An Introduction to Game Theory

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ISBN: 9780195128956 | 0195128958
Cover: Hardcover
Copyright: 8/7/2003

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Game theoretic reasoning pervades economic theory and is used widely in other social and behavioral sciences. An Introduction to Game Theory presents the main ideas underlying this theory and shows how it can be used to understand economic, social, political, and biological phenomena. Emphasizing the ideas behind the theory rather than their mathematical expression, it assumes no specific knowledge beyond basic mathematics. It defines all concepts precisely and uses logical reasoning throughout.

Preface

Introduction

(10)

What is game theory?

(3)

An outline of the history of game theory

(1)

John von Neumann

(1)

The theory of rational choice

(3)

Coming attractions: interacting decision-makers

(4)

Notes

(2)

I Games with Perfect Information

(260)

Nash Equilibrium: Theory

(42)

Strategic games

(1)

Example: the Prisoner's Dilemma

(4)

Example: Bach or Stravinsky?

(1)

Example: Matching Pennies

(1)

Example: the Stag Hunt

(1)

Nash equilibrium

(5)

John F. Nash, Jr.

(1)

Studying Nash equilibrium experimentally

(2)

Examples of Nash equilibrium

(9)

Experimental evidence on the Prisoner's Dilemma

(4)

Focal points

(3)

Best response functions

(10)

Dominated actions

(5)

Equilibrium in a single population: symmetric games and symmetric equilibria

(5)

Notes

(2)

Nash Equilibrium: Illustrations

(44)

Cournot's model of oligopoly

(8)

Bertrand's model of oligopoly

(7)

Cournot, Bertrand, and Nash: some historical notes

(1)

Electoral competition

(7)

The War of Attrition

(3)

Auctions

(11)

Auctions from Babylonia to eBay

(10)

Accident law

(8)

Notes

(2)

Mixed Strategy Equilibrium

(54)

Introduction

(7)

Some evidence on expected payoff functions

104

(2)

Strategic games in which players may randomize

106

(1)

Mixed strategy Nash equilibrium

107

(13)

Dominated actions

120

(2)

Pure equilibria when randomization is allowed

122

(1)

Illustration: expert diagnosis

123

(5)

Equilibrium in a single population

128

(3)

Illustration: reporting a crime

131

(3)

Reporting a crime: social psychology and game theory

133

(1)

The formation of players' beliefs

134

(3)

Extension: finding all mixed strategy Nash equilibria

137

(5)

Extension: games in which each player has a continuum of actions

142

(4)

Appendix: representing preferences by expected payoffs

146

(7)

Notes

150

(3)

Extensive Games with Perfect Information: Theory

153

(28)

Extensive games with perfect information

153

(6)

Strategies and outcomes

159

(2)

Nash equilibrium

161

(3)

Subgame perfect equilibrium

164

(5)

Finding subgame perfect equilibria of finite horizon games: backward induction

169

(12)

Ticktacktoe, chess, and related games

178

(1)

Notes

179

(2)

Extensive Games with Perfect Information: Illustrations

181

(24)

The ultimatum game, the holdup game, and agenda control

181

(6)

Experiments on the ultimatum game

183

(4)

Stackelberg's model of duopoly

187

(5)

Buying votes

192

(5)

A race

197

(8)

Notes

203

(2)

Extensive Games with Perfect Information: Extensions and Discussion

205

(34)

Allowing for simultaneous moves

205

(8)

More experimental evidence on subgame perfect equilibrium

211

(2)

Illustration: entry into a monopolized industry

213

(2)

Illustration: electoral competition with strategic voters

215

(2)

Illustration: committee decision-making

217

(4)

Illustration: exit from a declining industry

221

(4)

Allowing for exogenous uncertainty

225

(6)

Discussion: subgame perfect equilibrium and backward induction

231

(5)

Experimental evidence on the centipede game

234

(2)

Notes

236

(3)

Coalitional Games and the Core

239

(32)

Coalitional games

239

(4)

The core

243

(4)

Illustration: ownership and the distribution of wealth

247

(4)

Illustration: exchanging homogeneous horses

251

(5)

Illustration: exchanging heterogeneous houses

256

(4)

Illustration: voting

260

(3)

Illustration: matching

263

(6)

Matching doctors with hospitals

268

(1)

Discussion: other solution concepts

269

(2)

Notes

270

(1)

II Games with Imperfect Information

271

(88)

Bayesian Games

273

(40)

Motivational examples

273

(5)

General definitions

278

(4)

Two examples concerning information

282

(3)

Illustration: Cournot's duopoly game with imperfect information

285

(4)

Illustration: providing a public good

289

(2)

Illustration: auctions

291

(10)

Auctions of the radio spectrum

300

(1)

Illustration: juries

301

(6)

Appendix: auctions with an arbitrary distribution of valuations

307

(6)

Notes

311

(2)

Extensive Games with Imperfect Information

313

(46)

Extensive games with imperfect information

313

(4)

Strategies

317

(1)

Nash equilibrium

318

(5)

Beliefs and sequential equilibrium

323

(8)

Signaling games

331

(5)

Illustration: conspicuous expenditure as a signal of quality

336

(4)

Illustration: education as a signal of ability

340

(3)

Illustration: strategic information transmission

343

(8)

Illustration: agenda control with imperfect information

351

(8)

Notes

357

(2)

III Variants and Extensions

359

(148)

Strictly Competitive Games and Maxminimization

361

(16)

Maxminimization

361

(3)

Maxminimization and Nash equilibrium

364

(1)

Strictly competitive games

365

(2)

Maxminimization and Nash equilibrium in strictly competitive games

367

(10)

Maxminimization: some history

370

(3)

Empirical tests: experiments, tennis, and soccer

373

(2)

Notes

375

(2)

Rationalizability

377

(16)

Rationalizability

377

(8)

Iterated elimination of strictly dominated actions

385

(3)

Iterated elimination of weakly dominated actions

388

(3)

Dominance solvability

391

(2)

Notes

392

(1)

Evolutionary Equilibrium

393

(26)

Monomorphic pure strategy equilibrium

394

(6)

Evolutionary game theory: some history

399

(1)

Mixed strategies and polymorphic equilibrium

400

(6)

Asymmetric contests

406

(5)

Side-blotched lizards

407

(2)

Explaining the outcomes of contests in nature

409

(2)

Variation on a theme: sibling behavior

411

(3)

Variation on a theme: the nesting behavior of wasps

414

(2)

Variation on a theme: the evolution of the sex ratio

416

(3)

Notes

417

(2)

Repeated Games: The Prisoner's Dilemma

419

(32)

The main idea

419

(2)

Preferences

421

(2)

Repeated games

423

(1)

Finitely repeated Prisoner's Dilemma

424

(2)

Infinitely repeated Prisoner's Dilemma

426

(1)

Strategies in an infinitely repeated Prisoner's Dilemma

426

(2)

Some Nash equilibria of an infinitely repeated Prisoner's Dilemma

428

(3)

Nash equilibrium payoffs of an infinitely repeated Prisoner's Dilemma

431

(6)

Experimental evidence

436

(1)

Subgame perfect equilibria and the one-deviation property

437

(4)

Axelrod's tournaments

439

(2)

Some subgame perfect equilibria of an infinitely repeated Prisoner's Dilemma

441

(5)

Reciprocal altruism among sticklebacks

445

(1)

Subgame perfect equilibrium payoffs of an infinitely repeated Prisoner's Dilemma

446

(3)

Medieval trade fairs

448

(1)

Concluding remarks

449

(2)

Notes

449

(2)

Repeated Games: General Results

451

(14)

Nash equilibria of general infinitely repeated games

451

(4)

Subgame perfect equilibria of general infinitely repeated games

455

(5)

Finitely repeated games

460

(1)

Variation on a theme: imperfect observability

461

(4)

Notes

463

(2)

Bargaining

465

(28)

Bargaining as an extensive game

465

(12)

Illustration: trade in a market

477

(4)

Nash's axiomatic model

481

(8)

Relation between strategic and axiomatic models

489

(4)

Notes

491

(2)

Appendix: Mathematics

493

(14)

Numbers

493

(1)

Sets

494

(1)

Functions

495

(3)

Profiles

498

(1)

Sequences

499

(1)

Probability

499

(6)

Proofs

505

(2)

References

507

(18)

Index

525

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An Introduction to Game Theory

Summary

Table of Contents

Supplemental Materials