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- December 2014
- ISBN: 978-0-393-12444-6
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# Games of Strategy

**Fourth Edition**

Paperback

What makes this the best-selling text on Game Theory?

*Games of Strategy*, famous for its simple yet accurate exposition and its great examples and exercises, has been extensively revised for this Fourth Edition. The key to its broad success is that the authors assume no prior knowledge of game theory and present the material in the most accessible way possible. With new and improved features and compelling end-of-chapter exercises, this Fourth Edition of *Games of Strategy* continues to engage students around the world.

## New material on Behavioral and Experimental Economics and carefully revised chapters keep students in the know

This Fourth Edition includes expanded coverage of Behavioral Economics and Experimental Economics (Chapters 3 through 7) to ensure that students are kept up-to-date on these hot topics in game theory. In addition to an extensive revision of every chapter, there is also an updated coverage of Cheap Talk, Information, Repeated Games, and Collective Action and Incentives, among other topics.

## Increased number of end-of-chapter exercises—solved and unsolved

The authors have added even more new end-of-chapter exercises to this Fourth Edition. The solutions to half of the exercises are available for students on the free accompanying website.

## Lively and relevant examples and cases raise student interest

*Games of Strategy*, Fourth Edition, allows students to explore a variety of topics from the TV show *Survivor* to the lack of .400 hitters in modern baseball, from Kmart versus Toys-R-Us to side-blotched lizards in California. New to this edition are discussions regarding the U.S. and China Trade Policy and lending to Greece, and an entire chapter devoted to the Cuban Missile Crisis. Students can also delve into issues concerning Student Life, such as grade inflation and why roommates wait for the other to buy the common items (soap, ketchup, etc.) and therefore why they always run out.

- 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