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 Handbook of Dynamic Game Theory written by Tamer Basar and published by . This book was released on 19?? with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Résumé : "This will be a two-part handbook on Dynamic Game Theory and part of the Springer Reference program. Part I will be on the fundamentals and theory of dynamic games. It will serve as a quick reference and a source of detailed exposure to topics in dynamic games for a broad community of researchers, educators, practitioners, and students. Each topic will be covered in 2-3 chapters with one introducing basic theory and the other one or two covering recent advances and/or special topics. Part II will be on applications in fields such as economics, management science, engineering, biology, and the social sciences."
Download or read book Non Zero sum Differential Games written by Moddy Te'eni and published by . This book was released on 1998 with total page 72 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 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 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 Differential Games written by Avner Friedman and published by Courier Corporation. This book was released on 2013-06-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.
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 Nonzero sum Differential Games with Biased Information Patterns and Different Intervals of Play written by Cheng-i Chen and published by . This book was released on 1971 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential games where the sum of payoffs of the players is not equal to zero are called nonzero-sum differential games. In the report the concepts of solutions are widened, the formulations of the problem are generalized and some computational considerations are also given. The concepts of solutions for nonzero-sum differential games depend on the rationality assumed for each player. Some of the solutions that have been considered so far are Nash solutions, noninferior solutions and minimax solutions, each of which has desirable characteristics. A new solution concept based on a policy suggested by von Stackelberg for economic competition is investigated. (Author).
Download or read book Nonzero sum Differential Games written by Edward Brice Tennis and published by . This book was released on 1969 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notes on Zero sum and Nonzero sum Differential Games written by Tamer Başar and published by . This book was released on 1975 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Class of Nonzero sum Differential Games and a Class of Differential Games with Two Pursuers Versus One Evader written by Michael Hugh Foley and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Games written by Joseph Lewin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential games theory is the most appropriate discipline for the modelling and analysis of real life conflict problems. The theory of differential games is here treated with an emphasis on the construction of solutions to actual problems with singular surfaces. The reader is provided with the knowledge necessary to put the theory of differential games into practice.
Download or read book The Theory and Application of Differential Games written by NATO Advanced Study Institute Staff and published by Springer Science & Business Media. This book was released on 1975-02-01 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ~irst international con~erence on differential games was held at Amherst, Massachusetts, in September 1969. A second meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new theoretical results and applications, especially in economic problems, were presented. The present volume consists o~ the lectures presented at a N.A.T.O. Advanced Study Institute on the "Theory and Applications of Differential Games" held at the University of Warwick, Coventry, England, from 27th August to 6th September, 1974. The main contributions during the first week consisted of a survey of two person zero sum differential games by L. D. Berkovitz and four integrated lectures by R. J. Elliott and N. J. Kalton, who have made important contributions to the concept of "value" of a differential game. Applications were featured during the second week and included tactical air games, pursuit and evasion problems, as well as computational aspects. A closing lecture with historical perspectives was given by Rufus Issacs, the recognised pioneer of differential games theory.
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.
Download or read book Multivariable Technological Systems written by D.P. Atherton and published by Elsevier. This book was released on 2014-06-28 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent results in the development and application of analysis and design techniques for the control of multivariable systems are discussed in this volume.
Download or read book Linear Feedback Strategies in Nonzero sum Differential Games written by Wolfgang Bernhard Elsner and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
