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Tables of Contents for Game Theory Evolving
Chapter/Section Title
Page #
Page Count
Preface
xxi
Suggestions for Instructors
xxx
I Concepts and Problems
Game Theory: A Lexicon for Strategic Interaction
3
12
Introduction
3
1
Big Monkey and Little Monkey
3
7
The Extensive Form Game
10
2
The Normal Form Game
12
1
Nash Equilibrium
12
2
Reviewing the Terminology
14
1
Leading from Strength: Eliminating Dominated Strategies
15
12
Introduction
15
1
Dominant and Dominated Strategies
15
1
Backward Induction: Pruning the Game Tree
16
2
Eliminating Dominated Strategies
18
1
Concepts and Definitions
18
1
The Prisoner's Dilemma
19
1
An Armaments Game
20
1
Second-Price Auction
20
1
The Landlord and the Eviction Notice
21
1
Hagar's Battles
21
1
An Increasing-Bid Auction
21
1
The Debtor and His Creditors
22
1
Football Strategy
22
1
A Military Strategy Game
22
1
Strategic Voting
23
1
Eliminating Dominated Strategies ad Absurdum
23
1
Poker with Bluffing
24
1
The Centipede Game
25
2
Playing It Straight: Pure Strategy Nash Equilibria
27
27
Introduction
27
1
Pure Coordination Games
28
1
Competition on Main Street
28
1
A Pure Coordination Game
29
1
Twin Sisters
29
1
Variations on Duopoly
30
1
The Tobacco Market
31
1
Price-Matching as Tacit Collusion
31
1
The Klingons and the Snarks
32
1
Chess---The Trivial Pastime
33
1
The Samaritan's Dilemma
33
1
The Rotten Kid Theorem
34
1
The Illogic of Conflict Escalation
35
1
How to Value Lotteries
36
1
Payoffs in Games Where Nature Moves
37
1
Nature in Action: No-Draw, High-Low Poker
38
3
The Expected Utility Principle
41
1
Buying Fire Insurance
42
1
Neoclassical Economics and Game Theory
43
3
Markets as Disciplining Devices: Allied Widgets
46
5
The Truth Game
51
1
The Shopper and the Fish Merchant
52
1
Fathers and Sons
53
1
The Women of Sevitan
53
1
Catching 'em Off Guard: Mixed Strategy Nash Equilibria
54
36
Introduction
54
1
Mixed Strategies: Basic Definitions
55
1
The Fundamental Theorem
56
1
Solving for Mixed Strategy Nash Equilibria
57
1
Reviewing the Terminology
58
1
Big Monkey and Little Monkey Revisited
59
1
Dominance Revisited
59
1
Competition on Main Street Revisited
59
1
Battle of the Sexes
60
1
Throwing Fingers
60
1
One-Card Two-Round Poker with Bluffing
60
2
Trust in Networks
62
1
Behavioral Strategies in Extensive Form Games
63
2
Lions and Antelope
65
1
The Santa Fe Bar
66
1
Orange-Throat, Blue-Throat, and Yellow-Striped Lizards
67
1
Sex Ratios as Nash Equilibria
68
1
Tennis Strategy
69
1
A Mating Game
70
1
Preservation of Ecology Game
71
1
Hard Love
71
1
Coordination Failure
72
1
Advertising Game
72
1
Colonel Blotto Game
72
1
Number Guessing Game
73
1
Target Selection
73
1
A Reconnaissance Game
74
1
Attack on Hidden Object
74
1
Two-Person Zero-Sum Games
75
1
An Introduction to Forward Induction
76
1
Mutual Monitoring in a Partnership
77
1
Mutual Monitoring in Teams
78
1
Altruism(?) in Bird Flocks
79
1
Robin Hood and Little John
80
1
The Motorist's Dilemma
80
1
Family Politics
81
1
Frankie and Johnny
81
1
A Card Game
82
1
Cheater-Inspector
82
1
The Groucho Marx Game
82
2
Real Men Don't Eat Quiche
84
1
The Vindication of the Hawk
84
1
Correlated Equilibria
85
2
Poker with Bluffing Revisited
87
1
Equivalence of Behavioral and Mixed Strategies
87
3
Moving through the Game Tree: Subgames, Incredible Threats, and Trembling Hands
90
28
Introduction
90
2
Subgame Perfection
92
3
Stackelberg Leadership
95
1
The Subway Entry Deterrence Game
96
1
The Dr. Strangelove Game
96
1
The Rubinstein Bargaining Model
97
2
Huey, Dewey, and Louie Split a Dollar
99
1
The Little Miss Muffet Game
99
1
Nuisance Suits
100
2
Cooperation in an Overlapping-Generations Economy
102
1
The Finitely Repeated Prisoner's Dilemma
103
6
The Finitely Repeated Prisoner's Dilemma II
109
1
Fuzzy Subgame Perfection
110
2
Perfect Behavioral Nash Equilibria
112
2
Selten's Horse
114
1
Trembling Hand Perfection
115
2
Nature Abhors Low Probability Events
117
1
Repeated Games, Trigger Strategies, and Tacit Collusion
118
30
Introduction
118
1
Big Fish and Little Fish
119
2
Tacit Collusion
121
5
The Folk Theorem: An Embarras de richesses
126
1
Variations on the Folk Theorem
127
2
The One-Stage Deviation Principle
129
1
A Trembling Hand, Cooperative Equilibrium
130
1
Death and Discount Rates in Repeated Games
131
1
The Strategy of an Oil Cartel
132
1
Manny and Moe
132
1
Tit-for-Tat
132
1
A Public Goods Experiment
133
1
Reputational Equilibrium
134
1
Contingent Renewal Contracts
134
6
Contingent Renewal Labor Markets
140
5
I'd Rather Switch than Fight
145
3
Biology Meets Economics: Evolutionary Stability and the Birth of Dynamic Game Theory
148
16
The Birth of Evolutionary Stability
148
1
Properties of Evolutionarily Stable Strategies
149
3
Are Evolutionarily Stable Strategies Unbeatable?
152
1
Trust in Networks II
152
1
Cooperative Fishing
152
1
Nash Equilibrium That Is Not Evolutionarily Stable
153
1
Rock, Paper, and Scissors Is Not Evolutionarily Stable
153
1
Sex Ratios as Evolutionarily Stable Strategies
153
1
Invasion of the Pure Strategy Mutants
154
1
Multiple Evolutionarily Stable Strategies
154
1
The Logic of Animal Conflict
155
2
Hawks, Doves, and Bourgeois
157
1
Trogs and Farfel
158
1
Evolutionary Stability in Finite Populations
159
2
Evolutionary Stability in Asymmetric Games
161
3
Dynamical Systems and Differential Equations
164
24
Introduction
164
1
Dynamical Systems
165
1
Population Growth
166
1
Population Growth with Limited Carrying Capacity
166
2
The Lotka-Volterra Predator-Prey Model
168
4
Dynamical Systems Theory
172
3
Dynamical Systems in One Dimension
175
3
Dynamical Systems in Two Dimensions
178
3
Exercises in Two-Dimensional Linear Systems
181
1
Cultural Dynamics
182
1
Lotka-Volterra with Limited Carrying Capacity
183
1
Take No Prisoners
183
1
The Hartman-Grobman Theorem
184
1
Special Features of Two-Dimensional Dynamical Systems
185
1
A Non-Hyperbolic Dynamical System
185
1
Liapunov's Theorem
186
2
Evolutionary Dynamics
188
32
Introduction
188
1
The Origins of Evolutionary Dynamics
189
8
Properties of the Replicator System
197
1
Characterizing the Two-Variable Replicator Dynamic
198
1
Do Dominated Strategies Survive under a Replicator Dynamic?
199
2
Equilibrium and Stability with a Replicator Dynamic
201
1
Evolutionary Stability and Evolutionary Equilibrium
202
1
Trust in Networks III
203
1
Bayesian Perfection and Stable Sets
203
1
Invasion of the Pure Strategy Mutants, II
204
1
A Generalization of Rock, Paper, and Scissors
205
1
Uta stansburia in Motion
206
1
The Dynamics of Rock-Paper-Scissors and Related Games
207
1
Lotka-Volterra Model and Biodiversity
208
2
Asymmetric Evolutionary Games
210
4
Asymmetric Evolutionary Games: Reviewing the Troops
214
1
The Evolution of Trust and Honesty
214
2
The Loraxes and Thoraxes
216
1
Cultural Transmission and Social Imitation
217
3
Markov Economies and Stochastic Dynamical Systems
220
17
Introduction
220
1
The Emergence of Money in a Markov Economy
221
7
Good Vibrations
228
1
Adaptive Learning
229
4
Adaptive Learning When Not All Conventions are Equal
233
1
Adaptive Learning with Errors
234
1
Stochastic Stability
235
2
Homo reciprocans, Homo egualis, and Other Contributors to the Human Behavioral Repertoire
237
47
Introduction
237
2
Modeling the Human Actor
239
5
Behavioral Economics: Games against Nature and against Ourselves
244
7
Experimental Game Theory: The Laboratory Meets Strategic Interaction
251
7
Homo egualis
258
3
Homo reciprocans: Modeling Strong Reciprocity
261
5
Altruism and Assortative Interactions
266
5
The Evolution of Strong Reciprocity
271
7
Homo parochius: Modeling Insiders and Outsiders
278
6
Learning Who Your Friends Are: Bayes' Rule and Private Information
284
23
Private Information
284
5
The Role of Beliefs in Games with Private Information
289
2
Haggling at the Bazaar
291
3
Adverse Selection
294
1
A Market for Lemons
295
1
Choosing an Exorcist
296
3
A First-Price Sealed-Bid Auction
299
1
A Common Value Auction: The Winner's Curse
300
1
A Common Value Auction: Quantum Spin Decoders
300
2
Predatory Pricing: Pooling and Separating Equilibria
302
2
Limit Pricing
304
1
A Simple Limit-Pricing Model
305
2
When It Pays to Be Truthful: Signaling in Games with Friends, Adversaries, and Kin
307
25
Signaling as a Coevolutionary Process
307
1
A Generic Signaling Game
308
2
Introductory Offers
310
1
Web Sites (for Spiders)
310
2
Sex and Piety: The Darwin-Fisher Model of Sexual Selection
312
5
Biological Signals as Handicaps
317
2
The Shepherds Who Never Cry Wolf
319
2
My Brother's Keeper
321
2
Honest Signaling among Partial Altruists
323
2
Educational Signaling I
325
3
Education as a Screening Device
328
1
Capital as a Signaling Device
329
3
Bosses and Workers, Landlords and Peasants, and other Principal-Agent Models
332
13
Introduction to the Principal-Agent Model
332
1
Labor Discipline with Monitoring
333
2
Labor as Gift Exchange
335
1
Labor Discipline with Profit Signaling
336
4
Peasants and Landlords
340
1
Mr. Smith's Car Insurance
341
1
A Generic One-Shot Principal-Agent Game
342
3
Bargaining
345
12
Introduction
345
1
The Nash Bargaining Model
346
3
Risk Aversion and the Nash Bargaining Solution
349
1
Rubinstein Bargaining with Outside Options
350
2
Bargaining with Two-Sided Outside Options
352
1
Rubinstein Bargaining and Nash Bargaining
353
1
Zeuthen Lotteries and the Nash Bargaining Solution
354
1
Bargaining with Fixed Costs
355
1
Bargaining with Incomplete Information
355
2
Probability and Decision Theory
357
38
Probability Spaces
357
1
DeMorgan's Laws
357
1
Interocitors
358
1
The Direct Evaluation of Probabilities
358
1
Probability as Frequency
358
2
Sampling
360
1
Self presentation
360
1
Social Isolation
361
1
Aces Up
361
1
Mechanical Defection
361
1
Double Orders
361
1
Combinations and Sampling
361
1
Mass Defection
362
1
An Unlucky Streak
362
1
House Rules
362
1
The Powerball Lottery
362
1
The Addition Rule for Probabilities
362
1
Die, Die!
363
1
Les Cinq Tiroirs
363
1
A Guessing Game
363
1
Conditional Probability
363
1
Bayes' Rule
364
1
Drug Testing
365
1
A Bolt Factory
365
1
Color Blindness
365
1
Urns
365
1
The Monty Hall Game
365
2
The Logic of Murder and Abuse
367
2
Ah, Those Kids
369
1
The Greens and the Blacks
369
1
Laplace's Law of Succession
369
1
The Brain and Kidney Problem
370
1
Sexual Harassment on the Job
370
1
The Value of Eyewitness Testimony
370
1
The End of the World
371
1
Bill and Harry
371
1
When Weakness Is Strength
371
1
Markov Chains
372
9
Preferences and Expected Utility
381
4
Exceptions to the Expected Utility Principle
385
2
Risk Behavior and the Shape of the Utility Function
387
8
II Answers and Hints
Leading from Strength: Eliminating Dominated Strategies
395
4
Second-Price Auction
395
1
Hagar's Battles
395
1
A Military Strategy Game
396
1
Strategic Voting
397
2
Playing It Straight: Pure Strategy Nash Equilibria
399
11
The Tobacco Market
399
1
The Klingons and the Snarks
400
1
Chess---The Trivial Pastime
401
1
The Samaritan's Dilemma
401
2
The Rotten Kid Theorem
403
1
The Illogic of Conflict Escalation
404
1
How to Value Lotteries
404
1
The Truth Game
405
2
The Shopper and the Fish Merchant
407
1
The Women of Sevitan
408
2
Catching 'em Off Guard: Mixed Strategy Nash Equilibria
410
26
Battle of the Sexes
410
2
One-Card Two-Round Poker with Bluffing
412
1
The Santa Fe Bar
413
1
Sex Ratios as Nash Equilibria
414
2
A Mating Game
416
1
Preservation of Ecology Game
416
1
Coordination Failure
417
1
Advertising Game
417
2
Colonel Blotto Game
419
1
Number Guessing Game
420
1
Target Selection
420
1
A Reconnaissance Game
421
1
Attack on Hidden Object
422
1
Robin Hood and Little John
422
1
The Motorist's Dilemma
423
1
Frankie and Johnny
424
1
A Card Game
425
2
Cheater-Inspector
427
1
The Groucho Marx Game
428
3
Real Men Don't Eat Quiche
431
1
Equivalence of Behavioral and Mixed Strategies
432
4
Moving through the Game Tree: Subgames, Incredible Threats, and Trembling Hands
436
6
The Subway Entry Deterrence Game
436
1
The Dr. Strangelove Game
436
1
Huey, Dewey, and Louie Split a Dollar
437
1
Cooperation in an Overlapping-Generations Economy
438
1
The Finitely Repeated Prisoner's Dilemma II
439
1
Selten's Horse
440
1
Trembling Hand Perfection
441
1
Repeated Games, Trigger Strategies, and Tacit Collusion
442
1
Reputational Equilibrium
442
1
Biology Meets Economics: Evolutionary Stability and the Birth of Dynamic Game Theory
443
8
Properties of Evolutionarily Stable Strategies
443
3
Cooperative Fishing
446
1
Hawks, Doves, and Bourgeois
447
1
Trogs and Farfel
448
1
Evolutionary Stability in Finite Populations
449
2
Evolutionary Dynamics
451
6
Properties of the Replicator System
451
1
The Dynamics of Rock-Paper-Scissors and Related Games
451
3
Lotka-Volterra Model and Biodiversity
454
1
The Loraxes and Thoraxes
455
2
Learning Who Your Friends Are: Bayes' Rule and Private Information
457
9
Haggling at the Bazaar
457
1
A Common Value Auction: The Winner's Curse
458
1
A Common Value Auction: Quantum Spin Decoders
458
2
Predatory Pricing: Pooling and Separating Equilibria
460
1
Limit Pricing
461
3
A Simple Limit-Pricing Model
464
2
When It Pays to Be Truthful: Signaling in Games with Friends, Adversaries, and Kin
466
7
Introductory Offers
466
1
Web Sites (for Spiders)
466
2
The Shepherds Who Never Cry Wolf
468
1
Honest Signaling among Partial Altruists
469
1
Education as a Screening Device
470
1
Capital as a Signaling Device
471
2
Bosses and Workers, Landlords and Peasants, and Other Principal-Agent Models
473
10
Labor as Gift Exchange
473
1
Labor Discipline with Profit Signaling
474
1
Peasants and Landlords
475
3
Mr. Smith's Car Insurance
478
2
A Generic One-Shot Principal-Agent Game
480
3
Bargaining
483
6
The Nash Bargaining Model
483
1
Risk Aversion and the Nash Bargaining Solution
484
1
Rubinstein Bargaining with Outside Options
485
1
Rubinstein Bargaining and Nash Bargaining
486
1
Zeuthen Lotteries and the Nash Bargaining Solution
487
1
Bargaining with Fixed Costs
487
1
Bargaining with Incomplete Information
488
1
Probability and Decision Theory
489
11
Probability as Frequency
489
1
Sampling
489
1
Social Isolation
489
1
Aces Up
489
1
Mechanical Defection
490
1
Double Orders
490
1
Mass Defection
490
1
An Unlucky Streak
490
1
House Rules
491
1
The Powerball Lottery
491
1
Die, Die!
492
1
A Guessing Game
492
2
Drug Testing
494
1
The Greens and the Blacks
494
1
Laplace's Law of Succession
495
1
The Brain and Kidney Problem
496
1
Sexual Harassment on the Job
497
1
The Value of Eyewitness Testimony
497
1
Bill and Harry
497
1
When Weakness Is Strength
497
3
Sources for Problems
500
1
References
501
20
Index
521