Mathematical Game Theory and Applications

Mathematical Game Theory and Applications

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 modern branches of 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.

Covering 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.

VLADIMIR MAZALOV, Research Director of the Institute of Applied Mathematical Research, Karelia Research Center of Russian Academy of Sciences, Russia

Mathematical Game Theory and Applications

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 modern branches of 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.

Covering 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.

Zusammenfassung
Mathematical Game Theory and Applications

Mathematical Game Theory and Applications

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 modern branches of 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.

Covering 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.

Inhalt

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 …