Lq Dynamic Optimization And Differential Games

Author : Jacob Engwerda
Publisher : John Wiley & Sons
ISBN 13 : 0470015519
Total Pages : 510 pages
Book Rating : 4.13/5 ( download)

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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.

Author : Jacob Engwerda
Publisher : John Wiley & Sons
ISBN 13 : 9780470015247
Total Pages : 514 pages
Book Rating : 4.41/5 ( download)

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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.

Author : Terry L. Friesz
Publisher : Springer Science & Business Media
ISBN 13 : 0387727787
Total Pages : 509 pages
Book Rating : 4.83/5 ( download)

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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.

Author : Jiongmin Yong
Publisher : World Scientific
ISBN 13 : 9814596248
Total Pages : 336 pages
Book Rating : 4.44/5 ( download)

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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.

Author : Rene Carmona
Publisher : SIAM
ISBN 13 : 1611974240
Total Pages : 265 pages
Book Rating : 4.49/5 ( download)

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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.

Author : Martino Bardi
Publisher : Springer Science & Business Media
ISBN 13 : 9780817640293
Total Pages : 404 pages
Book Rating : 4.90/5 ( download)

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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.

Author : Vladislav I Zhukovskiy
Publisher : CRC Press
ISBN 13 : 9780415273411
Total Pages : 308 pages
Book Rating : 4.12/5 ( download)

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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.

Author : Michèle Breton
Publisher : Springer Science & Business Media
ISBN 13 : 0817680896
Total Pages : 581 pages
Book Rating : 4.93/5 ( download)

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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 581 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.

Author : Leon A Petrosjan
Publisher : World Scientific
ISBN 13 : 9814505552
Total Pages : 340 pages
Book Rating : 4.50/5 ( download)

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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

Author : Pierre Bernhard
Publisher : Springer Science & Business Media
ISBN 13 : 0817648348
Total Pages : 456 pages
Book Rating : 4.43/5 ( download)

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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.