Nonzero Sum Differential Games Concepts And Models
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Nonzero Sum Differential Games Concepts And Models
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Author : Alan W. Starr
language : en
Publisher:
Release Date : 1969
Nonzero Sum Differential Games Concepts And Models written by Alan W. Starr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
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).
Nonzero Sum Differential Games With Biased Information Patterns And Different Intervals Of Play
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Author : Cheng-i Chen
language : en
Publisher:
Release Date : 1971
Nonzero Sum Differential Games With Biased Information Patterns And Different Intervals Of Play written by Cheng-i Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Game theory categories.
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).
Non Zero Sum Differential Games
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Author : Moddy Te'eni
language : en
Publisher:
Release Date : 1998
Non Zero Sum Differential Games written by Moddy Te'eni and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Dynamic Noncooperative Game Theory
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Author : Tamer Basar
language : en
Publisher: SIAM
Release Date : 1999-01-01
Dynamic Noncooperative Game Theory written by Tamer Basar and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
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.
Nonzero Sum Differential Games
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Author : Alan Wilbor Starr
language : en
Publisher:
Release Date : 1968
Nonzero Sum Differential Games written by Alan Wilbor Starr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
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).
Stochastic And Differential Games
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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic And Differential Games written by Martino Bardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Some Theoretical Aspects Of Nonzero Sum Differential Games And Applications To Combat Problems
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Author :
language : en
Publisher:
Release Date : 1971
Some Theoretical Aspects Of Nonzero Sum Differential Games And Applications To Combat Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
The theory of nonzero sum differential games (NZSDG) is extended for a class of problems in which the nonlinear system equations have bounded control variables appearing linearly. For terminal cost functions this class of problems is shown to exhibit 'bang-bang' type control laws with the possibility of singular controls. A condition is derived to test for continuity of the influence functions when controls switch from a nonsingular to a singular control on singular surfaces. Two generalized forms of the transversality conditions are derived for NZSDG theory extending results of Dreyfus and Isaacs. NZSDG theory is shown to be useful in modeling combat problems in which the goals of the players are not diametrically opposed. A two player and three player penetrator-interceptor problem are presented as a NZSDG. Numerical solutions for a totally singular problem are carried out to illustrate application and a typical solution.
Notes On Zero Sum And Nonzero Sum Differential Games
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Author : Tamer Başar
language : en
Publisher:
Release Date : 1975
Notes On Zero Sum And Nonzero Sum Differential Games written by Tamer Başar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Differential games categories.
Nonzero Sum Differential Games
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Author : Edward Brice Tennis
language : en
Publisher:
Release Date : 1969
Nonzero Sum Differential Games written by Edward Brice Tennis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Game theory categories.
On Some Further Properties Of Nonzero Sum Differential Games
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Author : Alan Wilbor Starr
language : en
Publisher:
Release Date : 1968
On Some Further Properties Of Nonzero Sum Differential Games written by Alan Wilbor Starr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Differential games categories.
The general nonzero-sum differential game has N players, each controlling a different set of inputs to a single nonlinear dynamic system and each trying to minimize a different performance criterion. Several interesting new phenomena arise in these general games which are absent in the two best-known special cases (the optimal control problem and the two person zero-sum differential game). This paper considers some of the difficulties which arise in attempting to generalize ideas which are well-known in optimal control theory, such as the 'principle of optimality' and the relation between 'open-loop' and 'closed-loop' controls. Two types of 'solutions' are discussed: the 'Nash equilibrium' and the 'noninferior set.' Some simple multistage discrete (bimatrix) games are used to illustrate phenomena which also arise in the continuous formulation. (Author).