Scissors and Rock (eBook)

Preface: Introduction and Warnings 5
Contents 10
1 Playing for Susan 14
1.1Thinking Strategically 15
1.2Why not Learn Game Theory? 17
1.3The Working of the Invisible Hand 19
1.4The Real World and Its Models 23
1.5Winner-Takes-It-All and the Chicken Game 25
1.6The Essence of Game Theory, the Brain, and Empathy 28
1.7Strategic Thinking that Failed—Perhaps 31
References 33
2 No Mathematics 35
2.1Historical Note I: The Pioneers 35
2.2The Concept of Sets 39
2.3Prices and Quantities 42
2.4From Set to Mapping and Function 43
2.5Utilities, Payoff Functions, and Strategy Vectors 45
2.6Monkeys Write Shakespeare, but Where Is Hamlet? 47
References 50
3 The Prisoners’ Dilemma, but Who Are the Players? 51
3.1From Game Form to Payoff Matrix 51
3.2Equilibrium in Dominant Strategies 56
3.3Catch-22 and Other Social Traps 57
3.4Ways Out of the Dilemma 59
3.5Who Are the Players? 61
3.6Then Strike 64
3.7Tosca’s Dominant Strategy 67
References 69
4 The Nash Equilibrium 70
4.1On the Definition of the Nash Equilibrium 70
4.2Historical Note II: Nash and the Nash Equilibrium 73
4.3Nash Equilibria and Chicken Game 74
4.4Inefficient Equilibria in the QWERTY-DSK Game 78
4.5Who Are the Players in the QWERTY-DSK Game? 81
4.6Nash Equilibria in Kamasutra Games 83
References 84
5 Sequence of Moves and the Extensive Form 86
5.1The Shrinking of the Event Matrix 86
5.2Sequential Structure and Chicken Game 87
5.3Extensive Form and Game Tree 89
5.4Information: Perfect, Imperfect, Complete, and Incomplete 90
5.5Perfect Recall Missing 93
5.6The Battle of the Sexes 97
5.7What Is a Strategy? 100
5.8Sharing a Cake 102
5.9Theory of Moves 103
References 106
6 Chaos, Too Many and Too Few 107
6.1The El Farol Problem or “Too Many People at the Same Spot” 108
6.2Self-referential Systems 110
6.3Solutions to the El Farol Problem 111
6.4Market Congestion Game 113
6.5Viruses for Macintosh 114
6.6The Volunteer’s Dilemma 116
References 122
7 Which Strategy to Choose? 123
7.1Nash Equilibrium and Optimal Strategy 124
7.2Equilibrium Choice and Trembling Hand 126
7.3Trembling Hand Perfection and Market Congestion 128
7.4Rationalizable Strategies 131
References 133
8 Step-by-Step: The Subgame-Perfect Equilibrium 134
8.1Market Entry Game with Monopoly 135
8.2Backward Induction and Optimal Strategies 136
8.3The Ultimatum Game 139
8.4Social Trust and the Stag Hunt Game 142
8.5How Reciprocity Works 145
References 148
9 Forever and a Day 150
9.1The Competition Trap Closes 152
9.2Iterated Prisoners’ Dilemma and the “Ravages of Time” 154
9.3The Competition Trap Breaking Down 157
9.4Robert Axelrod’s “Tournament of Strategies” 161
9.5“The True Egoist Cooperates.”—Yes, but Why? 164
9.6The Folk Theorem and “What We Have Always Known” 167
References 172
10 Mixed Strategies and Expected Utility 174
10.1From Lottery to Expected Utility 175
10.2The Allais Paradox and Kahneman-Tversky 178
10.3Optimal Inspection in Mixed Strategies 181
10.4Maximin Solution and the Inspection Game 185
10.5Chicken Game Equilibria and Maximin Solution 188
10.6Miller’s Crucible and the Stag Hunt Game 189
10.7Zero-Sum Games and Minimax Theorem 192
10.8The Goalie’s Anxiety at the Penalty Kick 197
10.9Scissors and Rock 200
References 202
11 More Than Two Players 204
11.1The Value of Coalitions 205
11.2The Core 206
11.3Network Games 208
11.4Epilogue to the Core and Other Bargaining Solutions 213
11.5Competition and Cooperation in the Triad 216
References 220
12 Bargaining and Bargaining Games 221
12.1The Bargaining Problem and the Solution 222
12.2Rubinstein Game and the Shrinking Pie 227
12.3Binding Agreements and the Nash Solution 233
12.4Properties, Extensions, and the Nash Program 239
References 244
13 Goethe’s Price Games, Auctions, and Other Surprises 245
13.1The Story of a Second-Price Auction 246
13.2The Price-Setting Goethe 250
13.3Optimal Strategies in Auctions and the Revenue Equivalence Theorem 253
13.4All-Pay Auction, Attrition, and Pyrrhic Victory 258
13.5Who Likes to Pay High Prices? 260
References 262
Index 263