Games, Theory and Applications (Dover Books on Mathematics)

Front cover......Page 1
Dover books on mathematics......Page 2
Title......Page 4
Copyright......Page 5
Table of Contents......Page 7
Author\'s Preface......Page 11
Glossary of Symbols......Page 13
1.1 What is a game?......Page 15
1.2 Examples of games......Page 16
1.3 Terminology of game theory......Page 17
1.4 History of game theory......Page 20
Problems......Page 21
2.1 Extensive form......Page 23
2.2 Normal form......Page 27
2.3 Maximin criterion......Page 29
2.4 Mixed strategies......Page 30
2.5 Minimax theorem......Page 33
2.6 Domination......Page 34
2.8 Solutions of 2 x m games......Page 37
2.9 Equilibrium pairs......Page 42
2.10 Games with perfect information......Page 44
2.11 Solving ? x m games......Page 45
2.12 Further reading......Page 48
Problems......Page 50
3.2 Examples......Page 53
3.3 Equilibrium pairs and maximin-maximin pairs......Page 56
3.4 Sketch proof of Nash\'s theorem......Page 57
3.5 How to find equilibrium pairs (Swastika Method)......Page 59
3.6 Solution concepts of non-zero-sum games......Page 61
3.7 Cooperative games......Page 64
3.8 Bargaining or negotiation set......Page 66
3.9 Nash\'s bargaining axioms......Page 67
3.10 Maximin bargaining solution......Page 72
3.11 Threat bargaining solution......Page 75
Problems......Page 81
4.1 Non-cooperative games......Page 85
4.2 Characteristic function......Page 86
4.3 Strategic equivalence of characteristic functions......Page 89
4.4 Imputations......Page 90
4.5 The core......Page 91
4.6 Stable sets......Page 94
4.7 Nucleolus......Page 99
4.8 Shapley value......Page 101
4.9 Other solution concepts......Page 104
4.10 Further reading......Page 107
Problems......Page 108
5.2 [l,l]-marketgame......Page 112
5.3 [M,iV]-marketgame ,......Page 114
5.4 [l,N]-marketgame......Page 116
5.5 [N,N]-marketgame......Page 117
5.6 Duopoly and oligopoly......Page 118
5.7 Cournot equilibrium......Page 119
5.8 Other solution concepts in duopoly......Page 121
5.9 Quantity model, symmetric games and oligopoly theory......Page 125
Problems......Page 126
6.1 Objectives of metagames......Page 129
6.2 Metagames and metaequilibria......Page 130
6.3 Metarationality theorem......Page 134
6.4 Examples of metagame analysis......Page 136
6.5 Symmetric metaequilibria......Page 139
6.6 Analysis of options......Page 141
6.7 Analysis of options applied to market strategy......Page 142
6.8 Further reading......Page 145
Problems......Page 147
7.1 Multi-stage games......Page 150
7.2 Stochastic games, recursive games and supergames......Page 152
7.3 Discounted stochastic games......Page 153
7.4 Existence of value ,......Page 154
7.5 Advertising example......Page 157
7.6 Bounds on value iteration......Page 158
7.7 Recursive games......Page 160
7.8 Solution of recursive games......Page 161
7.9 Examples of recursive games......Page 162
7.10 Supergames......Page 164
7.11 Relationship between supergames and metagames: oligopoly example......Page 165
7.12 Further reading......Page 168
Problems......Page 170
8.1 Introduction......Page 176
8.2 Evolutionary stable strategies (ESS)......Page 177
8.3 Examples of evolutionary games......Page 178
8.4 Properties of evolutionary stable strategies......Page 181
8.5 How to find evolutionary stable strategies......Page 182
8.6 War of attrition......Page 184
8.7 Dynamic evolutionary games......Page 187
8.8 Stability in dynamic evolutionary games......Page 189
8.9 Evolutionary stable strategies in multi-type games......Page 192
8.10 Further reading......Page 195
Problems......Page 196
9.1 Types of auctions......Page 200
9.2 Dutch auction-discrete bids and known valuations......Page 202
9.3 Dutch auction-continuous bids and known valuations......Page 207
9.4 English auction-known valuations......Page 209
9.5 Auctions with unknown valuations......Page 211
9.6 Auctions of two or more objects......Page 214
9.7 Horse market auctions......Page 216
9.8 Further reading......Page 220
Problems......Page 221
10.1 What is gaming?......Page 223
10.2 Whydogaming?......Page 224
10.3 Running a gaming experiment......Page 228
10.4 Further reading......Page 231
Solutions to problems......Page 233
References......Page 265
Index......Page 275
Name index......Page 278
A catalog of selected Dover books......Page 281
Back cover......Page 286