The study of strategic action (game theory) is moving from a formal science of rational behavior to an evolutionary tool kit for studying behavior in a broad array of social settings. In this problem-oriented introduction to the field, Herbert Gintis exposes students to the techniques and applications of game theory through a wealth of sophisticated and surprisingly fun-to-solve problems involving human (and even animal) behavior.

Game Theory Evolving is innovative in several ways. First, it reflects game theory's expansion into such areas as cooperation in teams, networks, the evolution and diffusion of preferences, the connection between biology and economics, artificial life simulations, and experimental economics. Second, the book--recognizing that students learn by doing and that most game theory texts are weak on problems--is organized around problems, and introduces principles through practice. Finally, the quality of the problems is simply unsurpassed, and each chapter provides a study plan for instructors interested in teaching evolutionary game theory.

Reflecting the growing consensus that in many important contexts outside of anonymous markets, human behavior is not well described by classical "rationality," Gintis shows students how to apply game theory to model how people behave in ways that reflect the special nature of human sociality and individuality. This book is perfect for upper undergraduate and graduate economics courses as well as a terrific introduction for ambitious do-it-yourselfers throughout the behavioral sciences.

The study of strategic action (game theory) is moving from a formal science of rational behaviour to an evolutionary tool kit for studying behaviour in an array of social settings. In this introduction, Herbert Gintis offer techniques and applications of game theory through fun-to-solve problems.

"Mathematically rigorous, computationally adroit, rich in illuminating problems, and engagingly written, Game Theory Evolving will be invaluable to students and researchers across the social sciences."--Joshua M. Epstein, The Brookings Institution and Santa Fe Institute

"Herb Gintis weaves classical game theory together with recent work in experimental economics, biology, evolutionary game theory, and behavioral economics. His book has something new, possibly something to argue with, but always something intriguing, for everyone."--Larry Samuelson, "University of Wisconsin"

"For anyone interested in game theory as a conceptual framework for investigating and thinking about strategic behavior in the social world, broadly interpreted, this book is a must reference work. Herb Gintis is to be congratulated for integrating a large literature on theory, evolution, experimental and field observations into an accessible treatise."--Vernon Smith, "University of Arizona"

"There is a great need for a problem book in game theory, and Gintis is correct to emphasize that learning game theory requires the solving of problems."--Michael Suk-Young Chwe, New York University

"Simply to have all this material in one place is refreshing and a big step forward. Gintis is careful on technical detail and clearly loves these models."--Colin Camerer, "California Institute of Technology"

""Game Theory Evolving" is the most up-to-date textbook in game theory on the market. Gintis covers an extraordinary range of topics, including some of the most recent developments in theory, with both stylistic verve and mathematical rigor. More importantly, he shows how the theory illuminates a great variety ofreal-world situations that both students and professors can relate to."---H. Peyton Young, The Johns Hopkins University and The Brookings Institution

"Game Theory Evolving" is the most up-to-date textbook in game theory on the market. Gintis covers an extraordinary range of topics, including some of the most recent developments in theory, with both stylistic verve and mathematical rigor. More importantly, he shows how the theory illuminates a great variety of real-world situations that both students and professors can relate to.

Includes bibliographical references (p. 501-520) and index.

Contents

Preface xxi Suggestions for Instructors xxx

I Concepts and Problems

1 Game Theory: A Lexicon for Strategic Interaction 3

1.1 Introduction 3

1.2 Big Monkey and Little Monkey 3

1.3 The Extensive Form Game 10

1.4 The Normal Form Game 12

1.5 Nash Equilibrium 12

1.6 Reviewing the Terminology 14

2 Leading from Strength: Eliminating Dominated Strategies 15

2.1 Introduction 15

2.2 Dominant and Dominated Strategies 15

2.3 Backward Induction: Pruning the Game Tree 16

2.4 Eliminating Dominated Strategies 18

2.5 Concepts and Definitions 18

2.6 The Prisoner's Dilemma 19

2.7 An Armaments Game 20

2.8 Second-Price Auction 20

2.9 The Landlord and the Eviction Notice 21

2.10 Hagar's Battles 21

2.11 An Increasing-Bid Auction 21

2.12 The Debtor and His Creditors 22

2.13 Football Strategy 22

2.14 A Military Strategy Game 22

2.15 Strategic Voting 23

2.16 Eliminating Dominated Strategies ad Absurdum 23

2.17 Poker with Bluffing 24

2.18 The Centipede Game 25

3 Playing It Straight: Pure Strategy Nash Equilibria 27

3.1 Introduction 27

3.2 Pure Coordination Games 28

3.3 Competition on Main Street 28

3.4 A Pure Coordination Game' 29

3.5 Twin Sisters 29

3.6 Variations on Duopoly 30

3.7 The Tobacco Market 31

3.8 Price-Matching as Tacit Collusion 31

3.9 The Klingons and the Snarks 32

3.10 Chess-The Trivial Pastime 33

3.11 The Samaritan's Dilemma 33

3.12 The Rotten Kid Theorem 34

3.13 The Illogic of Conflict Escalation 35

3.14 How to Value Lotteries 36

3.15 Payoffs in Games Where Nature Moves 37

3.16 Nature in Action: No-Draw, High-Low Poker 38

3.17 The Expected Utility Principle 41

3.18 Buying Fire Insurance 42

3.19 Neoclassical Economics and Game Theory 43

3.20 Markets as Disciplining Devices: Allied Widgets 46

3.21 The Truth Game 51

3.22 The Shopper and the Fish Merchant 52

3.23 Fathers and Sons 53

3.24 The Women of Sevitan 53

4 Catching 'em Off Guard: Mixed Strategy Nash Equilibria 54

4.1 Introduction 54

4.2 Mixed Strategies: Basic Definitions 55

4.3 The Fundamental Theorem 56

4.4 Solving for Mixed Strategy Nash Equilibria 57

4.5 Reviewing the Terminology 58

4.6 Big Monkey and Little Monkey Revisited 59

4.7 Dominance Revisited 59

4.8 Competition on Main Street Revisited 59

4.9 Battle of the Sexes 60

4.10 Throwing Fingers 60

4.11 One-Card Two-Round Poker with Bluffing 60

4.12 Trust in Networks 62

4.13 Behavioral Strategies in Extensive Form Games 63

4.14 Lions and Antelope 65

4.15 The Santa Fe Bar 66

4.16 Orange-Throat, Blue-Throat, and Yellow-

Striped Lizards 67

4.17 Sex Ratios as Nash Equilibria 68

4.18 Tennis Strategy 69

4.19 A Mating Game 70

4.20 Preservation of Ecology Game 71

4.21 Hard Love 71

4.22 Coordination Failure 72

4.23 Advertising Game 72

4.24 Colonel Blotto Game 72

4.25 Number Guessing Game 73

4.26 Target Selection 73

4.27 A Reconnaissance Game 74

4.28 Attack on Hidden Object 74

4.29 Two-Person Zero-Sum Games 75

4.30 An Introduction to Forward Induction 76

4.31 Mutual Monitoring in a Partnership 77

4.32 Mutual Monitoring in Teams 78

4.33 Altruism(?) in Bird Flocks 79

4.34 Robin Hood and Little John 80

4.35 The Motorist's Dilemma 80

4.36 Family Politics 81

4.37 Frankie and Johnny 81

4.38 A Card Game 82

4.39 Cheater-Inspector 82

4.40 The Groucho Marx Game 82

4.41 Real Men Don't Eat Quiche 84

4.42 The Vindication of the Hawk 84

4.43 Correlated Equilibria 85

4.44 Poker with Bluffing Revisited 87

4.45 Equivalence of Behavioral and Mixed Strategies 87

5 Moving through the Game Tree: Subgames,

Incredible Threats, and Trembling Hands 90

5.1 Introduction 90

5.2 Subgame Perfection 92

5.3 Stackelberg Leadership 95

5.4 The Subway Entry Deterrence Game 96

5.5 The Dr. Strangelove Game 96

5.6 The Rubinstein Bargaining Model 97

5.7 Huey, Dewey, and Louie Split a Dollar 99

5.8 The Little Miss Muffet Game 99

5.9 Nuisance Suits 100

5.10 Cooperation in an Overlapping-Generations

Economy 102

5.11 The Finitely Repeated Prisoner's Dilemma 103

5.12 The Finitely Repeated Prisoner's Dilemma 11 109

5.13 Fuzzy Subgame Perfection 110

5.14 Perfect Behavioral Nash Equilibria 112

5.15 Selten's Horse 114

5.16 Trembling Hand Perfection 115

5.17 Nature Abhors Low Probability Events 117

6 Repeated Games, Trigger Strategies, and Tacit Collusion 118

6.1 Introduction 118

6.2 Big Fish and Little Fish 119

6.3 Tacit Collusion 121

6.4 The Folk Theorem: An Embarras de richesses 126

6.5 Variations on the Folk Theorem 127

6.6 The One-Stage Deviation Principle 129

6.7 A Trembling Hand, Cooperative Equilibrium 130

6.8 Death and Discount Rates in Repeated Games 131

6.9 The Strategy of an Oil Cartel 132

6.10 Manny and Moe 132

6.11 Tit-for-Tat 132

6.12 A Public Goods Experiment 133

6.13 Reputational Equilibrium 134

6.14 Contingent Renewal Contracts 134

6.15 Contingent Renewal Labor Markets 140

6.16 I'd Rather Switch than Fight 145

7 Biology Meets Economics: Evolutionary Stability

and the Birth of Dynamic Game Theory 148

7.1 The Birth of Evolutionary Stability 148

7.2 Properties of Evolutionarily Stable Strategies 149

7.3 Are Evolutionarily Stable Strategies Unbeatable? 152

7.4 Trust in Networks 11 152

7.5 Cooperative Fishing 152

7.6 Nash Equilibrium That Is Not Evolutionarily

Stable 153

7.7 Rock, Paper, and Scissors Is Not Evolutionarily

Stable 153

7.8 Sex Ratios as Evolutionarily Stable Strategies 153

7.9 Invasion of the Pure Strategy Mutants 154

7.10 Multiple Evolutionarily Stable Strategies 154

7.11 The Logic of Animal Conflict 155

7.12 Hawks, Doves, and Bourgeois 157

7.13 Trogs and Farfel 158

7.14 Evolutionary Stability in Finite Populations 159

7.15 Evolutionary Stability in Asymmetric Games 161

8 Dynamical Systems and Differential Equations 164

8.1 Introduction 164

8.2 Dynamical Systems 165

8.3 Population Growth 166

8.4 Population Growth with Limited Carrying

Capacity 166

8.5 The Lotka-Volterra Predator-Prey Model 168

8.6 Dynamical Systems Theory 172

8.7 Dynamical Systems in One Dimension 175

8.8 Dynamical Systems in Two Dimensions 178

8.9 Exercises in Two-Dimensional Linear Systems 181

8.10 Cultural Dynamics 182

8.11 Lotka-Volterra with Limited Carrying Capacity 183

8.12 Take No Prisoners 183

8.13 The Hartman-Grobman Theorem 184

8.14 Special Features of Two-Dimensional Dynamical

Systems 185

8.15 A Non-Hyperbolic Dynamical System 185

8.16 Liapunov's Theorem 186

9 Evolutionary Dynamics 188

9.1 Introduction 188

9.2 The Origins of Evolutionary Dynamics 189

9.3 Properties of the Replicator System 197

9.4 Characterizing the Two-Variable Replicator

Dynamic 198

9.5 Do Dominated Strategies Survive under a

Replicator Dynamic? 199

9.6 Equilibrium and Stability with a Replicator Dynamic 201

9.7 Evolutionary Stability and Evolutionary Equilibrium 202

9.8 Trust in Networks 111 203

9.9 Bayesian Perfection and Stable Sets 203

9.10 Invasion of the Pure Strategy Mutants, 11 204

9.11 A Generalization of Rock, Paper, and Scissors 205

9.12 Uta stansburia in Motion 206

9.13 The Dynamics of Rock-Paper-Scissors and

Related Games 207

9.14 Lotka-Volterra Model and Biodiversity 208

9.15 Asymmetric Evolutionary Games 210

9.16 Asymmetric Evolutionary Games: Reviewing

the Troops 214

9.17 The Evolution of Trust and Honesty 214

9.18 The Loraxes and Thoraxes 216

9.19 Cultural Transmission and Social Imitation 217

10 Markov Economies and Stochastic Dynamical Systems 220

10.1 Introduction 220

10.2 The Emergence of Money in a Markov Economy 221

10.3 Good Vibrations 228

10.4 Adaptive Learning 229

10.5 Adaptive Learning When Not All Conventions

are Equal 233

10.6 Adaptive Learning with Errors 234

10.7 Stochastic Stability 235

11 Homo reciprocans, Homo egualis, and Other Contributors

to the Human Behavioral Repertoire 237

11.1 Introduction 237

11.2 Modeling the Human Actor 239

11.3 Behavioral Economics: Games against Nature

and against Ourselves 244

11.4 Experimental Game Theory: The Laboratory

Meets Strategic Interaction 251

11.5 Homo egualis 258

11.6 Homo reciprocans: Modeling Strong Reciprocity 261

11.7 Altruism and Assortative Interactions 266

11.8 The Evolution of Strong Reciprocity 271

11.9 Homo parochius: Modeling Insiders and Outsiders 278

12 Learning Who Your Friends Are: Bayes' Rule

and Private Information 284

12.1 Private Information 284

12.2 The Role of Beliefs in Games with Private

Information 289

12.3 Haggling at the Bazaar 291

12.4 Adverse Selection 294

12.5 A Market for Lemons 295

12.6 Choosing an Exorcist 296

12.7 A First-Price Sealed-Bid Auction 299

12.8 A Common Value Auction: The Winner's Curse 300

12.9 A Common Value Auction: Quantum Spin

Decoders 300

12.10 Predatory Pricing: Pooling and Separating

Equilibria 302

12.11 Limit Pricing 304

12.12 A Simple Limit-Pricing Model 305

13 When It Pays to Be Truthful: Signaling in Games with

Friends, Adversaries, and Kin 307

13.1 Signaling as a Coevolutionary Process 307

13.2 A Generic Signaling Game 308

13.3 Introductory Offers 310

13.4 Web Sites (for Spiders) 310

13.5 Sex and Piety: The Darwin-Fisher Model

of Sexual Selection 312

13.6 Biological Signals as Handicaps 317

13.7 The Shepherds Who Never Cry Wolf 319

13.8 My Brother's Keeper 321

13.9 Honest Signaling among Partial Altruists 323

13.10 Educational Signaling 1 325

13.11 Education as a Screening Device 328

13.12 Capital as a Signaling Device 329

14 Bosses and Workers, Landlords and Peasants, and

Other Principal-Agent Models 332

14.1 Introduction to the Principal-Agent Model 332

14.2 Labor Discipline with Monitoring 333

14.3 Labor as Gift Exchange 335

14.4 Labor Discipline with Profit Signaling 336

14.5 Peasants and Landlords 340

14.6 Mr. Smith's Car Insurance 341

14.7 A Generic One-Shot Principal-Agent Game 342

15 Bargaining 345

15.1 Introduction 345

15.2 The Nash Bargaining Model 346

15.3 Risk Aversion and the Nash Bargaining Solution 349

15.4 Rubinstein Bargaining with Outside Options 350

15.5 Bargaining with Two-Sided Outside Options 352

15.6 Rubinstein Bargaining and Nash Bargaining 353

15.7 Zeuthen Lotteries and the Nash Bargaining

Solution 354

15.8 Bargaining with Fixed Costs 355

15.9 Bargaining with Incomplete Information 355

16 Probability and Decision Theory 357

16.1 Probability Spaces 357

16.2 DeMorgan's Laws 357

16.3 Interocitors 358

16.4 The Direct Evaluation of Probabilities 358

16.5 Probability as Frequency 358

16.6 Sampling 360

16.7 Self-presentation 360

16.8 Social Isolation 361

16.9 Aces Up 361

16.10 Mechanical Defection 361

16.11 Double Orders 361

16.12 Combinations and Sampling 361

16.13 Mass Defection 362

16.14 An Unlucky Streak 362

16.15 House Rules 362

16.16 The Powerball Lottery 362

16.17 The Addition Rule for Probabilities 362

16.18 Die, Die! 363

16.19 Les Cinq Tiroirs 363

16.20 A Guessing Game 363

16.21 Conditional Probability 363

16.22 Bayes' Rule 364

16.23 Drug Testing 365

16.24 A Bolt Factory 365

16.25 Color Blindness 365

16.26 Urns 365

16.27 The Monty Hall Game 365

16.28 The Logic of Murder and Abuse 367

16.29 Ah, Those Kids 369

16-30 The Greens and the Blacks 369

16-31 Laplace's Law of Succession 369

16.32 The Brain and Kidney Problem 370

16.33 Sexual Harassment on the Job 370

16.34 The Value of Eyewitness Testimony 370

16.35 The End of the World 371

16.36 Bill and Harry 371

16.37 When Weakness Is Strength 371

16.38 Markov Chains 372

16.39 Preferences and Expected Utility 381

16.40 Exceptions to the Expected Utility Principle 385

16.41 Risk Behavior and the Shape of the Utility

Function 387

II Answers and Hints

2 Leading from Strength: Eliminating Dominated Strategies 395

2.8 Second-Price Auction 395

2.10 Hagar's Battles 395

2.14 A Military Strategy Game 396

2.15 Strategic Voting 397

3 Playing It Straight: Pure Strategy Nash Equilibria 399

3.7 The Tobacco Market 399

3.9 The Klingons and the Snarks 400

3.10 Chess-The Trivial Pastime 401

3.11 The Samaritan's Dilemma 401

3.12 The Rotten Kid Theorem 403

3.13 The Illogic of Conflict Escalation 404

3.14 How to Value Lotteries 404

3.21 The Truth Game 405

3.22 The Shopper and the Fish Merchant 407

3.24 The Women of Sevitan 408

4 Catching 'em Off Guard: Mixed Strategy Nash Equilibria 410

4.9 Battle of the Sexes 410

4.11 One-Card Two-Round Poker with Bluffing 412

4.15 The Santa Fe Bar 413

4.17 Sex Ratios as Nash Equilibria 414

4.19 A Mating Game 416

4.20 Preservation of Ecology Game 416

4.22 Coordination Failure 417

4.23 Advertising Game 417

4.24 Colonel Blotto Game 419

4.25 Number Guessing Game 420

4.26 Target Selection 420

4.27 A Reconnaissance Game 421

4.28 Attack on Hidden Object 422

4.34 Robin Hood and Little John 422

4.35 The Motorist's Dilemma 423

4.37 Frankie and Johnny 424

4.38 A Card Game 425

4.39 Cheater-Inspector 427

4.40 The Groucho Marx Game 428

4.41 Real Men Don't Eat Quiche 431

4.45 Equivalence of Behavioral and Mixed

Strategies 432

5 Moving through the Game Tree: Subgames,

Incredible Threats, and Trembling Hands 436

5.4 The Subway Entry Deterrence Game 436

5.5 The Dr. Strangelove Game 436

5.7 Huey, Dewey, and Louie Split a Dollar 437

5.10 Cooperation in an Overlapping-Generations

Economy 438

5.12 The Finitely Repeated Prisoner's Dilemma 11 439

5.15 Selten's Horse 440

5.16 Trembling Hand Perfection 441

6 Repeated Games, Trigger Strategies, and Tacit Collusion 442

6.13 Reputational Equilibrium 442

7 Biology Meets Economics: Evolutionary Stability

and the Birth of Dynamic Game Theory 443

7.2 Properties of Evolutionarily Stable Strategies 443

7.5 Cooperative Fishing 446

7.12 Hawks, Doves, and Bourgeois 447

7.13 Trogs and Farfel 448

7.14 Evolutionary Stability in Finite Populations 449

9 Evolutionary Dynamics 451

9.3 Properties of the Replicator System 451

9.13 The Dynamics of Rock-Paper-Scissors and

Related Games 451

9.14 Lotka-Volteffa Model and Biodiversity 454

9.18 The Loraxes and Thoraxes 455

12 Learning Who Your Friends Are: Bayes' Rule

and Private Information 457

12.3 Haggling at the Bazaar 457

12.8 A Common Value Auction: The Winner's Curse 458

12.9 A Common Value Auction: Quantum Spin

Decoders 458

12.10 Predatory Pricing: Pooling and Separating

Equilibria 460

12.11 Limit Pricing 461

12.12 A Simple Limit-Pricing Model 464

13 When It Pays to Be Truthful: Signaling in Games with

Friends, Adversaries, and Kin 466

13.3 Introductory Offers 466

13.4 Web Sites (for Spiders) 466

13.7 The Shepherds Who Never Cry Wolf 468

13.9 Honest Signaling among Partial Altruists 469

13.11 Education as a Screening Device 470

13.12 Capital as a Signaling Device 471

14 Bosses and Workers, Landlords and Peasants, and

Other Principal-Agent Models 473

14.3 Labor as Gift Exchange 473

14.4 Labor Discipline with Profit Signaling 474

14.5 Peasants and Landlords 475

14.6 Mr. Smith's Car Insurance 478

14.7 A Generic One-Shot Principal-Agent Game 480

15 Bargaining 483

15.2 The Nash Bargaining Model 483

15.3 Risk Aversion and the Nash Bargaining Solution 484

15.4 Rubinstein Bargaining with Outside Options 485

15.6 Rubinstein Bargaining and Nash Bargaining 486

15.7 Zeuthen Lotteries and the Nash Bargaining

Solution 487

15.8 Bargaining with Fixed Costs 487

15.9 Bargaining with Incomplete Information 488

16 Probability and Decision Theory 489

16.5 Probability as Frequency 489

16.6 Sampling 489

16.8 Social Isolation 489

16.9 Aces Up 489

16.10 Mechanical Defection 490

16.11 Double Orders 490

16.13 Mass Defection 490

16.14 An Unlucky Streak 490

16.15 House Rules 491

16.16 The Powerball Lottery 491

16.18 Die, Die! 492

16.20 A Guessing Game 492

16.23 Drug Testing 494

16.30 The Greens and the Blacks 494

16.31 Laplace's Law of Succession 495

16.32 The Brain and Kidney Problem 496

16.33 Sexual Harassment on the Job 497

16.34 The Value of Eyewitness Testimony 497

16.36 Bill and Harry 497

16.37 When Weakness Is Strength 497

Sources for Problems 500

References 501

Index 521