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Lq Dynamic Optimization And Differential Games
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Book Synopsis LQ Dynamic Optimization and Differential Games by : Jacob Engwerda
Download or read book LQ Dynamic Optimization and Differential Games written by Jacob Engwerda and published by John Wiley & Sons. This book was released on 2005-11-01 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis LQ Dynamic Optimization and Differential Games by : Jacob Engwerda
Download or read book LQ Dynamic Optimization and Differential Games written by Jacob Engwerda and published by John Wiley & Sons. This book was released on 2005-06-17 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamic Optimization and Differential Games by : Terry L. Friesz
Download or read book Dynamic Optimization and Differential Games written by Terry L. Friesz and published by Springer Science & Business Media. This book was released on 2010-08-20 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Games: A Concise Introduction by : Jiongmin Yong
Download or read book Differential Games: A Concise Introduction written by Jiongmin Yong and published by World Scientific. This book was released on 2014-12-05 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by : Rene Carmona
Download or read book Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications written by Rene Carmona and published by SIAM. This book was released on 2016-02-18 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic and Differential Games by : Martino Bardi
Download or read book Stochastic and Differential Games written by Martino Bardi and published by Springer Science & Business Media. This book was released on 1999-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lyapunov Functions in Differential Games by : Vladislav I Zhukovskiy
Download or read book Lyapunov Functions in Differential Games written by Vladislav I Zhukovskiy and published by CRC Press. This book was released on 2003-01-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient criteria, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear-quadratic multi-player differential games. Those criteria apply when the players formulate their strategies independently (non co-operative games) and use non-Nash equilibria or when the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). This text is useful for researchers, engineers and students of applied mathematics, control theory and the engineering sciences.
Book Synopsis Advances in Dynamic Games by : Michèle Breton
Download or read book Advances in Dynamic Games written by Michèle Breton and published by Springer Science & Business Media. This book was released on 2010-11-18 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction.
Book Synopsis Differential Games of Pursuit by : Leon A Petrosjan
Download or read book Differential Games of Pursuit written by Leon A Petrosjan and published by World Scientific. This book was released on 1993-09-30 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Advances in Dynamic Games and Their Applications by : Pierre Bernhard
Download or read book Advances in Dynamic Games and Their Applications written by Pierre Bernhard and published by Springer Science & Business Media. This book was released on 2009-04-20 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current advances in the theory of dynamic games and their applications in several disciplines. The selected contributions cover a variety of topics ranging from purely theoretical developments in game theory, to numerical analysis of various dynamic games, and then progressing to applications of dynamic games in economics, finance, and energy supply. A unified collection of state-of-the-art advances in theoretical and numerical analysis of dynamic games and their applications, the work is suitable for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.
Book Synopsis Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems by : Cheng-ke Zhang
Download or read book Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems written by Cheng-ke Zhang and published by Springer. This book was released on 2016-09-02 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the achievements of differential game research. This book can be used as a reference book for non-cooperative differential game study, for graduate students majored in economic management, science and engineering of institutions of higher learning.
Book Synopsis Reinforcement Learning and Approximate Dynamic Programming for Feedback Control by : Frank L. Lewis
Download or read book Reinforcement Learning and Approximate Dynamic Programming for Feedback Control written by Frank L. Lewis and published by John Wiley & Sons. This book was released on 2013-01-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reinforcement learning (RL) and adaptive dynamic programming (ADP) has been one of the most critical research fields in science and engineering for modern complex systems. This book describes the latest RL and ADP techniques for decision and control in human engineered systems, covering both single player decision and control and multi-player games. Edited by the pioneers of RL and ADP research, the book brings together ideas and methods from many fields and provides an important and timely guidance on controlling a wide variety of systems, such as robots, industrial processes, and economic decision-making.
Book Synopsis Pursuit-Evasion Differential Games by : Y. Yavin
Download or read book Pursuit-Evasion Differential Games written by Y. Yavin and published by Elsevier. This book was released on 2014-06-28 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty papers are devoted to the treatment of a wide spectrum of problems in the theory and applications of dynamic games with the emphasis on pursuit-evasion differential games. The problem of capturability is thoroughly investigated, also the problem of noise-corrupted (state) measurements. Attention is given to aerial combat problems and their attendant modelling issues, such as variable speed of the combatants, the three-dimensionality of physical space, and the combat problem, i.e. problems related to 'role determination'.
Book Synopsis Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory by : Timothy L. Molloy
Download or read book Inverse Optimal Control and Inverse Noncooperative Dynamic Game Theory written by Timothy L. Molloy and published by Springer Nature. This book was released on 2022-02-18 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Optimization Theory and Operations Research by : Michael Khachay
Download or read book Mathematical Optimization Theory and Operations Research written by Michael Khachay and published by Springer. This book was released on 2019-06-12 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019, held in Ekaterinburg, Russia, in July 2019. The 48 full papers presented in this volume were carefully reviewed and selected from 170 submissions. MOTOR 2019 is a successor of the well-known International and All-Russian conference series, which were organized in Ural, Siberia, and the Far East for a long time. The selected papers are organized in the following topical sections: mathematical programming; bi-level optimization; integer programming; combinatorial optimization; optimal control and approximation; data mining and computational geometry; games and mathematical economics.
Book Synopsis Differential Games and Applications by : Tamer Başar
Download or read book Differential Games and Applications written by Tamer Başar and published by . This book was released on 1989 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory and Applications of Dynamic Games by : Elena Parilina
Download or read book Theory and Applications of Dynamic Games written by Elena Parilina and published by Springer Nature. This book was released on 2022-11-23 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive overview of noncooperative and cooperative dynamic games involving uncertain parameter values, with the stochastic process being described by an event tree. Primarily intended for graduate students of economics, management science and engineering, the book is self-contained, as it defines and illustrates all relevant concepts originally introduced in static games before extending them to a dynamic framework. It subsequently addresses the sustainability of cooperative contracts over time and introduces a range of mechanisms to help avoid such agreements breaking down before reaching maturity. To illustrate the concepts discussed, the book provides various examples of how dynamic games played over event trees can be applied to environmental economics, management science, and engineering.
