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
