Game Theory and Its Applications (eBook)

Preface 5
Contents 7
List of Figures 10
List of Tables 12
1 Introduction 14
Part I Noncooperative Games 17
2 Discrete Static Games 18
2.1 Examples of Two-Person Finite Games 18
2.2 General Description of Two-Person Finite Games 25
2.3 N-person Finite Games 30
3 Continuous Static Games 31
3.1 Examples of Two-Person Continuous Games 32
3.2 Examples of N-Person Continuous Games 51
4 Relation to Other Mathematical Problems 58
4.1 Nonlinear Optimization 58
4.2 Fixed Point Problems 59
5 Existence of Equilibria 62
5.1 General Existence Conditions 62
5.2 Bimatrix and Matrix Games 66
5.3 Mixed Extensions of N-person Finite Games 70
5.4 Multiproduct Oligopolies 71
6 Computation of Equilibria 74
6.1 Application of the Kuhn--Tucker Conditions 74
6.2 Reduction to an Optimization Problem 77
6.3 Solution of Bimatrix Games 79
6.4 Solution of Matrix Games 83
6.5 Solution of Oligopolies 86
7 Special Matrix Games 89
7.1 Matrix with Identical Elements 89
7.2 The Case of Diagonal Matrix 89
7.3 Symmetric Matrix Games 91
7.4 Relation Between Matrix Games and Linear Programming 92
7.5 Method of Fictitious Play 97
7.6 Method of von Neumann 100
8 Uniqueness of Equilibria 105
9 Repeated and Dynamic Games 112
9.1 Leader-Follower Games 112
9.2 Dynamic Games with Simultaneous Moves 117
9.3 Dynamic Games with Sequential Moves 122
9.4 Extensive Forms of Dynamic Games 130
9.5 Subgames and Subgame-Perfect Nash Equilibria 132
10 Games Under Uncertainty 134
10.1 Static Bayesian Games 138
10.2 Dynamic Bayesian Games 141
Part II Cooperative Games 147
11 Solutions Based on Characteristic Functions 148
11.1 The Core 155
11.2 Stable Sets 160
11.3 The Nucleolus 161
11.4 The Shapley Values 165
11.5 The Kernel and the Bargaining Set 169
12 Conflict Resolution 174
12.1 The Nash Bargaining Solution 176
12.2 Alternative Solution Concepts 180
12.3 N-person Conflicts 187
13 Multiobjective Optimization 189
13.1 Lexicographic Method 192
13.2 The ?-constraint Method 194
13.3 The Weighting Method 195
13.4 Distance-Based Methods 198
13.5 Direction-Based Methods 200
14 Social Choice 203
14.1 Methods with Symmetric Players 203
14.2 Methods with Powers of Players 207
15 Case Studies and Applications 212
15.1 A Salesman's Dilemma 212
15.2 Oligopoly in Water Management 216
15.3 A Forestry Management Problem 217
15.4 International Fishing 219
15.5 A Water Distribution Problem 222
15.6 Control in Oligopolies 226
15.7 Effect of Information Lag in Oligopoly 229
Appendix A Vector and Matrix Norms 233
Appendix B Convexity, Concavity 237
Appendix C Optimum Conditions 240
Appendix D Fixed Point Theorems 243
Appendix E Monotonic Mappings 247
Appendix F Duality in Linear Programming 250
Appendix G Multiobjective Optimization 252
Appendix H Stability and Controllability 255
References 259
Index 262