Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction (Second Edition)

Contents......Page 8
Preface......Page 16
1.1 Basic Set Theory and Mathematical Notation......Page 20
1.2 Probability Spaces......Page 21
1.5 The Direct Evaluation of Probabilities......Page 22
1.6 Probability as Frequency......Page 23
1.9 Sampling......Page 24
1.11 Permutations......Page 25
1.15 House Rules......Page 26
1.18 North Island, South Island......Page 27
1.20 Bayes' Rule......Page 28
1.23 Drug Testing......Page 29
1.27 The Logic of Murder and Abuse......Page 30
1.30 The Brain and Kidney Problem......Page 31
1.32 When Weakness Is Strength......Page 32
1.33 The Uniform Distribution......Page 35
1.35 From Uniform to Exponential......Page 36
2.1 The Rational Actor Model......Page 37
2.2 Time Consistency and Exponential Discounting......Page 39
2.3 The Expected Utility Principle......Page 41
2.4 Risk and the Shape of the Utility Function......Page 45
2.5 The Scientific Status of the Rational Actor Model......Page 49
3.1 Big John and Little John......Page 51
3.2 The Extensive Form......Page 57
3.3 The Normal Form......Page 60
3.4 Mixed Strategies......Page 61
3.5 Nash Equilibrium......Page 62
3.6 The Fundamental Theorem of Game Theory......Page 63
3.7 Solving for Mixed-Strategy Nash Equilibria......Page 64
3.9 Battle of the Sexes......Page 65
3.10 The Hawk-Dove Game......Page 67
3.11 The Prisoner’s Dilemma......Page 69
4.1 Dominated Strategies......Page 71
4.2 Backward Induction......Page 73
4.3 Exercises in Eliminating Dominated Strategies......Page 74
4.4 Subgame Perfection......Page 76
4.6 The Second-Price Auction......Page 78
4.7 The Mystery of Kidnapping......Page 79
4.9 Hagar’s Battles......Page 81
4.10 Military Strategy......Page 82
4.12 Strategic Voting......Page 83
4.13 Nuisance Suits......Page 84
4.15 Football Strategy......Page 86
4.16 Poker with Bluffing......Page 87
4.17 The Little Miss Muffet Game......Page 88
4.18 Cooperation with Overlapping Generations......Page 89
4.19 Dominance-Solvable Games......Page 90
4.20 Agent-based Modeling......Page 91
4.21 Why Play a Nash Equilibrium?......Page 94
4.22 Modeling the Finitely-Repeated Prisoner’s Dilemma......Page 96
4.23 Review of Basic Concepts......Page 98
5.1 Price Matching as Tacit Collusion......Page 99
5.3 Markets as Disciplining Devices: Allied Widgets......Page 100
5.5 The Klingons and the Snarks......Page 106
5.6 Chess: The Trivial Pastime......Page 107
5.7 No-Draw, High-Low Poker......Page 108
5.8 An Agent-based Model of No-Draw, High-Low Poker......Page 110
5.9 The Truth Game......Page 111
5.10 The Rubinstein Bargaining Model......Page 113
5.11 Bargaining with Heterogeneous Impatience......Page 115
5.12 Bargaining with One Outside Option......Page 116
5.13 Bargaining with Dual Outside Options......Page 117
5.14 Huey, Dewey, and Louie Split a Dollar......Page 121
5.16 The Samaritan’s Dilemma......Page 123
5.17 The Rotten Kid Theorem......Page 125
5.18 The Shopper and the Fish Merchant......Page 126
5.20 Pick Any Number......Page 128
5.21 Pure Coordination Games: Experimental Evidence......Page 129
5.22 Introductory Offers......Page 130
5.23 Web Sites (for Spiders)......Page 131
6.1 The Algebra of Mixed Strategies......Page 135
6.2 Lions and Antelope......Page 136
6.3 A Patent Race......Page 137
6.5 Preservation of Ecology Game......Page 138
6.7 Advertising Game......Page 139
6.9 The Motorist's Dilemma......Page 141
6.11 Frankie and Johnny......Page 142
6.12 A Card Game......Page 143
6.14 The Vindication of the Hawk......Page 145
6.15 Characterizing 2 x 2 Normal Form Games I......Page 146
6.18 Competition on Main Street Revisited......Page 147
6.20 Twin Sisters: An Agent-Based Model......Page 148
6.21 One-Card, Two-Round Poker with Bluffing......Page 150
6.22 An Agent-Based Model of Poker with Bluffing......Page 151
6.23 Trust in Networks......Page 152
6.24 El Farol......Page 153
6.25 Decorated Lizards......Page 154
6.26 Sex Ratios as Nash Equilibria......Page 156
6.27 A Mating Game......Page 159
6.29 Colonel Blotto Game......Page 160
6.32 A Reconnaissance Game......Page 161
6.34 Two-Person, Zero-Sum Games......Page 162
6.36 Mutual Monitoring in Teams......Page 164
6.37 Altruism(?) in Bird Flocks......Page 165
6.38 The Groucho Marx Game......Page 166
6.40 Correlated Equilibria......Page 170
6.41 Territoriality as a Correlated Equilibrium......Page 172
6.42 Haggling at the Bazaar......Page 173
6.43 Poker with Bluffing Revisited......Page 175
6.44 Algorithms for Finding Nash Equilibria......Page 176
6.45 Why Play Mixed Strategies?......Page 179
6.46 Reviewing of Basic Concepts......Page 180
7.1 Gift Exchange......Page 181
7.2 Contract Monitoring......Page 182
7.3 Profit Signaling......Page 183
7.4 Properties of the Employment Relationship......Page 187
7.5 Peasant and Landlord......Page 188
7.6 Bob’s Car Insurance......Page 192
7.7 A Generic Principal-Agent Model......Page 193
8.1 Signaling as a Coevolutionary Process......Page 198
8.2 A Generic Signaling Game......Page 199
8.3 Sex and Piety: The Darwin-Fisher Model......Page 201
8.4 Biological Signals as Handicaps......Page 206
8.5 The Shepherds Who Never Cry Wolf......Page 208
8.6 My Brother’s Keeper......Page 209
8.7 Honest Signaling among Partial Altruists......Page 212
8.8 Educational Signaling......Page 214
8.9 Education as a Screening Device......Page 216
8.10 Capital as a Signaling Device......Page 218
9 Repeated Games......Page 220
9.2 Big Fish and Little Fish......Page 221
9.3 Alice and Bob Cooperate......Page 223
9.5 Reputational Equilibrium......Page 224
9.6 Tacit Collusion......Page 225
9.7 The One-Stage Deviation Principle......Page 227
9.8 Tit for Tat......Page 228
9.9 I’d Rather Switch Than Fight......Page 229
9.10 The Folk Theorem......Page 232
9.11 The Folk Theorem and the Nature of Signaling......Page 235
9.12 The Folk Theorem Fails in Large Groups......Page 236
9.13 Contingent Renewal Markets Do Not Clear......Page 238
9.14 Short-Side Power in Contingent Renewal Markets......Page 241
9.16 The Economy Is Controlled by the Wealthy......Page 242
9.17 Contingent Renewal Labor Markets......Page 243
10 Evolutionarily Stable Strategies......Page 248
10.1 Evolutionarily Stable Strategies: Definition......Page 249
10.2 Properties of Evolutionarily Stable Strategies......Page 251
10.3 Characterizing Evolutionarily Stable Strategies......Page 252
10.5 A Dynamic Battle of the Sexes......Page 255
10.6 Symmetrical Throwing Fingers......Page 256
10.9 Cooperative Fishing......Page 257
10.11 A Nash Equilibrium That Is Not an EES......Page 259
10.13 Invasion of the Pure-Strategy Mutants......Page 260
10.15 Evolutionarily Stable Strategies in Finite Populations......Page 261
10.16 Evolutionarily Stable Strategies in Asymmetric Games......Page 263
11.1 Dynamical Systems: Definition......Page 266
11.2 Population Growth......Page 267
11.3 Population Growth with Limited Carrying Capacity......Page 268
11.4 The Lotka-Volterra Predator-Prey Model......Page 270
11.5 Dynamical Systems Theory......Page 274
11.6 Existence and Uniqueness......Page 275
11.7 The Linearization Theorem......Page 276
11.8 Dynamical Systems in One Dimension......Page 277
11.9 Dynamical Systems in Two Dimensions......Page 279
11.10 Exercises in Two-Dimensional Linear Systems......Page 283
11.12 Take No Prisoners......Page 285
11.13 The Hartman-Grobman Theorem......Page 286
11.14 Features of Two-Dimensional Dynamical Systems......Page 287
12 Evolutionary Dynamics......Page 289
12.1 The Origins of Evolutionary Dynamics......Page 290
12.2 Strategies as Replicators......Page 291
12.3 A Dynamic Hawk-Dove Game......Page 293
12.4 Sexual Reproduction and the Replicator Dynamic......Page 295
12.5 Properties of the Replicator System......Page 297
12.6 The Replicator Dynamic in Two Dimensions......Page 298
12.7 Dominated Strategies and the Replicator Dynamic......Page 299
12.8 Equilibrium and Stability with a Replicator Dynamic......Page 301
12.10 Trust in Networks III......Page 303
12.11 Characterizing 2 x 2 Normal Form Games II......Page 304
12.12 Invasion of the Pure-Strategy Nash Mutants II......Page 305
12.14 Uta stansburiana in Motion......Page 306
12.16 The Lotka-Volterra Model and Biodiversity......Page 307
12.17 Asymmetric Evolutionary Games......Page 309
12.19 The Evolution of Trust and Honesty......Page 314
13.1 Markov Chains......Page 316
13.2 The Ergodic Theorem for Markov Chains......Page 324
13.3 The Infinite Random Walk......Page 326
13.4 The Sisyphean Markov Chain......Page 327
13.5 Andrei Andreyevich's Two-Urn Problem......Page 328
13.6 Solving Linear Recursion Equations......Page 329
13.7 Good Vibrations......Page 330
13.8 Adaptive Learning......Page 331
13.9 The Steady State of a Markov Chain......Page 333
13.10 Adaptive Learning II......Page 334
13.11 Adaptive Learning with Errors......Page 335
13.12 Stochastic Stability......Page 336
14 Table of Symbols......Page 338
15 Answers......Page 340
Sources for Problems......Page 392
References......Page 394
C......Page 404
F......Page 405
M......Page 406
R......Page 407
S......Page 408
Z......Page 409