Games of Strategy

All introductory textbooks begin by attempting to convince the student readers that the subject is of great importance in the world, and therefore merits their attention. The physical sciences and engineering claim to be the basis of modern technology and therefore of modern life; the social sciences discuss big issues of governance, for example, democracy and taxation; the humanities claim that they revive your soul after it has been deadened by exposure to the physical and social sciences and to engineering. Where does the subject "games of strategy," often also called game theory, fit into this picture, and why should you study it?

Dixit and Skeath's Games of Strategy offers a practical motivation much more individual and closer to your personal concerns than most other subjects. You play games of strategy all the time: with your parents, siblings, friends, enemies, even with your professors. You have probably acquired a lot of instinctive expertise, and we hope you will recognize in what follows some of the lessons you have already learned. This book's authors will build on this experience, systematize it, and develop it to the point where you will be able to improve your strategic skills and use them more methodically. Opportunities for such uses will appear throughout the rest of your life; you will go on playing such games with your employers, employees, spouses, children, and even strangers.

Not that the subject lacks wider importance. Similar games are played in business, politics, diplomacy, wars — in fact, whenever people interact to strike mutually agreeable deals or to resolve conflicts. Being able to recognize such games will enrich your understanding of the world around you, and will make you a better participant in all its affairs.

• 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
1. Which Passing Shot?
2. The GPA Trap
3. "We Can't Take the Exam Because We Had a Flat Tire"
4. Why Are Professors So Mean?
5. Roommates and Families on the Brink
6. The Dating Game
3. Our Strategy for Studying Games of Strategy
• Summary
2. How to Think About Strategic Games
1. Decisions versus Games
2. Classifying Games
1. Are the Moves in the Game Sequential or Simultaneous?
2. Are the Players' Interests in Total Conflict, or Is There Some Commonalities?
3. is the Game Played Once or Repeatedly, and with the Same or Changing Opponents?
4. Do the Players Have Full or Equal Information?
5. Are the Rules of the Game Fixed or Manipulable?
6. Are Agreements to Cooperate Enforceable?
3. Some Terminology and Background Assumptions
1. Strategies
2. Payoffs
3. Rationality
4. Common Knowledge of Rules
5. Equilibrium
6. Dynamics and Evolutionary Games
7. 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. A Senate Race as a Sequential-Move Game
2. Illustrating Sequential-Move Games
3. Describing Strategies
4. Rollback Equilibrium
5. A Sequential-Move Game with Only "One" Player
6. Order Advantages
7. Adding More Players
8. Adding More Moves
1. Tic-Tac-Toe
2. Chess
9. Experiments in Strategy
• Summary
• Key Terms
• Exercises
4. Games with Simultaneous Moves
1. Illustrating Simultaneous-Move Games
1. Zero-Sum Versus Non-Zero-Sum Games
2. Constructing an Actual Game Table
2. Nash Equilibrium
3. Dominant Strategies
4. When Both Players Have Dormant Strategies
5. When Only One Player has a Dominant Strategy
6. Successive Elimination of Dominated Strategies
1. Symmetric Games
2. Weak Versus Strict Dominance
7. Minimax Strategies in Zero-Sum Games
8. Cell-by-Cell Inspection
9. Pure Strategies that are Continuous Variables
10. Three Players
11. Multiple Equilibria in Pure Strategies
1. Assurance
2. Chicken
3. The Battle of the Two Cultures
4. Weak Dominance
12. No Equilibrium in Pure Strategies
• Summary
• Key Terms
• Exercises
5. Simultaneous-Move Games with Mixed Strategies
1. What is a Mixed Strategy?
2. What Does a Mixed Strategy Accomplish?
1. The Row Player's Perspective
2. The Column Player's Perspective
3. Equilibrium in Mixed Strategies
4. Mixing in Non-Zero-Sum Games
1. Chicken
2. The Battle of the Two Cultures
5. Further Discussion of Mixed Strategies
1. The Odds Method
2. Counterintuitive Outcomes with Mixed Strategies
3. Using Mixed Strategies in Practice
6. Mixing When One Player has Three or More Pure Strategies
1. A General Case
2. Coincidental Case
• Summary
• Key Terms
• Exercises
• Appendix: Probability and Expected Utility
1. The Basic Algebra of Probabilities
1. The Addition Rule
2. The Modified Addition Rule
3. The Multiplication Rule
4. The Modified Multiplication Rule
5. The Combination Rule
6. Expected Values
2. Inferring Event Probabilities from Observing Consequences
3. Attitudes Toward Risk and Expected Utility
• Summary
• Key terms
6. Combining Simultaneous and Sequential Moves
1. Illustrating Games in Both Extensive and Strategic Form
2. Games with Both Simultaneous and Sequential Moves
3. Combined Sequential-Play and Mixed-Strategy Equilibria
4. Rules Change I: Converting from Sequential to Simultaneous Play
5. Solving the Sequential-Move Game from Its Strategic Form
6. Subgame-Perfect Equilibria
7. Rules Change II: Convering from Simultaneous to Sequential Play
• Summary
• Key Terms
• Exercises
7. Consolidation, Extension, and Discussion
1. Validity of the Nash Equilibrium Concept
1. Is the Nash Equilibrium Concept Too Imprecise?
2. Do Players in Actual Games Play Nash Equilibrium Strategies?
3. Does Rationality by Itself Imply Nash Equilibrium?
4. Does the Nash Equilibrium Account for Risks Properly?
5. Is the Expected-Payoff Maximization Assumption Reasonable?
2. Games of Dynamic Competition
1. Calculating the Probabilities of Winning at Tennis
2. Strategy in Tennis
3. Applying Tennis Analysis to Business
3. Nash Equilibrium with Continuous Strategies
4. Mixing Among Many Strategies: Examples
1. A Zero-Sum, Three-by-Three Game
2. A Three-by-Three Example with Unused Strategies
5. Mixing Among Many Strategies: General theory
• Summary
• Key Terms
• Exercises
• Part Three: Some Broad Classes of Games and Strategies
8. The Prisoners' Dilemma Game
1. The Basic Game (Review)
2. Solutions I: Repetition
1. Finite Repetition
2. Infinite Repetition
3. Games of Unknown Length
4. General Theory
3. Solutions II: Penalties and Rewards
4. Solutions III: Leadership
5. Experimental Evidence
6. Real-World Dilemmas
1. Policy Setting
2. Labor Arbitration
3. Evolutionary Biology
4. Price Matching
• Summary
• Key Terms
• Exercises
9. Games with Strategic Moves
1. A Classification of Strategic Moves
1. Unconditional Strategic Moves
2. Conditional Strategic Moves
2. Credibility of Strategic Moves
3. Commitments
4. Threats and Promises
1. Example of a Threat: U.S.-Japanese Trade Relations
2. Example of a Promise: The Pizza Pricing game
3. Example Combining Threat and Promise: Joint U.S.-European Military Operations
5. Some Additional Issues
1. When Do Strategic Moves Help?
2. Deterrence Versus Compellence
6. Acquiring Credibility
1. Reducing Your Freedom of Action
2. Changing Your Payoffs
7. Countering Your Opponent's Strategic Moves
1. Irrationality
2. Cutting Off Communication
3. Leaving Escape Routes Open
4. Undermining Your Opponent's Motive to Uphold His Reputation
5. Salami Tactics
• Summary
• Key Terms
• Exercises
10. Evolutionary Games
1. The Framework
2. The Prisoners' Dilemma
1. The Twice-Played Prisoners' Dilemma
2. Multiple Repetitions
3. Comparing the Evolutionary and Rational-Player Models
3. Chicken
4. The Assurance Game
5. Interactions Across Species
6. The Hawk-Dove Game
1. Rational Strategic Choice and Equilibrium
2. Evolutionary Stability for V > C
3. Evolutionary Stability for V < C
4. V < C: Stable Polymorphic Population
5. V < C_ Each Individual Mixes Strategy
7. Some General Theory
8. Dynamics with Three Types in the Population
9. Evolution of Cooperation and Altruism
• Summary
• Key Terms
• Exercises
11. Collective Action Games
1. Collective-Action Games with Two Players
1. Numerical Examples
2. Generalization of the Two-Person Case
2. Collective-Action Problems in Large Groups
3. A Brief History of Ideas
4. Solving Collective-Action Problems
1. Analysis
2. Applications
5. Spillovers, or Externalities
1. The Calculus of the General Case
2. Negative Spillovers
3. Positive Spillovers
6. "Help!" — A Game of Chicken with Mixed Strategies
• Summary
• Key Terms
• Exercises
12. Uncertainty and Information
1. Controlling and Manipulating Risk
1. Strategies to Reduce Risk
2. Using Risk
3. Manipulating Risk in Contests
2. Some Strategies to Manipulate Information
1. Literal and Strategic Liars
2. King Solomon's Unwisdom
3. Incentives to Induce Effort
4. Screening and Signaling
5. Separation and Pooling
1. Separating Equilibrium
2. Pooling Equilibrium
3. Semiseparating Equilibrium
6. Some Evidence for Signaling and Screening
7. Additional Reading on Information Manipulation
• Summary
• Key Terms
• Exercises
• Part Four: Applications to Specific Strategic Situations
13. Brinkmanship: The Cuban Missile Crisis
1. A Brief Narration of Events
2. A Simple Game-Theoretic Explanation
3. Accounting for Additional Complexities
4. A Probabilistic Threat
5. Practicing Brinkmanship
• Summary
• Key Terms
• Exercises
14. Strategy and Voting
1. Voting Rules and Procedures
1. Binary Methods
2. Plurative Methods
3. Mixed Methods
2. Voting Paradoxes
1. The Condorcet Paradox
2. The Reversal Paradox
3. The Agenda Paradox
4. Change theVoting Method, Change the Outcome
3. Evaluating Vote Aggregation Methods
4. Strategic Voting
1. Plurality Rule
2. Pairwise Voting
3. The Borda Count
5. The Median Voter Theorem
1. Discrete Political Spectrum
2. Continuous Political Spectrum
• Summary
• Key Terms
• Exercises
15. Bidding Strategies and Auction Design
1. Types of Auctions
2. The Winner's Curse
3. Bidding Strategies
4. Vickrey's Truth Serum
5. All-Pay Auctions
6. How to Sell at Auction
1. Risk-Neutral Bidders and Independent Estimates
2. Correlated Estimates
3. Risk-Averse Bidders
7. Some Added Twists to Consider
1. Multiple Objects
2. Defeating the System
3. Information Disclosure
8. The Airwave Spectrum Auctions
1. Designing the Rules
2. How the Auctions Have Fared
3. Two Specific Bidding Issues
• Summary
• Key Terms
• Exercises
16. Bargaining
1. Nash's Cooperative Solution
1. Numerical Examples
2. General Theory
2. Variable-Threat Bargaining
3. Alternating-Offer Model I: Total Value Decays
4. Experimental Evidence
5. Alternating-Offer Model II: Impatience
6. Manipulating Information in Bargaining
7. Bargaining with Many Parties and Issues
1. Multi-Issue Bargaining
2. Multiparty Bargaining
• Summary
• Key Terms
• Exercises
17. Markets and Competition
1. A Simple Trading Game
2. The Core
1. Numerical Examples
2. Some Properties of the Core
3. Discussion
3. The Market Mechanism
1. Properties of the Market Mechanism
2. Experimental Evidence
4. The Shapley Value
1. Power in Legislature and Committees
2. Allocation of Joint Costs
5. Fair Division Mechanisms
• Summary
• Key Terms
• Exercises

Game theory that can be used practically. Thank you.