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"Provides introductory material to game theory, including bargaining, parlour games, sport, networking games and dynamic games"--
Sommario
Preface xi
Introduction xiii
1 Strategic-Form Two-Player Games 1
Introduction 1
1.1 The Cournot Duopoly 2
1.2 Continuous Improvement Procedure 3
1.3 The Bertrand Duopoly 4
1.4 The Hotelling Duopoly 5
1.5 The Hotelling Duopoly in 2D Space 6
1.6 The Stackelberg Duopoly 8
1.7 Convex Games 9
1.8 Some Examples of Bimatrix Games 12
1.9 Randomization 13
1.10 Games 2 ×2 16
1.11 Games 2 × n and m ×2 18
1.12 The Hotelling Duopoly in 2D Space with Non-Uniform Distribution of Buyers 20
1.13 Location Problem in 2D Space 25
Exercises 26
2 Zero-Sum Games 28
Introduction 28
2.1 Minimax and Maximin 29
2.2 Randomization 31
2.3 Games with Discontinuous Payoff Functions 34
2.4 Convex-Concave and Linear-Convex Games 37
2.5 Convex Games 39
2.6 Arbitration Procedures 42
2.7 Two-Point Discrete Arbitration Procedures 48
2.8 Three-Point Discrete Arbitration Procedures with Interval Constraint 53
2.9 General Discrete Arbitration Procedures 56
Exercises 62
3 Non-Cooperative Strategic-Form n-Player Games 64
Introduction 64
3.1 Convex Games. The Cournot Oligopoly 65
3.2 Polymatrix Games 66
3.3 Potential Games 69
3.4 Congestion Games 73
3.5 Player-Specific Congestion Games 75
3.6 Auctions 78
3.7 Wars of Attrition 82
3.8 Duels, Truels, and Other Shooting Accuracy Contests 85
3.9 Prediction Games 88
Exercises 93
4 Extensive-Form n-Player Games 96
Introduction 96
4.1 Equilibrium in Games with Complete Information 97
4.2 Indifferent Equilibrium 99
4.3 Games with Incomplete Information 101
4.4 Total Memory Games 105
Exercises 108
5 Parlor Games and Sport Games 111
Introduction 111
5.1 Poker. A Game-Theoretic Model 112
5.2 The Poker Model with Variable Bets 118
5.3 Preference. A Game-Theoretic Model 129
5.4 The Preference Model with Cards Play 136
5.5 Twenty-One. A Game-Theoretic Model 145
5.6 Soccer. A Game-Theoretic Model of Resource Allocation 147
Exercises 152
6 Negotiation Models 155
Introduction 155
6.1 Models of Resource Allocation 155
6.2 Negotiations of Time and Place of a Meeting 166
6.3 Stochastic Design in the Cake Cutting Problem 171
6.4 Models of Tournaments 182
6.5 Bargaining Models with Incomplete Information 190
6.6 Reputation in Negotiations 221
Exercises 228
7 Optimal Stopping Games 230
Introduction 230
7.1 Optimal Stopping Game: The Case of Two Observations 231
7.2 Optimal Stopping Game: The Case of Independent Observations 234
7.3 The Game GammaN(G) Under N >= 3 237
7.4 Optimal Stopping Game with Random Walks 241
7.5 Best Choice Games 250
7.6 Best Choice Game with Stopping Before Opponent 254
7.7 Best Choice Game with Rank Criterion. Lottery 259
7.8 Best Choice Game with Rank Criterion. Voting 264
7.9 Best Mutual Choice Game 269
Exercises 276
8 Cooperative Games 278
Introduction 278
8.1 Equivalence of Cooperative Games 278
8.2 Imputations and Core 281
8.3 Balanced Games 285
8.4 The -Value of a Cooperative Game 286
8.5 Nucleolus 289
8.6 The Bankru
Info autore
VLADIMIR MAZALOV, Research Director of the Institute of Applied Mathematical Research, Karelia Research Center of Russian Academy of Sciences, Russia
Riassunto
An authoritative and quantitative approach to modern game theory with applications from diverse areas including economics, political science, military science, and finance. Explores areas which are not covered in current game theory texts, including a thorough examination of zero-sum game.
