Game Theory in Action: An Introduction to Classical and Evolutionary Models

Cover
Title Page
Copyright Page
Dedication Page
Table of Contents
Preface and Acknowledgements
Chapter 1. Backward induction
	1.1 Tony’s Accident
	1.2 Games in extensive form with complete information
	1.3 Strategies
	1.4 Backward induction
	1.5 Big Monkey and Little Monkey 1
	1.6 Threats, promises, commitments
	1.7 Ultimatum Game
	1.8 Rosenthal’s Centipede Game
	1.9 Continuous games
	1.10 Stackelberg’s model of duopoly 1
	1.11 Stackelberg’s model of duopoly 2
	1.12 Backward induction for finite horizon games
	1.13 Critique of backward induction
	1.14 Problems
Chapter 2. Eliminating dominated strategies
	2.1 Prisoner’s Dilemma
	2.2 Games in normal form
	2.3 Dominated strategies
	2.4 Israelis and Palestinians
	2.5 Global Warming
	2.6 Hagar’s Battles
	2.7 Second-price auctions
	2.8 Iterated elimination of dominated strategies
	2.9 The Battle of the Bismarck Sea
	2.10 Normal form of a game in extensive form with complete information
	2.11 Big Monkey and Little Monkey 2
	2.12 Backward induction
	2.13 Critique of elimination of dominated strategies
	2.14 Problems
Chapter 3. Nash equilibria
	3.1 Big Monkey and Little Monkey 3 and the definition of Nash equilibria
	3.2 Finding Nash equilibria by inspection: Important examples
	3.3 Water Pollution 1
	3.4 Arguing over Marbles
	3.5 Tobacco Market
	3.6 Iterated elimination of dominated strategies
	3.7 Big Monkey and Little Monkey 4
	3.8 Finding Nash equilibria using best response
	3.9 Big Monkey and Little Monkey 5
	3.10 Water Pollution 2
	3.11 Cournot’s model of duopoly
	3.12 Problems
Chapter 4. Games in extensive form with incomplete information
	4.1 Utility functions and lotteries
	4.2 Buying Fire Insurance
	4.3 Games in extensive form with incomplete information
	4.4 Buying a Used Car
	4.5 The Travails of Boss Gorilla 1
	4.6 Cuban Missile Crisis
	4.7 Problems
Chapter 5. Mixed strategy Nash equilibria
	5.1 Mixed strategy Nash equilibria
	5.2 Tennis
	5.3 Other ways to find mixed strategy Nash equilibria
	5.4 One-card Two-round Poker
	5.5 Two-player zero-sum games
	5.6 The Ultimatum Minigame
	5.7 Colonel Blotto vs. the People’s Militia
	5.8 Water Pollution 3
	5.9 Equivalent games
	5.10 Software for computing Nash equilibria
	5.11 Critique of Nash equilibrium
	5.12 Problems
Chapter 6. More about games in extensive form with complete information
	6.1 Subgame perfect Nash equilibria
	6.2 Big Monkey and Little Monkey 6
	6.3 Subgame perfect equilibria and backward induction
	6.4 Duels and Truels
	6.5 The Rubinstein bargaining model
	6.6 Discount factor and repeated games
	6.7 The Wine Merchant and the Connoisseur
	6.8 The Folk Theorem
	6.9 Maximum value of a function
	6.10 The Samaritan’s Dilemma
	6.11 The Rotten Kid Theorem
	6.12 Problems
Chapter 7. Symmetries of games
	7.1 Interchangeable players
	7.2 Reporting a Crime
	7.3 Sex Ratio 1
	7.4 Other symmetries of games
	7.5 Problems
Chapter 8. Alternatives to the Nash equilibrium
	8.1 Correlated equilibrium
	8.2 Epistemic game theory
	8.3 Evolutionary stability
	8.4 Evolutionary stability with two pure strategies
	8.5 Sex Ratio 2
	8.6 Problems
Chapter 9. Differential equations
	9.1 Differential equations and scientific laws
	9.2 The phase line
	9.3 Vector fields
	9.4 Functions and differential equations
	9.5 Linear differential equations
	9.6 Linearization
Chapter 10. Evolutionary dynamics
	10.1 Replicator system
	10.2 Microsoft vs. Apple
	10.3 Evolutionary dynamics with two pure strategies
	10.4 Hawks and Doves revisited
	10.5 Side-blotched Lizards
	10.6 Equilibria of the replicator system
	10.7 Cooperators, Defectors, and Tit-for-Tatters
	10.8 Dominated strategies and the replicator system
	10.9 Asymmetric evolutionary games
	10.10 Big Monkey and Little Monkey 7
	10.11 Hawks and Doves with Unequal Value
	10.12 The Ultimatum Minigame revisited
	10.13 Problems
Appendix. Sources for examples and problems
References
Index