Lq 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 : 2005-11-01
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 2005-11-01 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.
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.
This book has been written to address the increasing number of Operations Research and Management Science problems (that is, applications) that involve the explicit consideration of time and of gaming among multiple agents. It is a book that will be used both as a textbook and as a reference and guide by those whose work involves the theoretical aspects of dynamic optimization and differential games.
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.
Lectures On Bsdes Stochastic Control And Stochastic Differential Games With Financial Applications
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Author : Rene Carmona
language : en
Publisher: SIAM
Release Date : 2016-02-18
Lectures On Bsdes Stochastic Control And Stochastic Differential Games With Financial Applications written by Rene Carmona and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-18 with Mathematics categories.
The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
Differential Games
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Author : Jiongmin Yong
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2015
Differential Games written by Jiongmin Yong and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Business & Economics 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.
Lyapunov Functions In Differential Games
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Author : Vladislav I Zhukovskiy
language : en
Publisher: CRC Press
Release Date : 2003-01-16
Lyapunov Functions In Differential Games written by Vladislav I Zhukovskiy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-16 with Mathematics categories.
A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theor
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 Mathematics 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 Of Pursuit
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Author : Leon A Petrosjan
language : en
Publisher: World Scientific
Release Date : 1993-09-30
Differential Games Of Pursuit written by Leon A Petrosjan 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. Contents:PreliminariesDefinition of Differential Game of Pursuit and Existence Theorem of Equilibrium PointsClass of Pursuit-Evasion Games with Optimal Open-Loop Strategy for EvaderExamples of Differential Games of Pursuit“Life Line” Game of PursuitDifferential Games with Incomplete InformationNoncooperative Differential GamesCooperative Differential Games with Side PaymentsNew Optimality Principles in n-Person Differential Games Readership: Postgraduates and researchers in applied mathematics. keywords:Pursuier;Evader;Saddle Point;Invariant Center of Pursuit;Value Function;Bellmann-Isaaks Equation;Time Optimal Pursuit Game;Time-Consistency;Optimal Strategy;Lifeline Game
Differential Games And Applications
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Author : Tamer Başar
language : en
Publisher:
Release Date : 1989
Differential Games And Applications written by Tamer Başar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Control theory categories.
This volume contains fifteen articles on the topic of differential and dynamic games, focusing on both theory and applications. It covers a variety of areas and presents recent developments on topics of current interest. It should be useful to researchers in differential and dynamic games, systems and control, operations research and mathematical economics.
Inverse Optimal Control And Inverse Noncooperative Dynamic Game Theory
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Author : Timothy L. Molloy
language : en
Publisher: Springer Nature
Release Date : 2022-02-18
Inverse Optimal Control And Inverse Noncooperative Dynamic Game Theory written by Timothy L. Molloy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Mathematics categories.
This book presents a novel unified treatment of inverse problems in optimal control and noncooperative dynamic game theory. It provides readers with fundamental tools for the development of practical algorithms to solve inverse problems in control, robotics, biology, and economics. The treatment involves the application of Pontryagin's minimum principle to a variety of inverse problems and proposes algorithms founded on the elegance of dynamic optimization theory. There is a balanced emphasis between fundamental theoretical questions and practical matters. The text begins by providing an introduction and background to its topics. It then discusses discrete-time and continuous-time inverse optimal control. The focus moves on to differential and dynamic games and the book is completed by consideration of relevant applications. The algorithms and theoretical results developed in Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory provide new insights into information requirements for solving inverse problems, including the structure, quantity, and types of state and control data. These insights have significant practical consequences in the design of technologies seeking to exploit inverse techniques such as collaborative robots, driver-assistance technologies, and autonomous systems. The book will therefore be of interest to researchers, engineers, and postgraduate students in several disciplines within the area of control and robotics.