Download or read book Cooperative Stochastic Differential Games written by David W.K. Yeung and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
Download or read book Cooperative Stochastic Differential Games written by David W.K. Yeung and published by Springer. This book was released on 2008-11-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
Download or read book Stochastic Differential Games Theory and Applications written by Kandethody M. Ramachandran and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.
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 196 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.
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 Monitoring Cooperative Equilibria in a Stochastic Differential Game written by Alain Haurie and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.
Download or read book Stochastic and Differential Games written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 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.
Download or read book Cooperative and Non Cooperative Many Players Differential Games written by George Leitmann and published by Springer. This book was released on 2014-05-04 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Trigger Strategy Equilibriums in Stochastic Differential Games with Information Time Lags written by Tao Yao and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the current literature of differential games, most studies formulate optimal strategies in feedback (Markovian) equilibriums and ignore repeated interactions among players. In many real-world settings, however, the competitors' action history may have impacts on a firm's decisions. This paper considers the production strategies for several competing firms in an oligopolistic industry. A firm's profit is determined by a continuous-time stochastic demand shock process together with the production strategies of all firms in the industry. A firm's decision is only observable by other firms after an information time lag, induced by the production lead time. We study a history-dependent trigger strategy, whereby firms adopt the cooperative strategy until a firm fails to do so, and thereafter punish the deviating firm by applying the noncooperative equilibrium. We show that, as long as the information time lag is less than a threshold, the trigger strategy is both a Nash equilibrium and a Pareto optimum. We obtain the analytical solutions to the threshold and investigate how the threshold is affected by market growth rate, market volatility, the number of competitors in the industry, and the risk-free rate. Moreover, we investigate the repeated games in a continuous-time setting and provide a tractable approach to derive the trigger-type repeated equilibrium in a Nash-Cournot framework. While the derivation of equilibrium strategies in a stochastic continuous-time setting can be quite challenging, we obtain a solution that is not only analytically simple but also practically applicable.
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 Stochastic Game Strategies and their Applications written by Bor-Sen Chen and published by CRC Press. This book was released on 2019-07-31 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.
Download or read book Cooperative and Non Cooperative Many Players Differential Games written by George Leitmann and published by . This book was released on 2014-09-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Optimal Control Theory written by Suresh P. Sethi and published by Taylor & Francis US. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.
Download or read book Stochastic Dynamics written by Hans Crauel and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.
Download or read book Advances in Dynamic Game Theory written by Steffen Jorgensen and published by Springer Science & Business Media. This book was released on 2007-04-13 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters include stochastic and differential games; dynamic games and their applications in various areas, such as ecology and economics; pursuit-evasion games; and evolutionary game theory and applications. The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.
Download or read book Essays on Pareto Optimality in Cooperative Games written by Yaning Lin and published by Springer Nature. This book was released on 2022-09-21 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on Pareto optimality in cooperative games. Most of the existing works focus on the Pareto optimality of deterministic continuous-time systems or for the regular convex LQ case. To expand on the available literature, we explore the existence conditions of Pareto solutions in stochastic differential game for more general cases. In addition, the LQ Pareto game for stochastic singular systems, Pareto-based guaranteed cost control for uncertain mean-field stochastic systems, and the existence conditions of Pareto solutions in cooperative difference game are also studied in detail. Addressing Pareto optimality for more general cases and wider systems is one of the major features of the book, making it particularly suitable for readers who are interested in multi-objective optimal control. Accordingly, it offers a valuable asset for researchers, engineers, and graduate students in the fields of control theory and control engineering, economics, management science, mathematics, etc.
