Mathematical game theory and applications / Vladimir Mazalov.

Format:

Book

Author/Creator:

Mazalov, V. V. (Vladimir Viktorovich), author.

Language:

English

Subjects (All):

Game theory.

Genre:

Electronic books.

Physical Description:

1 online resource (431 pages) : illustrations

Place of Publication:

West Sussex, England : John Wiley and Sons, Limited, 2014.

System Details:

text file

Summary:

An authoritative and quantitative approach to modern game theory with applications from economics, political science, military science and finance. Mathematical Game Theory and Applications combines both the theoretical and mathematical foundations of game theory with a series of complex applications along with topics presented in a logical progression to achieve a unified presentation of research results. This book covers topics such as two-person games in strategic form, zero-sum games, N-person non-cooperative games in strategic form, two-person games in extensive form, parlor and sport games, bargaining theory, best-choice games, co-operative games and dynamic games. Several classical models used in economics are presented which include Cournot, Bertrand, Hotelling and Stackelberg as well as coverage of modem branches or game theory such as negotiation models, potential games, parlor games and best choice games. Mathematical Game Theory and Applications: Presents a good balance of both theoretical foundations and complex applications of game theory. Features an in-depth analysis of parlor and sport games, networking games, and bargaining models. Provides fundamental results in new branches of game theory, best choice games, network games and dynamic games. Presents numerous examples and exercises along with detailed solutions at the end of each chapter. Is supported by an accompanying website featuring course slides and lecture content. Coveting a host of important topics, this book provides a research springboard for graduate students and a reference for researchers who might be working in the areas of applied mathematics, operations research, computer science or economical cybernetics. Book jacket.

Contents:

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 2x2 16

1.11 Games 2xn and mx2 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 Poly matrix 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 Gaines 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

5.1.1 Optimal Strategies 113

5.1.2 Some Features of Optimal Behavior in Poker 116

5.2 The Poker Model with Variable Bets 118

5.2.1 The Poker Model with Two Bets 118

5.2.2 The Poker Model with n Bets 122

5.2.3 The Asymptotic Properties of Strategies in the Poker Model with Variable Bets 127

5.3 Preference. A Game-Theoretic Model 129

5.3.1 Strategies and Payoff Function 130

5.3.2 Equilibrium in the Case of $$$ 132

5.3.3 Equilibrium in the Case of $$$ 134

5.3.4 Some Features of Optimal Behavior in Preference 136

5.4 The Preference Model with Cards Play 136

5.4.1 The Preference Model with Simultaneous Moves 137

5.4.2 The Preference Model with Sequential Moves 139

5.5 Twenty-One. A Game-Theoretic Model 145

5.5.1 Strategies and Payoff Functions 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

6.1.1 Cake Cutting 155

6.1.2 Principles of Fair Cake Cutting 157

6.1.3 Cake Cutting with Subjective Estimates by Players 158

6.1.4 Fair Equal Negotiations 160

6.1.5 Strategy-Proofness 161

6.1.6 Solution with the Absence of Envy 161

6.1.7 Sequential Negotiations 163

6.2 Negotiations of Time and Place of a Meeting 166

6.2.1 Sequential Negotiations of Two Players 166

6.2.2 Three Players 168

6.2.3 Sequential Negotiations. The General Case 170

6.3 Stochastic Design in the Cake Cutting Problem 171

6.3.1 The Cake Cutting Problem with Three Players 172

6.3.2 Negotiations of Three Players with Non-Uniform Distribution 176

6.3.3 Negotiations of n Players 178

6.3.4 Negotiations of n Players. Complete Consent 181

6.4 Models of Tournaments 182

6.4.1 A Game-Theoretic Model of Tournament Organization 182

6.4.2 Tournament for Two Projects with the Gaussian Distribution 184

6.4.3 The Correlation Effect 186

6.4.4 The Model of a Tournament with Three Players and Non-Zero Sum 187

6.5 Bargaining Models with Incomplete Information 190

6.5.1 Transactions with Incomplete Information 190

6.5.2 Honest Negotiations in Conclusion of Transactions 193

6.5.3 Transactions with Unequal Forces of Players 195

6.5.4 The "Offer-Counteroffer" Transaction Model 196

6.5.5 The Correlation Effect 197

6.5.6 Transactions with Non-Uniform Distribution of Reservation Prices 199

6.5.7 Transactions with Non-Linear Strategies 202

6.5.8 Transactions with Fixed Prices 207

6.5.9 Equilibrium Among n-Threshold Strategies 210

6.5.10 Two-Stage Transactions with Arbitrator 218

6.6 Reputation in Negotiations 221

6.6.1 The Notion of Consensus in Negotiations 221

6.6.2 The Matrix Form of Dynamics in the Reputation Model 222

6.6.3 Information Warfare 223

6.6.4 The Influence of Reputation in Arbitration Committee. Conventional Arbitration 224

6.6.5 The Influence of Reputation in Arbitration Committee, Final-Offer Arbitration 225

6.6.6 The Influence of Reputation on Tournament Results 226

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 T_N(G) Under N ≥ 3 237

7.4 Optimal Stopping Game with Random Walks 241

7.4.1 Spectra of Strategies: Some Properties 243

7.4.2 Equilibrium Construction 245

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

7.8.1 Solution in the Case of Three Players 265

7.8.2 Solution in the Case of m Players 268

7.9 Best Mutual Choice Game 269

7.9.1 The Two-Shot Model of Mutual Choice 270

7.9.2 The Multi-Shot Model of Mutual Choice 272

Exercises 276

8 Cooperative Games 278

Introduction 278

8.1 Equivalence of Cooperative Games 278

8.2 Imputations and Core 281

8.2.1 The Core of the Jazz Band Game 282

8.2.2 The Core of the Glove Market Game 283

8.2.3 The Core of the Scheduling Game 284

8.3 Balanced Games 285

8.3.1 The Balance Condition for Three-Player Games 286

8.4 The τ-Value of a Cooperative Game 286

8.4.1 The τ- Value of the Jazz Band Game 289

8.5 Nucleolus 289

8.5.1 The Nucleolus of the Road Construction Game 291

8.6 The Bankruptcy Game 293

8.7 The Shapley Vector 298

8.7.1 The Shapley Vector in the Road Construction Game 299

8.7.2 Shapley's Axioms for the Vector φ_ι(ν) 300

8.8 Voting Games. The Shapley-Shubik Power Index and the Banzhaf Power Index 302

8.8.1 The Shapley-Shubik Power Index for Influence Evaluation in the 14th Bundestag 305

8.8.2 The Banzhaf Power Index for Influence Evaluation in the 3rd State Duma 307

8.8.3 The Holler Power Index and the Deegan-Packel Power Index for Influence Evaluation in the National Diet (1998) 309

8.9 The Mutual Influence of Players. The Hoede-Bakker Index 309

Exercises 312

9 Network Games 314

Introduction 314

9.1 The KP-Model of Optimal Routing with Indivisible Traffic. The Price of Anarchy 315

9.2 Pure Strategy Equilibrium. Braess's Paradox 316

9.3 Completely Mixed Equilibrium in the Optimal Routing Problem with Inhomogeneous Users and Homogeneous Channels 319

9.4 Completely Mixed Equilibrium in the Optimal Routing Problem with Homogeneous Users and Inhomogeneous Channels 320

9.5 Completely Mixed Equilibrium: The General Case 322

9.6 The Price of Anarchy in the Model with Parallel Channels and Indivisible Traffic 324

9.7 The Price of Anarchy in the Optimal Routing Model with Linear Social Costs and Indivisible Traffic for an Arbitrary Network 328

9.8 The Mixed Price of Anarchy in the Optimal Routing Model with Linear Social Costs and Indivisible Traffic for an Arbitrary Network 332

9.9 The Price of Anarchy in the Optimal Routing Model with Maximal Social Costs and Indivisible Traffic for an Arbitrary Network 335

9.10 The Wardrop Optimal Routing Model with Divisible Traffic 337

9.11 The Optimal Routing Model with Parallel Channels. The Pigou Model. Braess's Paradox 340

9.12 Potential in the Optimal Routing Model with Indivisible Traffic for an Arbitrary Network 341

9.13 Social Costs in the Optimal Routing Model with Divisible Traffic for Convex Latency Functions 343

9.14 The Price of Anarchy in the Optimal Routing Model with Divisible Traffic for Linear Latency Functions 344

9.15 Potential in the Wardrop Model with Parallel Channels for Player-Specific Linear Latency Functions 346

9.16 The Price of Anarchy in an Arbitrary Network for Player-Specific Linear Latency Functions 349

Exercises 351

10 Dynamic Games 352

Introduction 352

10.1 Discrete-Time Dynamic Games 353

10.1.1 Nash Equilibrium in the Dynamic Game 353

10.1.2 Cooperative Equilibrium in the Dynamic Game 356

10.2 Some Solution Methods for Optimal Control Problems with One Player 358

10.2.1 The Hamilton Jacobi-Bellman Equation 358

10.2.2 Pontryagin's Maximum Principle 361

10.3 The Maximum Principle and the Bellman Equation in Discrete- and Continuous Time Games of N Players 368

10.4 The Linear-Quadratic Problem on Finite and infinite Horizons 375

10.5 Dynamic Games in Bioresource Management Problems. The Case of Finite Horizon 378

10.5.1 Nash-Optimal Solution 379

10.5.2 Stackelberg-Optimal Solution 381

10.6 Dynamic Games in Bioresource Management Problems. The Case of Infinite Horizon 383

10.6.1 Nash-Optimal Solution 383

10.6.2 Stackelberg-Optimal Solution 385

10.7 Time-Consistent Imputation Distribution Procedure 388

10.7.1 Characteristic Function Construction and Imputation Distribution Procedure 390

10.7.2 Fish Wars. Model without Information 393

10.7.3 The Shapley Vector and Imputation Distribution Procedure 398

10.7.4 The Model with Informed Players 399

Exercises 402.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Local Notes:

Electronic reproduction. Palo Alto, Calif. : ebrary, 2014. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.

Other Format:

Print version: Mazalov, V. V. (Vladimir Viktorovich) Mathematical game theory and applications.

ISBN:

9781118899649

OCLC:

880672220

Access Restriction:

Restricted for use by site license.