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 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 Asymptotic Analysis of Nash Equilibria in Nonzero sum Linear quadratic Differential Games written by Arie J. Weeren and published by . This book was released on 1994 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Open Loop Nash Equilibrium of N person Non zero Sum Linear quadratic Differential Games with Magnitude Restraints written by Ronald J. Stern and published by . This book was released on 1972 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book N person Differential Games Part 1 Duality finite Element Methods written by and published by . This book was released on 1983 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonzero sum Differential Games Concepts and Models written by Alan W. Starr and published by . This book was released on 1969 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general class of differential games, where the N players try to minimize different cost criteria by controlling inputs to a single dynamic system, is investigated as an extension of optimal control theory. Dropping the usual zero-sum assumption makes it possible to model a more realistic class of competitive situations where mutual interest is important. The nonzero-sum formulation has several interesting analytic and conceptual features not found in zero-sum differential games. It is no longer obvious what should be demanded of a 'solution, ' and three types of solution concepts are discussed: Nash equilibrium, minimax, and noninferior (or Pareto optimal) strategies. For one special case, the 'linear-quadratic' differential game, all of these solutions can be computed exactly by solving sets of coupled ordinary matrix differential equations. Some simple examples are solved, and series of more difficult but more realistic nonzero-sum differential game situations are presented (but not solved) for models of economic oligopoly, advertising policy, labor-management negotiations, and international trade. (Author).
Download or read book Asymptotic Analysis of Nash Equilibria in Nonzero sum Linear quadratic Differential Games written by A. J. T. M. Weeren and published by . This book was released on 1994 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Pursuit Evasion Differential Games written by Y. Yavin and published by Elsevier. This book was released on 2014-06-28 with total page 352 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'.
Download or read book Nonzero sum Differential Games written by Alan Wilbor Starr and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of differential games is extended to the situation where there are N players and where the game is nonzero-sum, i.e., the players wish to minimize different performance criteria. Dropping the usual zero-sum condition adds several interesting new features. It is no longer obvious what should be demanded of a 'solution, ' and three types of solutions are discussed: the 'Nash equilibrium, ' the 'minimax, ' and the 'noninferior set of strategies.' For one special case, the linear-quadratic game, all three of these solutions can be obtained by solving sets of ordinary matrix differential equations. To illustrate the differences between zero-sum and nonzero-sum games, the results are applied to a nonzero-sum version of a simple pursuit-evasion problem first considered by Ho, Bryson and Baron in 1965. 'Negotiated' solutions are found to exist which give better results for both players than the usual 'saddle-point' solution. To illustrate that the theory may find interesting applications in economic analysis, a problem is outlined involving the dividend policies of firms operating in an imperfectly competitive market. (Author).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 System Structure and Control 2004 written by Sabine Mondie and published by Elsevier. This book was released on 2005-05-11 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 A Concise Introduction written by Jiongmin Yong and published by World Scientific. This book was released on 2014-12-05 with total page 337 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.
