Download or read book On Various Equilibrium Solutions for Linear Quadratic Noncooperative Games written by Xu Wang and published by . This book was released on 2007 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Game theory has been widely used to model decision making processes because it can capture the nature of multi-player problems: the determination of one player's control strategy is not only subject to the system state evolution but is also tightly coupled to the determination of the other players' strategies and vice versa. In this dissertation, we categorize linear quadratic (LQ) games into three groups: definite, singular and indefinite. For singular LQ games: 1) a new equilibrium concept: asymptotic [epsilon]-Nash equilibrium is proposed for a two-player nonzero-sum game where each player has a control-free cost functional quadratic in the system states over an infinite horizon and each player's control strategy is constrained to be continuous linear state feedback; 2) a group of algebraic equations of system coefficients is found whose solution can constitute the partial state feedback asymptotic [epsilon]-Nash equilibrium for the singular LQ games. Conditions on initial states and the parameter [epsilon] are provided such that the asymptotic [epsilon]-Nash equilibrium will be an [epsilon]-Nash equilibrium or a Nash equilibrium; 3) for a class of 2nd-order singular LQ games, the closed-form asymptotic [epsilon]-Nash equilibrium is explicitly found in terms of system coefficients. Robust equilibrium solutions for two-player asymmetric games with an additive uncertainty are studied: 1) regarding the uncertainty as the third player, a three-player non-cooperative nonzero-sum game is formed and each player's cost functional value resulting from the output feedback Nash equilibrium of this three-player game is not as conservative as his/her individual rationality; 2) regarding the coalition of the original two players as one player and the uncertainty as another player, a two-player non-cooperative nonzero-sum game is formed to find un-improvable robust a equilibrium for the original game. Inverse problems for indefinite games are investigated (for which weighting matrices in the cost functional such that the given linear state feedback control strategy can constitute a Nash equilibrium solution): 1) a necessary and sufficient condition for the inverse problem is provided using a group of algebraic equations linear in the variables and the weighting matrices; 2) the inverse problem for a class of 2nd-order two-player LQ game is thoroughly discussed.

Download or read book Dynamic Noncooperative Game Theory written by Tamer Basar and published by SIAM. This book was released on 1999-01-01 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent interest in biological games and mathematical finance make this classic 1982 text a necessity once again. Unlike other books in the field, this text provides an overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and simultaneously stresses the role of different information patterns. The first edition was fully revised in 1995, adding new topics such as randomized strategies, finite games with integrated decisions, and refinements of Nash equilibrium. Readers can now look forward to even more recent results in this unabridged, revised SIAM Classics edition. Topics covered include static and dynamic noncooperative game theory, with an emphasis on the interplay between dynamic information patterns and structural properties of several different types of equilibria; Nash and Stackelberg solution concepts; multi-act games; Braess paradox; differential games; the relationship between the existence of solutions of Riccati equations and the existence of Nash equilibrium solutions; and infinite-horizon differential games.

Download or read book Series Nash Solution of Two person Nonzero sum Linear quadratic Differential Games written by J. B Cruz (Jr) and published by . This book was released on 1970 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well-known that the Nash equilibrium solution of a two-person nonzero-sum linear differential game with a quadratic cost function can be expressed in terms of the solution of coupled generalized Riccati-type matrix differential equations. For high order games the numerical determination of the solution of the nonlinear coupled equations may be difficult or even not possible when the application dictates the use of small memory computers. In this paper a series solution is suggested by means of a parameter imbedding method. Instead of solving a high order Riccati matrix equation a lower order matrix Riccati equation corresponding to a zero-sum game is solved. In addition, lower order linear equations have to be solved. These solutions to lower order equations are the coefficients of the series solution for the nonzero-sum game. Cost functions corresponding to truncated solutions are compared with those for exact Nash equilibrium solutions. (Author).

Download or read book Dynamic Noncooperative Game Theory written by Tamer Basar and published by SIAM. This book was released on 1999-01-01 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent interest in biological games and mathematical finance make this classic 1982 text a necessity once again. Unlike other books in the field, this text provides an overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and simultaneously stresses the role of different information patterns. The first edition was fully revised in 1995, adding new topics such as randomized strategies, finite games with integrated decisions, and refinements of Nash equilibrium. Readers can now look forward to even more recent results in this unabridged, revised SIAM Classics edition. Topics covered include static and dynamic noncooperative game theory, with an emphasis on the interplay between dynamic information patterns and structural properties of several different types of equilibria; Nash and Stackelberg solution concepts; multi-act games; Braess paradox; differential games; the relationship between the existence of solutions of Riccati equations and the existence of Nash equilibrium solutions; and infinite-horizon differential games.

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.

Download or read book Differential Games in Economics and Management Science written by Engelbert Dockner and published by Cambridge University Press. This book was released on 2000-11-16 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Foundations of Game Theory written by Nicolai N. Vorob'ev and published by Birkhäuser. This book was released on 2012-12-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The English edition differs only slightly from the Russian original. The main struc tural difference is that all the material on the theory of finite noncooperative games has been collected in Chapter 2, with renumbering of the material of the remain ing chapters. New sections have been added in this chapter: devoted to general questions of equilibrium theory in nondegenerate games, subsections 3.9-3.17, by N.N. Vorob'ev, Jr.; and § 4, by A.G. Chernyakov; and § 5, by N.N. Vorob'ev, Jr., on the computational complexity of the process of finding equilibrium points in finite games. It should also be mentioned that subsections 3.12-3.14 in Chapter 1 were written by E.B. Yanovskaya especially for the Russian edition. The author regrets that the present edition does not reflect the important game-theoretical achievements presented in the splendid monographs by E. van Damme (on the refinement of equilibrium principles for finite games), as well as those by J.e. Harsanyi and R. Selten, and by W. Giith and B. Kalkofen (on equilibrium selection). When the Russian edition was being written, these direc tions in game theory had not yet attained their final form, which appeared only in quite recent monographs; the present author has had to resist the temptation of attempting to produce an elementary exposition of the new theories for the English edition; readers of this edition will find only brief mention of the new material.

Download or read book Mean Field Type Games for Engineers written by Julian Barreiro-Gomez and published by CRC Press. This book was released on 2021-11-18 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of this book comprise an appropriate background to start working and doing research on mean-field-type control and game theory. To make the exposition and explanation even easier, we first study the deterministic optimal control and differential linear-quadratic games. Then, we progressively add complexity step-by-step and little-by-little to the problem settings until we finally study and analyze mean-field-type control and game problems incorporating several stochastic processes, e.g., Brownian motions, Poisson jumps, and random coefficients. We go beyond the Nash equilibrium, which provides a solution for non- cooperative games, by analyzing other game-theoretical concepts such as the Berge, Stackelberg, adversarial/robust, and co-opetitive equilibria. For the mean-field-type game analysis, we provide several numerical examples using a Matlab-based user-friendly toolbox that is available for the free use to the readers of this book. We present several engineering applications in both continuous and discrete time. Among these applications we find the following: water distribution systems, micro-grid energy storage, stirred tank reactor, mechanism design for evolutionary dynamics, multi-level building evacuation problem, and the COVID-19 propagation control. Julian Barreiro-Gomez Hamidou Tembine With such a demand from engineering audiences, this book is very timely and provides a thorough study of mean-field-type game theory. The strenuous protagonist of this book is to bridge between the theoretical findings and engineering solutions. The book introduces the basics first, and then mathematical frameworks are elaborately explained. The engineering application examples are shown in detail, and the popular learning approaches are also investigated. Those advantageous characteristics will make this book a comprehensive handbook of many engineering fields for many years, and I will buy one when it gets published. Zhu Han

Download or read book Subgame Consistent Cooperation written by David W.K. Yeung and published by Springer. This book was released on 2016-09-23 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strategic behavior in the human and social world has been increasingly recognized in theory and practice. It is well known that non-cooperative behavior could lead to suboptimal or even highly undesirable outcomes. Cooperation suggests the possibility of obtaining socially optimal solutions and the calls for cooperation are prevalent in real-life problems. Dynamic cooperation cannot be sustainable if there is no guarantee that the agreed upon optimality principle at the beginning is maintained throughout the cooperation duration. It is due to the lack of this kind of guarantees that cooperative schemes fail to last till its end or even fail to get started. The property of subgame consistency in cooperative dynamic games and the corresponding solution mechanism resolve this “classic” problem in game theory. This book is a comprehensive treatise on subgame consistent dynamic cooperation covering the up-to-date state of the art analyses in this important topic. It sets out to provide the theory, solution techniques and applications of subgame consistent cooperation in a wide spectrum of paradigms for analysis which includes cooperative dynamic game models with stochastic state dynamics, with uncertain future payoffs, with asynchronous players’ horizons, with random cooperation duration, with control spaces switching and with transferable and nontransferable payoffs. The book would be a significant research reference text for researchers in game theory, economists, applied mathematicians, policy-makers, corporate decision-makers, and graduate students in applied mathematics, game theory, decision sciences, economics and management sciences.

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.

Download or read book Advances in Statistical Control Algebraic Systems Theory and Dynamic Systems Characteristics written by Chang-Hee Won and published by Springer Science & Business Media. This book was released on 2010-07-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. The book will be a useful reference for researchers and graduate students in systems and control, algebraic systems theory, and applied mathematics. Requiring only knowledge of undergraduate-level control and systems theory, the work may be used as a supplementary textbook in a graduate course on optimal control or algebraic systems theory.

Download or read book Frontiers of Dynamic Games written by Leon A. Petrosyan and published by Springer Nature. This book was released on 2022-03-09 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

Download or read book The Golden Rule of Ethics written by Vladislav I. Zhukovskiy and published by CRC Press. This book was released on 2021-04-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement called the Golden Rule of ethics (GR). This rule states "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread, and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. This book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book by the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: 1) a modification of N.N. Krasovskii’s mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; 2) the method of guiding control, proposed by N.N. Krasovskii; and 3) the Germier convolution of the payoff functions of different players. Additionally, this book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2 to 4. This book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications.

Download or read book Intelligent Robotics and Applications written by Huayong Yang and published by Springer Nature. This book was released on 2023-11-13 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 9-volume set LNAI 14267-14275 constitutes the proceedings of the 16th International Conference on Intelligent Robotics and Applications, ICIRA 2023, which took place in Hangzhou, China, during July 5–7, 2023. The 413 papers included in these proceedings were carefully reviewed and selected from 630 submissions. They were organized in topical sections as follows: Part I: Human-Centric Technologies for Seamless Human-Robot Collaboration; Multimodal Collaborative Perception and Fusion; Intelligent Robot Perception in Unknown Environments; Vision-Based Human Robot Interaction and Application. Part II: Vision-Based Human Robot Interaction and Application; Reliable AI on Machine Human Reactions; Wearable Sensors and Robots; Wearable Robots for Assistance, Augmentation and Rehabilitation of Human Movements; Perception and Manipulation of Dexterous Hand for Humanoid Robot. Part III: Perception and Manipulation of Dexterous Hand for Humanoid Robot; Medical Imaging for Biomedical Robotics; Advanced Underwater Robot Technologies; Innovative Design and Performance Evaluation of Robot Mechanisms; Evaluation of Wearable Robots for Assistance and Rehabilitation; 3D Printing Soft Robots. Part IV: 3D Printing Soft Robots; Dielectric Elastomer Actuators for Soft Robotics; Human-like Locomotion and Manipulation; Pattern Recognition and Machine Learning for Smart Robots. Part V: Pattern Recognition and Machine Learning for Smart Robots; Robotic Tactile Sensation, Perception, and Applications; Advanced Sensing and Control Technology for Human-Robot Interaction; Knowledge-Based Robot Decision-Making and Manipulation; Design and Control of Legged Robots. Part VI: Design and Control of Legged Robots; Robots in Tunnelling and Underground Space; Robotic Machining of Complex Components; Clinically Oriented Design in Robotic Surgery and Rehabilitation; Visual and Visual-Tactile Perception for Robotics. Part VII: Visual and Visual-Tactile Perception for Robotics; Perception, Interaction, and Control of Wearable Robots; Marine Robotics and Applications; Multi-Robot Systems for Real World Applications; Physical and Neurological Human-Robot Interaction. Part VIII: Physical and Neurological Human-Robot Interaction; Advanced Motion Control Technologies for Mobile Robots; Intelligent Inspection Robotics; Robotics in Sustainable Manufacturing for Carbon Neutrality; Innovative Design and Performance Evaluation of Robot Mechanisms. Part IX: Innovative Design and Performance Evaluation of Robot Mechanisms; Cutting-Edge Research in Robotics.

Download or read book Multiple Objective and Goal Programming written by Tadeusz Trzaskalik and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is dedicated to multi-objective methods in decision making. The first part which is devoted to theoretical aspects, covers a broad range of multi-objective methods such as multiple linear programming, vector optimisation, fuzzy goal programming, data envelopment analysis, game theory, and dynamic programming. The reader who is interested in practical applications, will find in the remaining parts a variety of approaches applied in numerous fields including production planning, logistics, marketing, and finance.

Download or read book Proceedings of 2023 7th Chinese Conference on Swarm Intelligence and Cooperative Control written by Guo-Ping Jiang and published by Springer Nature. This book was released on with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamic Games in Economics written by Josef Haunschmied and published by Springer. This book was released on 2014-07-08 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic game theory serves the purpose of including strategic interaction in decision making and is therefore often applied to economic problems. This book presents the state-of-the-art and directions for future research in dynamic game theory related to economics. It was initiated by contributors to the 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics and combines a selection of papers from the workshop with invited papers of high quality.