The Theory of Positional Games with Applications in Economics

The Theory of Positional Games with Applications in Economics

1st Edition - January 28, 1981

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  • Authors: Iosif A. Krass, Shawkat M. Hammoudeh
  • eBook ISBN: 9781483258089

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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.

Table of Contents

  • Preface

    Part I General Games

    Chapter 1 Games in Extensive and Normal Forms

    1.1 Games in Extensive Form

    1.2 Pure Strategies and the Normal Form

    1.3 Solution of a Game

    1.4 Games with Complete Information

    Chapter 2 Information Extension of Games

    2.1 Some Properties of Nash Equilibrium

    2.2 Information Extension of Games: The Germeir Approach

    Chapter 3 Probabilistic Extension of Games

    3.1 Definitions and Basic Properties

    3.2 Finite Antagonistic Games via Linear Programming

    Chapter 4 Infinite Games

    4.1 Existence Theorem

    4.2 Infinite Antagonistic Games in the von Neumann Models: An Example

    Part II Difference Games

    Chapter 5 Difference Games with Constant Control Sets

    5.1 Strategies and Control Sets

    5.2 Continuous Difference Games with Constant Control Sets

    Chapter 6 Difference Games with Variable Control Sets

    6.1 Continuous Difference Games with State-Dependent Control Sets

    6.2 A Solution of the Difference Game: “War between One-Commodity Models”

    Part III Differential Games

    Chapter 7 Differential Games: Basic Definitions

    7.1 Strategies and Solutions

    7.2 Differential Equations with a Discontinuous Right-Hand Side

    7.3 Strategies, Objective Functions, and Bellman’s Function

    Chapter 8 Isaacs’ Approach to Differential Games

    8.1 Isaacs’ Equations

    8.2 Application of the Regression Equations to War between One-Commodity Models

    8.3 Continuity and Differentiability of Bellman’s Function

    8.4 Existence of Solutions

    Chapter 9 Other Approaches to Differential Games

    9.1 The Geometric Approach with Application to War between One-Commodity Models

    9.2 Friedman’s Approach

    9.3 Krasovsky’s Approach



Product details

  • No. of pages: 240
  • Language: English
  • Copyright: © Academic Press 1981
  • Published: January 28, 1981
  • Imprint: Academic Press
  • eBook ISBN: 9781483258089

About the Authors

Iosif A. Krass

Shawkat M. Hammoudeh

About the Editor

Karl Shell

Affiliations and Expertise

Cornell University

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