Games of Strategy

, by Dixit, Avinash K.; Skeath, Susan

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ISBN: 9780393974218 | 0393974219
Cover: Hardcover
Copyright: 6/1/1999

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Supplemental Materials

Preface

xix

PART ONE Introduction and General Principles

Basic Ideas and Examples

(14)

What is a Game of Strategy?

(2)

Some Examples and Stories of Strategic Games

(8)

Which Passing Shot?

(1)

The GPA Trap

(1)

``We Can't Take the Exam Because We Had a Flat Tire''

(2)

Why Are Professors So Mean?

(1)

Roommates and Families on the Brink

(2)

The Dating Game

(1)

Our Strategy For Studying Games of Strategy

(3)

Summary

(1)

How to Think About Strategic Games

(28)

Decisions Versus Games

(2)

Classifying Games

(6)

Are the Moves in the Game Sequential or Simultaneous?

(1)

Are the Players' Interests in Total Conflict, or Is There Some Commonality?

(1)

Is the Game Played Once or Repeatedly, and with the Same or Changing Opponents?

(1)

Do the Players Have Full or Equal Information?

(1)

Are the Rules of the Game Fixed or Manipulable?

(1)

Are Agreements to Cooperate Enforceable?

(1)

Some Terminology and Background Assumptions

(10)

Strategies

(1)

Payoffs

(1)

Rationality

(2)

Common Knowledge of Rules

(1)

Equilibrium

(2)

Dynamics and Evolutionary Games

(1)

Observation and Experiment

(1)

The Uses of Game Theory

(1)

The Structure of The Chapters to Follow

(8)

Summary

(1)

Key Terms

(1)

Exercises

(4)

PART TWO Concepts and Techniques

Games with Sequential Moves

(36)

A Senate Race as a Sequential-Move Game

(2)

Illustrating Sequential-Move Games

(1)

Describing Strategies

(2)

Rollback Equilibrium

(4)

A Sequential-Move Game with Only ``One'' Player

(3)

Order Advantages

(2)

Adding More Players

(5)

Adding More Moves

(7)

Tic-Tac-Toe

(2)

Chess

(5)

Experiments in Strategy

(9)

Summary

(1)

Key Terms

(1)

Exercises

(5)

Games with Simultaneous Moves

(45)

Illustrating Simultaneous-Move Games

(2)

Zero-Sum Versus Non-Zero-Sum Games

(1)

Constructing an Actual Game Table

(1)

Nash Equilibrium

(1)

Dominant Strategies

(2)

When Both Players Have Dominant Strategies

(2)

When Only One Player Has a Dominant Strategy

(2)

Successive Elimination of Dominated Strategies

(4)

Symmetric Games

(1)

Weak Versus Strict Dominance

(1)

Minimax Strategies in Zero-Sum Games

(4)

Cell-by-Cell Inspection

(2)

Pure Strategies That are Continuous Variables

(5)

Three Players

104

(3)

Multiple Equilibria in Pure Strategies

107

(9)

Assurance

107

(3)

Chicken

110

(2)

The Battle of the Two Cultures

112

(2)

Weak Dominance

114

(2)

No Equilibrium in Pure Strategies

116

(8)

Summary

118

(1)

Key Terms

118

(1)

Exercises

119

(5)

Simultaneous-Move Games with Mixed Strategies

124

(39)

What is a Mixed Strategy?

125

(1)

What does a Mixed Strategy Accomplish?

125

(7)

The Row Player's Perspective

127

(4)

The Column Player's Perspective

131

(1)

Equilibrium in Mixed Strategies

132

(4)

Mixing in Non-Zero-Sum Games

136

(7)

Chicken

136

(4)

The Battle of the Two Cultures

140

(3)

Further Discussion of Mixed Strategies

143

(8)

The Odds Method

143

(4)

Counterintuitive Outcomes with Mixed Strategies

147

(2)

Using Mixed Strategies in Practice

149

(2)

Mixing when one Player has Three or More Pure Strategies

151

(12)

A General Case

152

(4)

A Coincidental Case

156

(3)

Summary

159

(1)

Key Terms

160

(1)

Exercises

160

(3)

Appendix: Probability and Expected Utility

163

(122)

The Basic Algebra of Probabilities

163

(7)

The Addition Rule

165

(1)

The Modified Addition Rule

166

(1)

The Multiplication Rule

166

(1)

The Modified Multiplication Rule

167

(1)

The Combination Rule

168

(1)

Expected Values

169

(1)

Inferring Event Probabilities from Observing Consequences

170

(3)

Attitudes Toward Risk and Expected Utility

173

(5)

Summary

176

(1)

Key Terms

177

(1)

Combining Simultaneous And Sequential Moves

178

(31)

Illustrating Games in Both Extensive and Strategic Form

179

(3)

Games with Both Simultaneous and Sequential Moves

182

(3)

Combined Sequential-Play and Mixed-Strategy Equilibria

185

(4)

Rules Change I: Converting From Sequential to Simultaneous Play

189

(3)

Solving the Sequential-Move Game From its Strategic Form

192

(3)

Subgame-Perfect Equilibria

195

(4)

Rules Change II: Converting From Simultaneous to Sequential Play

199

(10)

Summary

205

(1)

Key Terms

206

(1)

Exercises

206

(3)

Consolidation, Extension, and Discussion

209

(46)

Validity of the Nash Equilibrium Concept

210

(13)

Is the Nash Equilibrium Concept Too Imprecise?

211

(2)

Do Players in Actual Games Play Nash Equilibrium Strategies?

213

(3)

Does Rationality by Itself Imply Nash Equilibrium?

216

(2)

Does the Nash Equilibrium Account for Risks Properly?

218

(1)

Is the Expected-Payoff Maximization Assumption Reasonable?

219

(4)

Games of Dynamic Competition

223

(9)

Calculating the Probabilities of Winning at Tennis

225

(4)

Strategy in Tennis

229

(2)

Applying Tennis Analysis to Business

231

(1)

Nash Equilibrium With Continuous Strategies

232

(2)

Mixing Among Many Strategies: Examples

234

(6)

A Zero-Sum, Three-by-Three Games

234

(4)

A Three-by-Three Example with Unused Strategies

238

(2)

Mixing Among Many Strategies: General Theory

240

(15)

Summary

247

(1)

Key Terms

248

(1)

Exercises

248

(7)

PART THREE Some Broad Classes of Games and Strategies

The Prisoners' Dilemma Game

255

(30)

The Basic Game (Review)

256

(1)

Solutions I: Repetition

257

(9)

Finite Repetition

258

(1)

Infinite Repetition

259

(3)

Games of Unknown Length

262

(1)

General Theory

263

(3)

Solutions II: Penalties and Rewards

266

(3)

Solutions III: Leadership

269

(2)

Experimental Evidence

271

(3)

Real-World Dilemmas

274

(11)

Policy Setting

274

(2)

Labor Arbitration

276

(1)

Evolutionary Biology

277

(1)

Price Matching

278

(2)

Summary

280

(1)

Key Terms

281

(1)

Exercises

281

(4)

Appendix: Infinite Sums

285

(298)

Games with Strategic Moves

288

(32)

A Classification of Strategic Moves

289

(3)

Unconditional Strategic Moves

290

(1)

Conditional Strategic Moves

291

(1)

Credibility of Strategic Moves

292

(2)

Commitments

294

(4)

Threats and Promises

298

(8)

Example of a Threat: U.S.---Japanese Trade Relations

298

(5)

Example of a Promise: The Pizza Pricing Game

303

(1)

Example Combining Threat and Promise: Joint U.S.---European Military Operations

304

(2)

Some Additional Issues

306

(2)

When Do Strategic Moves Help?

306

(1)

Deterrence Versus Compellence

307

(1)

Acquiring Credibility

308

(5)

Reducing Your Freedom of Action

308

(2)

Changing Your Payoffs

310

(3)

Countering Your Opponent's Strategic Moves

313

(7)

Irrationality

314

(1)

Cutting Off Communication

314

(1)

Leaving Escape Routes Open

314

(1)

Undermining Your Opponent's Motive to Uphold His Reputation

314

(1)

Salami Tactics

315

(1)

Summary

315

(1)

Key Terms

316

(1)

Exercises

316

(4)

Evolutionary Games

320

(36)

The Framework

321

(3)

The Prisoners' Dilemma

324

(7)

The Twice-Played Prisoners' Dilemma

326

(3)

Multiple Repetitions

329

(1)

Comparing the Evolutionary and Rational-Player Models

330

(1)

Chicken

331

(3)

The Assurance Game

334

(3)

Interactions Across Species

337

(4)

The Hawk-Dove Game

341

(4)

Rational Strategic Choice and Equilibrium

341

(1)

Evolutionary Stability for V>C

342

(1)

Evolutionary Stability for V<C

342

(1)

V<C: Stable Polymorphic Population

343

(1)

V<C: Each Individual Mixes Strategies

344

(1)

Some General Theory

345

(2)

Dynamics With Three Types in The Population

347

(3)

Evolution of Cooperation and Altruism

350

(6)

Summary

352

(1)

Key Terms

353

(1)

Exercises

354

(2)

Collective-Action Games

356

(41)

Collective-Action Games with Two Players

357

(5)

Numerical Examples

358

(3)

Generalization of the Two-Person Case

361

(1)

Collective-Action Problems in Large Groups

362

(6)

A Brief History of Ideas

368

(1)

Solving Collective-Action Problems

369

(8)

Analysis

371

(4)

Applications

375

(2)

Spillovers, or Externalities

377

(11)

The Calculus of the General Case

380

(1)

Negative Spillovers

381

(4)

Positive Spillovers

385

(3)

``Help!''---a Game of Chicken With Mixed Strategies

388

(9)

Summary

392

(1)

Key Terms

393

(1)

Exercises

394

(3)

Uncertainty and Information

397

(38)

Controlling and Manipulating Risk

398

(5)

Strategies to Reduce Risk

398

(3)

Using Risk

401

(1)

Manipulating Risk in Contests

402

(1)

Some Strategies to Manipulate Information

403

(6)

Literal and Strategic Liars

405

(1)

King Solomon's Unwisdom

406

(3)

Incentives to Induce Effort

409

(3)

Screening and Signaling

412

(4)

Separation and Pooling

416

(8)

Separating Equilibrium

419

(1)

Pooling Equilibrium

420

(1)

Semiseparating Equilibrium

421

(3)

Some Evidence for Signaling and Screening

424

(2)

Additional Reading on Information Manipulation

426

(9)

Summary

427

(1)

Key Terms

428

(1)

Exercises

429

(6)

PART FOUR Applications to Specific Strategic Situations

Brinkmanship: The Cuban Missile Crisis

435

(27)

A Brief Narration of Events

436

(7)

A Simple Game-Theoretic Explanation

443

(2)

Accounting For Additional Complexities

445

(6)

A Probabilistic Threat

451

(3)

Practicing Brinkmanship

454

(8)

Summary

459

(1)

Key Terms

459

(1)

Exercises

460

(2)

Strategy and Voting

462

(32)

Voting Rules and Procedures

463

(4)

Binary Methods

463

(1)

Plurative Methods

464

(1)

Mixed Methods

465

(2)

Voting Paradoxes

467

(6)

The Condorcet Paradox

467

(2)

The Reversal Paradox

469

(1)

The Agenda Paradox

470

(1)

Change the Voting Method, Change the Outcome

471

(2)

Evaluating Vote Aggregation Methods

473

(1)

Strategic Voting

474

(7)

Plurality Rule

475

(2)

Pairwise Voting

477

(4)

The Borda Count

481

(1)

The Median Voter Theorem

481

(13)

Discrete Political Spectrum

482

(4)

Continuous Political Spectrum

486

(2)

Summary

488

(1)

Key Terms

489

(1)

Exercises

490

(4)

Bidding Strategy and Auction Design

494

(27)

Types of Auctions

495

(2)

The Winner's Curse

497

(3)

Bidding Strategies

500

(1)

Vickrey's Truth Serum

501

(2)

All-Pay Auctions

503

(2)

How to Sell at Auction

505

(4)

Risk-Neutral Bidders and Independent Estimates

506

(1)

Correlated Estimates

507

(1)

Risk-Averse Bidders

508

(1)

Some Added Twists to Consider

509

(3)

Multiple Objects

509

(2)

Defeating the System

511

(1)

Information Disclosure

511

(1)

The Airwave Spectrum Auctions

512

(9)

Designing the Rules

513

(2)

How the Auctions Have Fared

515

(1)

Two Specific Bidding Issues

516

(2)

Summary

518

(1)

Key Terms

518

(1)

Exercises

519

(2)

Bargaining

521

(29)

Nash's Cooperative Solution

523

(6)

Numerical Example

523

(1)

General Theory

524

(5)

Variable-Threat Bargaining

529

(2)

Alternating-Offers Model I: Total Value Decays

531

(3)

Experimental Evidence

534

(3)

Alternating-Offers Model II: Impatience

537

(5)

Manipulating Information in Bargaining

542

(2)

Bargaining With Many Parties and Issues

544

(6)

Multi-Issue Bargaining

545

(1)

Multiparty Bargaining

546

(1)

Summary

547

(1)

Key Terms

547

(1)

Exercises

548

(2)

Markets and Competition

550

(33)

A Simple Trading Game

552

(8)

The Core

560

(7)

Numerical Example

562

(1)

Some Properties of the Core

563

(2)

Discussion

565

(2)

The Market Mechanism

567

(5)

Properties of the Market Mechanism

569

(2)

Experimental Evidence

571

(1)

The Shapley Value

572

(5)

Power in Legislatures and Committees

574

(1)

Allocation of Joint Costs

575

(2)

Fair Division Mechanisms

577

(6)

Summary

579

(1)

Key Terms

580

(1)

Exercises

580

(3)

Index

583

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Games of Strategy

Table of Contents

Supplemental Materials