Game theory in action: an introduction to classical and evolutionary models
Schecter, Stephen
creator
Gintis, Herbert
text
nju
Princeton
Princeton University Press
2016
monographic
eng
274 p.
Game Theory in Action is a textbook about using game theory across a range of real-life scenarios. From traffic accidents to the sex lives of lizards, Stephen Schecter and Herbert Gintis show students how game theory can be applied in diverse areas including animal behavior, political science, and economics.
The book's examples and problems look at such fascinating topics as crime-control strategies, climate-change negotiations, and the power of the Oracle at Delphi. The text includes a substantial treatment of evolutionary game theory, where strategies are not chosen through rational analysis, but emerge by virtue of being successful. This is the side of game theory that is most relevant to biology; it also helps to explain how human societies evolve.
Aimed at students who have studied basic calculus and some differential equations, Game Theory in Action is the perfect way to learn the concepts and practical tools of game theory.
Aimed at students who have studied calculus and some differential equations
Examples are drawn from diverse scenarios, ranging from traffic accidents to the sex lives of lizards
A substantial treatment of evolutionary game theory
Useful problem sets at the end of each chapter
Stephen Schecter is professor of mathematics at North Carolina State University. Herbert Gintis is external professor at the Santa Fe Institute. He is the author of Game Theory Evolving and The Bounds of Reason, and the coauthor (with Samuel Bowles) of A Cooperative Species (all Princeton).
http://press.princeton.edu/titles/10739.html
Contents
Preface and acknowledgments xi
Chapter 1. Backward induction 1
1.1 Tony’s Accident 1
1.2 Games in extensive form with complete information 3
1.3 Strategies 5
1.4 Backward induction 6
1.5 Big Monkey and Little Monkey 1 9
1.6 Threats, promises, commitments 10
1.7 Ultimatum Game 12
1.8 Rosenthal’s Centipede Game 13
1.9 Continuous games 15
1.10 Stackelberg’s model of duopoly 1 16
1.11 Stackelberg’s model of duopoly 2 20
1.12 Backward induction for finite horizon games 24
1.13 Critique of backward induction 25
1.14 Problems 27
Chapter 2. Eliminating dominated strategies 37
2.1 Prisoner’s Dilemma 37
2.2 Games in normal form 39
2.3 Dominated strategies 40
2.4 Israelis and Palestinians 41
2.5 Global Warming 44
2.6 Hagar’s Battles 45
2.7 Second-price auctions 47
2.8 Iterated elimination of dominated strategies 49
2.9 The Battle of the Bismarck Sea 49
2.10 Normal form of a game in extensive form with complete information 51
2.11 Big Monkey and Little Monkey 2 51
2.12 Backward induction 53
2.13 Critique of elimination of dominated strategies 55
2.14 Problems 55
Chapter 3. Nash equilibria 61
3.1 Big Monkey and Little Monkey 3 and the definition of Nash equilibria 61
3.2 Finding Nash equilibria by inspection: Important examples 63
3.3 Water Pollution 1 66
3.4 Arguing over Marbles 67
3.5 Tobacco Market 69
3.6 Iterated elimination of dominated strategies 71
3.7 Big Monkey and Little Monkey 4 74
3.8 Finding Nash equilibria using best response 75
3.9 Big Monkey and Little Monkey 5 76
3.10 Water Pollution 2 77
3.11 Cournot’s model of duopoly 77
3.12 Problems 79
Chapter 4. Games in extensive form with incomplete information 88
4.1 Utility functions and lotteries 88
4.2 Buying Fire Insurance 89
4.3 Games in extensive form with incomplete information 90
4.4 Buying a Used Car 91
4.5 The Travails of Boss Gorilla 1 95
4.6 Cuban Missile Crisis 98
4.7 Problems 104
Chapter 5. Mixed strategy Nash equilibria 114
5.1 Mixed strategy Nash equilibria 114
5.2 Tennis 120
5.3 Other ways to find mixed strategy Nash equilibria 122
5.4 One-card Two-round Poker 123
5.5 Two-player zero-sum games 128
5.6 The Ultimatum Minigame 132
5.7 Colonel Blotto vs. the People’s Militia 134
5.8 Water Pollution 3 140
5.9 Equivalent games 141
5.10 Software for computing Nash equilibria 142
5.11 Critique of Nash equilibrium 143
5.12 Problems 144
Chapter 6. More about games in extensive form with
complete information 151
6.1 Subgame perfect Nash equilibria 152
6.2 Big Monkey and Little Monkey 6 152
6.3 Subgame perfect equilibria and backward induction 153
6.4 Duels and Truels 155
6.5 The Rubinstein bargaining model 160
6.6 Discount factor and repeated games 163
6.7 The Wine Merchant and the Connoisseur 165
6.8 The Folk Theorem 168
6.9 Maximum value of a function 172
6.10 The Samaritan’s Dilemma 173
6.11 The Rotten Kid Theorem 177
6.12 Problems 180
Chapter 7. Symmetries of games 186
7.1 Interchangeable players 186
7.2 Reporting a Crime 189
7.3 Sex Ratio 1 191
7.4 Other symmetries of games 193
7.5 Problems 198
Chapter 8. Alternatives to the Nash equilibrium 203
8.1 Correlated equilibrium 203
8.2 Epistemic game theory 205
8.3 Evolutionary stability 206
8.4 Evolutionary stability with two pure strategies 209
8.5 Sex Ratio 2 213
8.6 Problems 214
Chapter 9. Differential equations 217
9.1 Differential equations and scientific laws 217
9.2 The phase line 219
9.3 Vector fields 220
9.4 Functions and differential equations 222
9.5 Linear differential equations 225
9.6 Linearization 228
Chapter 10. Evolutionary dynamics 232
10.1 Replicator system 232
10.2 Microsoft vs. Apple 235
10.3 Evolutionary dynamics with two pure strategies 237
10.4 Hawks and Doves revisited 238
10.5 Side-blotched Lizards 240
10.6 Equilibria of the replicator system 244
10.7 Cooperators, Defectors, and Tit-for-Tatters 246
10.8 Dominated strategies and the replicator system 249
10.9 Asymmetric evolutionary games 251
10.10 Big Monkey and Little Monkey 7 253
10.11 Hawks and Doves with Unequal Value 255
10.12 The Ultimatum Minigame revisited 256
10.13 Problems 258
Appendix. Sources for examples and problems 265
References 269
Index 271
Game theory
Games of strategy (Mathematics)
Global warming
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