The Existence of Value in Differential Games PDF Download
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Author: Robert James Elliott
Publisher: American Mathematical Soc.
ISBN: 0821818260
Category : Control theory
Languages : en
Pages : 75
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Book Description
In the manner described in the introduction we show the existence of value for all two person, zero-sum differential games of prescribed duration. Using the concept of relaxed controls from control theory we relate the approaches to differential games of A. Friedman and W. Fleming. We show that if the 'Isaacs' condition' is satisfied then the game has a value in the sense of Friedman. Over the relaxed controls Isaacs' condition is always satisfied and so the game always has a value in this setting. We do not need Friedman's hypothesis that the two sets of control variables appear separated in the dynamical equations and payoff. The introduction of probabilistic ideas into differential games by relaxed controls thus gives a value, as the introduction of mixed strategies by von Neumann does for two person zero-sum matrix games.
Author: Robert James Elliott
Publisher: American Mathematical Soc.
ISBN: 0821818260
Category : Control theory
Languages : en
Pages : 75
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Book Description
In the manner described in the introduction we show the existence of value for all two person, zero-sum differential games of prescribed duration. Using the concept of relaxed controls from control theory we relate the approaches to differential games of A. Friedman and W. Fleming. We show that if the 'Isaacs' condition' is satisfied then the game has a value in the sense of Friedman. Over the relaxed controls Isaacs' condition is always satisfied and so the game always has a value in this setting. We do not need Friedman's hypothesis that the two sets of control variables appear separated in the dynamical equations and payoff. The introduction of probabilistic ideas into differential games by relaxed controls thus gives a value, as the introduction of mixed strategies by von Neumann does for two person zero-sum matrix games.
Author: Tamer Basar
Publisher:
ISBN: 9783319273358
Category : Differential games
Languages : en
Pages :
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Book Description
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."
Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486153274
Category : Mathematics
Languages : en
Pages : 372
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Book Description
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.
Author: NATO Advanced Study Institute Staff
Publisher: Springer Science & Business Media
ISBN: 9789027705815
Category : Mathematics
Languages : en
Pages : 334
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Book Description
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.
Author: Michèle Breton
Publisher: Springer Science & Business Media
ISBN: 0817680896
Category : Mathematics
Languages : en
Pages : 581
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Book Description
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: Steffen Jorgensen
Publisher: Springer Science & Business Media
ISBN: 0817645535
Category : Mathematics
Languages : en
Pages : 718
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Book Description
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.
Author: Martino Bardi
Publisher: Springer Science & Business Media
ISBN: 1461215927
Category : Mathematics
Languages : en
Pages : 388
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Book Description
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: Y. Yavin
Publisher: Elsevier
ISBN: 1483295931
Category : Mathematics
Languages : en
Pages : 352
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Book Description
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'.
Author: Kandethody M. Ramachandran
Publisher: Springer Science & Business Media
ISBN: 9491216473
Category : Mathematics
Languages : en
Pages : 253
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Book Description
The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.
Author: Leon A Petrosjan
Publisher: World Scientific
ISBN: 9814505552
Category : Mathematics
Languages : en
Pages : 340
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Book Description
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
