Game Theory: Strategies, Equilibria, and Theorems

GAME THEORY: STRATEGIES, EQUILIBRIA, AND THEOREMS......Page 4
CONTENTS......Page 6
PREFACE......Page 8
1.Introduction......Page 14
2.Introductory Concepts of Quantum Mechanics......Page 16
3.1.Introduction......Page 20
3.2.The Eisert Model......Page 21
3.3.Similar Models for 2×2 Quantum Games......Page 22
3.4.Quantum versus Classical Players......Page 24
3.5.New “Equilibria” in Two-Parameter Strategic Spaces......Page 25
3.6.Three-Parameter Strategic Spaces and the Loss of the New“Equilibria”......Page 26
3.7.Decoherence in Quantum Games......Page 27
3.8.Evolutionarily Stable Strategies......Page 30
4.1.General Considerations for Multi-player Quantum Games......Page 31
4.2.Quantum Public Goods Game......Page 32
4.3.QuantumMinorityGame......Page 34
5.1.Formalism for Repeated Quantum Games......Page 35
5.2.Iterated Quantum Games as Quantum Walks......Page 36
6.1.Introduction......Page 38
6.3.Quantum Market Games......Page 39
6.4.Quantum Monty Hall......Page 40
6.5.Quantum Games with Nonfactorizable Join tProbabilities......Page 41
7.Are Quantum Games “Quantum”?......Page 42
8.Physical Implementation of Quantum Games......Page 43
9.Conclusion......Page 44
References......Page 45
Abstract......Page 54
1. Introduction......Page 55
2.1. Game Theory......Page 56
2.2. Error Correction......Page 58
2.3. Reversible Logic......Page 66
2.4. Quantum Computing......Page 67
3. Reversible Game Theory (RGT)......Page 71
4. Reversible Error Correction of Games......Page 73
5. Multiple-valued (m-valued) Quantum Computing of Game Theory......Page 77
6. Conclusion and Future Work......Page 92
References......Page 93
Abstract......Page 96
2.1.2.Strategies......Page 97
2.1.4.EquilibriumNotions......Page 98
2.2.Evolutionary Game Theory......Page 99
2.2.2.TheReplicatorDynamic......Page 100
3.1.Physical System Representation......Page 102
3.2.1.Schrodinger & von Neumann Equations......Page 103
3.4.Quantum Entanglement......Page 104
3.5.Von Neumann Entropy & Quantum Information Theory......Page 105
4.Quantum Game Theory......Page 106
4.1.Quantum Strategies......Page 107
4.2.2.Evolutionary Prisoners Dilemma......Page 109
4.2.3.Quantum Prisoners Dilemma......Page 110
4.3.Marinatto & Weber’s Quantum Approach......Page 111
4.4.Quantum Evolutionary Game Theory......Page 112
5.1.Lax Form of the Replicator Dynamics & Its Properties......Page 114
5.2.Actual Relationships between Quantum Mechanics & Game Theory......Page 116
6.3.Games Analysis from Quantum Information Theory......Page 117
6.3.1.Quantum Games Entropy......Page 118
6.5. Econophysics: from Physics to Economics......Page 119
6.6.The Collective Welfare Principle......Page 120
6.7.1.Globalization:BigCommunities&StrongCurrencies......Page 121
6.7.2.TheEquilibriumProcesscalledGlobalization......Page 122
7.Conclusion......Page 123
References......Page 124
1.Introduction......Page 130
2.Mixed Equilibrium and Variational Inequality Problems......Page 132
3.Decomposable Mixed Equilibrium Problems......Page 140
4.Existence and Uniqueness Results......Page 143
Iterative Methods for Mixed Variational
Inequalities......Page 145
5.2.Regularized Gap Function Approach......Page 146
5.3.D-gap Function Approach......Page 148
5.4.Primal Gap Function Approach......Page 149
5.5.Combined Descentand Regularization Methods......Page 154
5.6.Combined Descent and Proximal Point Methods......Page 156
5.7.Modifications and Applications......Page 161
6.Combined Relaxation Method for Mixed Variational Inequalities......Page 164
References......Page 169
Abstract......Page 174
1. Introduction......Page 175
2.1. Strategies to Win......Page 176
2.2. Existence of Equilibrium......Page 178
2.3. Uniqueness of Equilibrium......Page 181
3. Geometric Study of the Equilibrium: The Weighted Case......Page 183
3.2. Uniqueness of Equilibrium......Page 184
4.1. Existence of Equilibrium......Page 185
4.2. Examples......Page 187
4.3. Maximum Number of Positions of Weak Equilibrium with PartiesChoosing Positions of Voters......Page 188
4.3.1. Examples......Page 190
5. Conclusion......Page 193
References......Page 194
Abstract......Page 196
2.Introduction......Page 197
2.1.ApplicationstotheGooreGame......Page 198
2.2.1.ContributionsoftheChapter......Page 199
3.Learning Automata and the Goore Game......Page 200
4.1.LearningAutomataandCyberneti......Page 201
4.2.History,LiteratureSourcesandApplicationsofLA......Page 202
4.3.TheLA-EnvironmentModel......Page 203
4.4.LearningCriteria......Page 204
4.6.VariableStructureLearningAutomata......Page 205
4.7.TheContinuousLinearReward-InactionScheme(LRI)......Page 208
4.8.RemarksontheAccuracy/RateofConvergence......Page 209
5.1. Modeling the LA Solutions to the GG......Page 210
5.2. Fundamental Convergence Properties of the Goore Game......Page 211
6.Continuous Goore Game with Adaptive d-ary Search......Page 212
6.2.Construction of the Learning Automata......Page 213
7. Convergence Properties of CGG–AdS......Page 215
8.1. Implementation of the CGG–AdS Strategy......Page 218
9.Conclusions......Page 222
References......Page 226
1.Introduction......Page 230
2.TheModel......Page 232
3.The Nash Equilibrium and Its Analysis......Page 234
3.1.The Impact of ICT Progress for Solving the Intra-brand Effect......Page 235
3.2.The Impact of ICT Progress for Solving the Inter-brand Effect......Page 236
Appendix......Page 239
References......Page 241
1.Introduction......Page 244
2.Cooperative Transferable Utility Games with Individual
Goals......Page 245
3. Finding Allocations by a Goal Programming Approach......Page 249
3.1.Min-Max Goal Programming Approach......Page 250
4.Conclusion......Page 252
References......Page 253
1. Introduction......Page 254
The Model......Page 257
Equilibrium......Page 259
3. Experimental Method and Design......Page 261
4. Test of the Equilibrium Solutions......Page 262
5. Cognitive Hierarchy Model......Page 269
Acknowledgement......Page 271
Appendix......Page 272
Summary......Page 277
References......Page 278
1. Introduction......Page 280
2.1. Capital Budgeting Practices......Page 281
2.2. Firm-Specific Conditions......Page 282
2.3. The Effectiveness of Sophisticated Capital Budgeting Practices......Page 284
2.4. Control Variables......Page 285
3.2.1. Sophisticated Capital Budgeting Practices......Page 286
3.2.2. Uncertainty......Page 287
3.2.4. Effectiveness......Page 289
3.2.5. Control Variables......Page 290
4.1. Statistical Analysis......Page 291
5. Conclusion......Page 296
References......Page 297
1. Introduction......Page 302
2. Preliminaries......Page 303
3. θ-β-I-Irresolute Functions......Page 304
References......Page 309
Abstract......Page 310
Introduction......Page 311
The Plant Growth Model......Page 312
Simulations with Isolated Plants......Page 313
Calculations on the Frequency Development of Plant Genotypes......Page 314
Isolated Plants......Page 315
Simulations on Competing Plants......Page 316
Calculations on the Frequency Development of Plant Genotypes......Page 317
Reintroduction of Plant Genotypes......Page 318
Conclusion......Page 319
1. Shape of the Model plant......Page 321
3. Leaf and Plant Photosynthetic Rates......Page 322
4. Carbon Balance and the Allocation Program......Page 323
5. The Seasonal Light Climate......Page 325
Appendix B. Invasion and Coexistence......Page 326
References......Page 327
Abstract......Page 332
1.Introduction......Page 333
2.Networks and Games......Page 334
3.Nash Equilibria......Page 339
4.Phase Transitions......Page 343
References......Page 347
Abstract......Page 350
2. Game Theory as a Tool for Describing Relationships andInteractions......Page 351
3.1. Multiple Decision Makers in Deregulated Electricity Market......Page 353
3.2. Game Theoretic Approach to Competitive Market Model......Page 355
3.3. Strategic Bidding Model of GENCO Based on Offer Stack......Page 357
3.4. Computerized Tool for Strategic Bidding Based on Game Theory......Page 361
3.5. MAS (Multi-agent System) Based Market Simulator......Page 363
4.1. SCADA System Introduction......Page 366
4.2. Cyber Security Problem in SCADA System......Page 367
4.3. Encryption Methods - Symmetric and Asymmetric Encryption Methods......Page 368
4.4. Encryption Method for SCADA Communication......Page 369
4.5. MAS1 Applied Key Distribution Process......Page 371
4.6.1. Nash Bargaining Solution......Page 374
4.6.2. Application of NBS to Relationship Model between Agents......Page 375
4.7. Block Matrix Model for Decision Making on Choosing Security Methods......Page 376
5. Conclusions......Page 379
References......Page 380
INDEX......Page 382