The Theory of Positional Games, With Applications in Economics (ECONOMIC THEORY, ECONOMETRICS, AND MATHEMATICAL ECONOMICS)

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. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Pages xi-xii CHAPTER 1 - Games in Extensive and Normal Forms, Pages 3-16 CHAPTER 2 - Information Extension of Games, Pages 17-34 CHAPTER 3 - Probabilistic Extension of Games, Pages 35-53 CHAPTER 4 - Infinite Games, Pages 55-67 CHAPTER 5 - Difference Games with Constant Control Sets, Pages 71-90 CHAPTER 6 - Difference Games with Variable Control Sets, Pages 91-113 CHAPTER 7 - Differential Games: Basic Definitions, Pages 117-130 CHAPTER 8 - Isaacs' Approach to Differential Games, Pages 131-162 CHAPTER 9 - Other Approaches to Differential Games, Pages 163-212 Bibliography, Pages 213-215 Index, Pages 217-221 ECONOMIC THEORY, ECONOMETRICS, AND MATHEMATICAL ECONOMICS, Pages ibc1-ibc2 Iosif A. Krass, Shawkat M. Hammoudeh. Includes Index. Bibliography: P. 213-215.