Theory of Positional Games with Applications in Economics (eBook)

Shawkat M. Hammoudeh, Iosif A. Krass (Autoren)

Karl Shell (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
240 Seiten
Elsevier Science (Verlag)
978-1-4832-5808-9 (ISBN)

Infos

The Theory of Positional Games with Applications in Economics deals with information and probabilistic extension of games in extensive forms, in normal forms, and to the existence of solutions of infinite games. The text also explains the application of existence of a solution to a von Neumann model with conflict interaction, and the theory of differential games based on Isaac's equations. The text describes in detail the definitions of a difference game, control sets of players, general strategies, optimal behavioral strategies. Isaac's approach to differential games is based primarily on the assumption of the sufficient smoothness of a Bellman's function. Bellman's function becomes smooth if control functions satisfy certain regularity conditions and smoothness conditions. Other approaches to differential games include the geometric properties of games and those of Avner Friedman and Nokolai Krasovsky. The computation of behavioral strategies in the Friedman approach is primarily based on Isaac's approach. Krasovky's approach is somewhat a generalization of both the geometrical approach and Friedman's approximation approach. The book is suitable for economists, statistician, mathematicians, students or professors of economics, business, and games theory.

Inhalt

Front Cover 1
The Theory of Positional Games: With Applications in Economics 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 12
Part I: GENERAL GAMES 14
Chapter 1. Games in Extensive and Normal Forms 16
1.1 Games in Extensive Form 17
1.2 Pure Strategies and the Normal Form 20
1.3 Solution of a Game 24
1.4 GAMES WITH COMPLETE INFORMATION 27
Chapter 2. Information Extension of Games 30
2.1 Some Properties of Nash Equilibrium 30
2.2 Information Extension of Games: The Germeir Approach 32
Chapter 3. Probabilistic Extension of Games 48
3.1 Definitions and Basic Properties 48
3.2 Finite Antagonistic Games via Linear Programming 54
Chapter 4. Infinite Games 68
4.1 Existence Theorem 68
4.2 Infinite Antagonistic Games in the von Neumann Models: An Example 74
Part II: DIFFERENCE GAMES 82
Chapter 5. Difference Games with Constant Control Sets 84
5.1 Strategies and Control Sets 84
5.2 Continuous Difference Games with Constant Control Sets 91
Chapter 6. Difference Games with Variable Control Sets 104
6.1 Continuous Difference Games with State-Dependent Control Sets 105
6.2 A Solution of the Difference Game: "War between One-Commodity Models" 112
Part III: DIFFERENTIAL GAMES 128
Chapter 7. Differential Games: Basic Definitions 130
7.1 Strategies and Solutions 131
7.2 Differential Equations with a Discontinuous Right-Hand Side 135
7.3 Strategies, Objective Functions, and 
139 
Chapter 8. Isaacs' Approach to Differential Games 144
8.1 Isaacs' Equations 145
8.2 Application of the Regression Equations to War between One-Commodity Models 159
8.3 Continuity and Differentiability of Bellman's Function 166
8.4 Existence of Solutions 172
Chapter 9. Other Approaches to Differential Games 176
9.1 The Geometric Approach with Application to War between One-Commodity Models 177
9.2 Friedman's Approach 192
9.3 Krasovsky's Approach 207
Bibliography 226
Index 230

Produkt-Details

• Erscheint lt. Verlag: 12.5.2014
• Sprache: englisch
• Themenwelt: Schulbuch / Wörterbuch ► Lexikon / Chroniken
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• ISBN-10: 1-4832-5808-4 / 1483258084
• ISBN-13: 978-1-4832-5808-9 / 9781483258089