Joint U.S.–China Political Action
5. Some Additional Topics
A. When Do Strategic Moves Help?
B. Deterrence versus Compellence
6. Acquiring Credibility
A. Reducing Your Freedom of Action
B. Changing Your Payoffs
7. Countering Your Opponent’s Strategic Moves
A. Irrationality
B. Cutting Off Communication
C. Leaving Escape Routes Open
D. Undermining Your Opponent’s Motive to Uphold His Reputation
E. Salami Tactics
Summary
Key Terms
Exercises
10. The Prisoners’ Dilemma and Repeated Games
1. The Basic Game (Review)
2. Solutions I: Repetition
A. Finite Repetition
B. Infinite Repetition
C. Games of Unknown Length
D. General Theory
3. Solutions II: Penalties and Rewards
4. Solutions III: Leadership
5. Experimental Evidence
6. Real-World Dilemmas
A. Evolutionary Biology
B. Price Matching
C. International Environmental Policy: The Kyoto Protocol
Summary
Key Terms
Exercises
Appendix: Infinite Sums
11. Collective-Action Games
1. Collective-Action Games with Two Players
A. Collective Action as a Prisoners’ Dilemma
B. Collective Action as Chicken
C. Collective Action as Assurance
D. Collective Inaction
2. Collective-Action Problems in Large Groups
A. Multiplayer Prisoners’ Dilemma
B. Multiplayer Chicken
C. Multiplayer Assurance
3. Spillovers, or Externalities
A. Commuting and Spillovers
B. Spillovers: The General Case
C. Commuting Revisited: Negative Externalities
D. Positive Spillovers
4. A Brief History of Ideas
A. The Classics
B. Modern Approaches and Solutions
C. Applications
5. “Help!”: A Game of Chicken with Mixed Strategies
Summary
Key Terms
Exercises
12. Evolutionary Games
1. The Framework
2. Prisoners’ Dilemma
A. The Repeated Prisoners’ Dilemma
B. Multiple Repetitions
C. Comparing the Evolutionary and Rational-Player Models
3. Chicken
4. The Assurance Game
5. Three Phenotypes in the Population
A. Testing for ESS
B. Dynamics
6. The Hawk–Dove Game
A. Rational Strategic Choice and Equilibrium
B. Evolutionary Stability for V > C
C. Evolutionary Stability for V < C
D. V < C: Stable Polymorphic Population
E. V < C: Each Player Mixes Strategies
F. Some General Theory
7. Interactions by Population and across Species
A. Playing the Field
B. Interactions across Species
8. Evolution of Cooperation and Altruism
Summary
Key Terms
Exercises
13. Mechanism Design
1. Price Discrimination
2. Some Terminology
3. Cost-Plus and Fixed-Price Contracts
A. Highway Construction: Full Information
B. Highway Construction: Asymmetric Information
4. Evidence Concerning Information Revelation Mechanisms
5. Incentives for Effort: The Simplest Case
A. Managerial Supervision
B. Insurance Provision
6. Incentives for Effort: Evidence and Extensions
A. Nonlinear Incentive Schemes
B. Incentives in Teams
C. Multiple Tasks and Outcomes
D. Incentives over Time
Summary
Key Terms
Exercises
Part Four
Applications to Specific Strategic Situations
14. Brinkmanship: The Cuban Missile Crisis
1. A Brief Narrative of Events
2. A Simple Game-Theoretic Explanation
3. Accounting for Additional Complexities
4. A Probabilistic Threat
5. Practicing Brinkmanship
Summary
Key Terms
Exercises
15. Strategy and Voting
1. Voting Rules and Procedures
A. Binary Methods
B. Plurative Methods
C. Mixed Methods
2. Voting Paradoxes
A. The Condorcet Paradox
B. The Agenda Paradox
C. The Reversal Paradox
D. Change the Voting Method, Change the Outcome
3. Evaluating Voting Systems
A. Black’s Condition
B. Robustness
C. Intensity Ranking
4. Strategic Manipulation of Votes
A. Plurality Rule
B. Pairwise Voting
C. Strategic Voting with Incomplete Information
D. Scope for Manipulability
5. The Median Voter Theorem
A. Discrete Political Spectrum
B. Continuous Political Spectrum
Summary
Key Terms
Exercises
16. Bidding Strategy and Auction Design
1. Types of Auctions
A. Auction Rules
B. Auction Environments
2. The Winner’s Curse
3. Bidding Strategies
A. The English Auction
B. First-Price ,Sealed Bids and Dutch Auctions: The Incentive to Shade
C. Second-Price, Sealed Bid Auctions: Vickrey’s Truth Serum
4. All-Pay Auctions
5. How to Sell at Auction
A. Risk-Neutral Bidders and Independent Estimates
B. Risk-Averse Bidders
C. Correlated Estimates
6. Some Added Twists to Consider
A. Multiple Objects
B. Defeating the System
C. Information Disclosure
D. Online Auctions
7. Additional Reading
Summary
Key Terms
Exercises
17. Bargaining
1. Nash’s Cooperative Solution
A. Numerical Example
B. General Theory
2. Variable-Threat Bargaining
3. Alternating-Offers Model I: Total Value Decays
4. Experimental Evidence
5. Alternating-Offers Model II: Impatience
6. Manipulating Information in Bargaining
7. Bargaining with Many Parties and Issues
A. Multi-Issue Bargaining
B. Multiparty Bargaining
Summary
Key Terms
Exercises
Glossary
Index