Krass / Hammoudeh / Shell The Theory of Positional Games with Applications in Economics

1. Auflage 2014
ISBN: 978-1-4832-5808-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 240 Seiten, Web PDF

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.

Autoren/Hrsg.

Krass, Iosif A.

Hammoudeh, Shawkat M.

Shell, Karl

Inhaltsverzeichnis

1;Front Cover;1
2;The Theory of Positional Games: With Applications in Economics;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;12
7;Part I: GENERAL GAMES;14
7.1;Chapter 1. Games in Extensive and Normal Forms;16
7.1.1;1.1 Games in Extensive Form;17
7.1.2;1.2 Pure Strategies and the Normal Form;20
7.1.3;1.3 Solution of a Game;24
7.1.4;1.4 GAMES WITH COMPLETE INFORMATION;27
7.2;Chapter 2. Information Extension of Games;30
7.2.1;2.1 Some Properties of Nash Equilibrium;30
7.2.2;2.2 Information Extension of Games: The Germeir Approach;32
7.3;Chapter 3. Probabilistic Extension of Games;48
7.3.1;3.1 Definitions and Basic Properties;48
7.3.2;3.2 Finite Antagonistic Games via Linear Programming;54
7.4;Chapter 4. Infinite Games;68
7.4.1;4.1 Existence Theorem;68
7.4.2;4.2 Infinite Antagonistic Games in the von Neumann Models: An Example;74
8;Part II: DIFFERENCE GAMES;82
8.1;Chapter 5. Difference Games with Constant Control Sets;84
8.1.1;5.1 Strategies and Control Sets;84
8.1.2;5.2 Continuous Difference Games with Constant Control Sets;91
8.2;Chapter 6. Difference Games with Variable Control Sets;104
8.2.1;6.1 Continuous Difference Games with State-Dependent Control Sets;105
8.2.2;6.2 A Solution of the Difference Game: "War between One-Commodity Models";112
9;Part III: DIFFERENTIAL GAMES;128
9.1;Chapter 7. Differential Games: Basic Definitions;130
9.1.1;7.1 Strategies and Solutions;131
9.1.2;7.2 Differential Equations with a Discontinuous Right-Hand Side;135
9.1.3;7.3 Strategies, Objective Functions, and
Bellman's Function;139
9.2;Chapter 8. Isaacs' Approach to Differential Games;144
9.2.1;8.1 Isaacs' Equations;145
9.2.2;8.2 Application of the Regression Equations to War between One-Commodity Models;159
9.2.3;8.3 Continuity and Differentiability of Bellman's Function;166
9.2.4;8.4 Existence of Solutions;172
9.3;Chapter 9. Other Approaches to Differential Games;176
9.3.1;9.1 The Geometric Approach with Application to War between One-Commodity Models;177
9.3.2;9.2 Friedman's Approach;192
9.3.3;9.3 Krasovsky's Approach;207
10;Bibliography;226
11;Index;230