Dynamic Optimization And Differential Games
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LQ Dynamic Optimization and Differential Games
Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.
LQ Dynamic Optimization and Differential Games
Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.
Dynamic Optimization and Differential Games
Author: Terry L. Friesz
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-08-20
Dynamic Optimization and Differential Games has been written to address the increasing number of Operations Research and Management Science problems that involve the explicit consideration of time and of gaming among multiple agents. With end-of-chapter exercises throughout, it is a book that can be used both as a reference and as a textbook. It will be useful as a guide to engineers, operations researchers, applied mathematicians and social scientists whose work involves both the theoretical and computational aspects of dynamic optimization and differential games. Included throughout the text are detailed explanations of several original dynamic and game-theoretic mathematical models which are of particular relevance in today’s technologically-driven-global economy: revenue management, oligopoly pricing, production planning, supply chain management, dynamic traffic assignment and dynamic congestion pricing. The book emphasizes deterministic theory, computational tools and applications associated with the study of dynamic optimization and competition in continuous time. It develops the key results of deterministic, continuous time, optimal control theory from both the classical calculus of variations perspective and the more modern approach of infinite dimensional mathematical programming. These results are then generalized for the analysis of differential variational inequalities arising in dynamic game theory for open loop environments. Algorithms covered include steepest descent in Hilbert space, gradient projection in Hilbert space, fixed point methods, and gap function methods.