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Dynamic Optimization And Differential Games

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Lq Dynamic Optimization And Differential Games

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Author : Jacob Engwerda
language : en
Publisher: John Wiley & Sons
Release Date : 2005-06-17

Lq Dynamic Optimization And Differential Games written by Jacob Engwerda and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-17 with Business & Economics categories.

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

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Author : Jacob Engwerda
language : en
Publisher: John Wiley & Sons
Release Date : 2005-11-01

Dynamic Optimization And Differential Games

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Author : Terry L. Friesz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-20

Dynamic Optimization And Differential Games written by Terry L. Friesz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-20 with Business & Economics categories.

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.

Differential Games In Industrial Economics

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Author : Luca Lambertini
language : en
Publisher: Cambridge University Press
Release Date : 2018-04-26

Differential Games In Industrial Economics written by Luca Lambertini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Business & Economics categories.

Game theory has revolutionised our understanding of industrial organisation and the traditional theory of the firm. Despite these advances, industrial economists have tended to rely on a restricted set of tools from game theory, focusing on static and repeated games to analyse firm structure and behaviour. Luca Lambertini, a leading expert on the application of differential game theory to economics, argues that many dynamic phenomena in industrial organisation (such as monopoly, oligopoly, advertising, R&D races) can be better understood and analysed through the use of differential games. After illustrating the basic elements of the theory, Lambertini guides the reader through the main models, spanning from optimal control problems describing the behaviour of a monopolist through to oligopoly games in which firms' strategies include prices, quantities and investments. This approach will be of great value to students and researchers in economics and those interested in advanced applications of game theory.

Games And Dynamic Games

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Author : Alain Haurie
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-03-23

Games And Dynamic Games written by Alain Haurie and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-23 with Mathematics categories.

Dynamic games arise between players (individuals, firms, countries, animals, etc.) when the strategic interactions among them recur over time and decisions made during one period affect both current and future payoffs. Dynamic games provide conceptually rich paradigms and tools to deal with these situations.This volume provides a uniform approach to game theory and illustrates it with present-day applications to economics and management, including environmental, with the emphasis on dynamic games.At the end of each chapter a case study called game engineering (GE) is provided, to help readers understand how problems of high social priority, such as environmental negotiations, exploitation of common resources, can be modeled as games and how solutions can be engineered.

Differential Games Of Pursuit

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Author : Leon A Petrosyan
language : en
Publisher: World Scientific
Release Date : 1993-09-30

Differential Games Of Pursuit written by Leon A Petrosyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-30 with Mathematics categories.

The classical optimal control theory deals with the determination of an optimal control that optimizes the criterion subjects to the dynamic constraint expressing the evolution of the system state under the influence of control variables. If this is extended to the case of multiple controllers (also called players) with different and sometimes conflicting optimization criteria (payoff function) it is possible to begin to explore differential games. Zero-sum differential games, also called differential games of pursuit, constitute the most developed part of differential games and are rigorously investigated. In this book, the full theory of differential games of pursuit with complete and partial information is developed. Numerous concrete pursuit-evasion games are solved (”life-line” games, simple pursuit games, etc.), and new time-consistent optimality principles in the n-person differential game theory are introduced and investigated.

Stochastic And Differential Games

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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06

Stochastic And Differential Games written by Martino Bardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06 with Business & Economics categories.

The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.

Differential Games

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Author : Rufus Isaacs
language : en
Publisher: Courier Corporation
Release Date : 1999-01-01

Differential Games written by Rufus Isaacs and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.

One of the definitive works in game theory, this volume takes an original and expert look at conflict solutions. Drawing on game theory, the calculus of variations, and control theory, the author solves an amazing array of problems relating to military situations, pursuit and evasion tactics, athletic contests, and many more. Clearly detailed examples; numerous calculations. 1965 edition.

Differential Games A Concise Introduction

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Author : Jiongmin Yong
language : en
Publisher: World Scientific
Release Date : 2014-12-05

Differential Games A Concise Introduction written by Jiongmin Yong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Mathematics categories.

This book uses a small volume to present the most basic results for deterministic two-person differential games. The presentation begins with optimization of a single function, followed by a basic theory for two-person games. For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games.The book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. Researchers in some other related areas, such as engineering, social science, etc. will also find the book useful.

Differential Games In Economics And Management Science

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Author : Engelbert Dockner
language : en
Publisher: Cambridge University Press
Release Date : 2000-11-16

Differential Games In Economics And Management Science written by Engelbert Dockner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-16 with Business & Economics categories.

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.

Dynamic Optimization And Differential Games

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