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 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 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: An overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and the role of different information patterns.
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 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 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 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 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 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 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 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 Nash Equilibria in Non zero Sum Differential Games with Impulse Control written by Utsav Sadana and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Various Equilibrium Solutions for Linear Quadratic Noncooperative Games written by Xu Wang and published by . This book was released on 2007 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Game theory has been widely used to model decision making processes because it can capture the nature of multi-player problems: the determination of one player's control strategy is not only subject to the system state evolution but is also tightly coupled to the determination of the other players' strategies and vice versa. In this dissertation, we categorize linear quadratic (LQ) games into three groups: definite, singular and indefinite. For singular LQ games: 1) a new equilibrium concept: asymptotic [epsilon]-Nash equilibrium is proposed for a two-player nonzero-sum game where each player has a control-free cost functional quadratic in the system states over an infinite horizon and each player's control strategy is constrained to be continuous linear state feedback; 2) a group of algebraic equations of system coefficients is found whose solution can constitute the partial state feedback asymptotic [epsilon]-Nash equilibrium for the singular LQ games. Conditions on initial states and the parameter [epsilon] are provided such that the asymptotic [epsilon]-Nash equilibrium will be an [epsilon]-Nash equilibrium or a Nash equilibrium; 3) for a class of 2nd-order singular LQ games, the closed-form asymptotic [epsilon]-Nash equilibrium is explicitly found in terms of system coefficients. Robust equilibrium solutions for two-player asymmetric games with an additive uncertainty are studied: 1) regarding the uncertainty as the third player, a three-player non-cooperative nonzero-sum game is formed and each player's cost functional value resulting from the output feedback Nash equilibrium of this three-player game is not as conservative as his/her individual rationality; 2) regarding the coalition of the original two players as one player and the uncertainty as another player, a two-player non-cooperative nonzero-sum game is formed to find un-improvable robust a equilibrium for the original game. Inverse problems for indefinite games are investigated (for which weighting matrices in the cost functional such that the given linear state feedback control strategy can constitute a Nash equilibrium solution): 1) a necessary and sufficient condition for the inverse problem is provided using a group of algebraic equations linear in the variables and the weighting matrices; 2) the inverse problem for a class of 2nd-order two-player LQ game is thoroughly discussed.
Download or read book European Control Conference 1995 written by and published by European Control Association. This book was released on 1995-09-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the European Control Conference 1995, Rome, Italy 5-8 September 1995
Download or read book A Global Theory for Linear Quadratic Differential Games written by Dahlard L. Lukes and published by . This book was released on 1968 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper analyses a class of many player nonzero-sum linear games in Hilbert space with quadratic cost functionals. The existence and stability of equilibrium strategies is studied. The results are then applied to differential games and a feedback synthesis of the equilibrium strategies is developed. (Author).
Download or read book Matrix Riccati Equations in Control and Systems Theory written by Hisham Abou-Kandil and published by Birkhäuser. This book was released on 2012-12-06 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.
Download or read book Dynamic Games and Applications in Economics written by Tamer Başar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eleven articles which deal with different aspects of dynaoic and differential game theory and its applications in economic modeling and decision making. All but one of these were presented as invited papers in special sessions I organized at the 7th Annual Conference on Economic Dynamics and Control in London, England, during the period June 26-28, 1985. The first article, which comprises Chapter 1, provides a general introduction to the topic of dynamic and differential game theory, discusses various noncooperative equilibrium solution concepts, includ ing Nash, Stackelberg, and Consistent Conjectural Variations equilibria, and a number of issues such as feedback and time-consistency. The second chapter deals with the role of information in Nash equilibria and the role of leadership in Stackelberg problems. A special type of a Stackelberg problem is the one in which one dominant player (leader) acquires dynamic information involving the actions of the others (followers), and constructs policies (so-called incentives) which enforce a certain type of behavior on the followers; Chapter 3 deals with such a class of problems and presents some new theoretical results on the existence of affine incentive policies. The topic of Chapter 4 is the computation of equilibria in discounted stochastic dynamic games. Here, for problems with finite state and decision spaces, existing algorithms are reviewed, with a comparative study of their speeds of convergence, and a new algorithm for the computation of nonzero-sum game equilibria is presented.
