Stochastic and differential games : theory and numerical methods
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Bibliographic Information
Stochastic and differential games : theory and numerical methods
（Annals of the International Society of Dynamic Games, v. 4）
Birkhäuser, c1999
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Includes bibliographical references
Description and Table of Contents
- Volume
-
ISBN 9780817640293
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.
Table of Contents
I. Zero-Sum Differential Games and Numerical Methods.- 1 Constructive Theory of Positional Differential Games and Generalized Solutions to Hamilton-Jacobi Equations.- 2 Two-Player, Zero-Sum Differential Games and Viscosity Solutions.- 3 Numerical Methods for Pursuit-Evasion Games via Viscosity Solutions.- 4 Set-Valued Numerical Analysis for Optimal Control and Differential Games.- II. Stochastic and Nonzero-Sum Games and Applications.- 5 An Introduction to Gambling Theory and Its Applications to Stochastic Games.- 6 Discounted Stochastic Games: A Complex Analytic Perspective.- 7 Nonzero-Sum Stochastic Games.- 8 The Power of Threats in Stochastic Games.- 9 A Markov Game Approach for Optimal Routing Into a Queuing Network.- 10 On Linear Complementarity and A Discounted Polystochastic Game.
- Volume
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ISBN 9783764340292
Description
This text is aimed at control engineers, applied mathematicians, operations research specialists and research workers. The first part deals with zero-sum differential games and numerical methods, and the second part with stochastic and nonzero-sums.
Table of Contents
- Part 1 Zero-sum differential games and numerical methods: constructive theory of positional differential games and generalized solutions of Hamilton-Jacobi equations, A. Subbotin
- two-player, zero-sum differential games and viscosity solutions, P.E. Souganidis
- numerical methods for pursuit-evasion games via viscosity solutions, M. Bardi et al
- set-valued numerical analysis for optimal control and differential games, P. Cardaliaguet et al. Part 2 Stochastic and nonzero-sum games and applications: intro to gambling theory and its application to stochastic games, A. Maitra et al
- discounted stochastic games, a complex analytic perspective, S.A. Connell et al
- nonzero-sum stochastic games, A.S. Nowak et al
- the power of threats on stochastic games, F. Thuijsman et al
- a Markov game approach for optimal routing into a queuing network, Eitan Altman
- linear complementarity and discounted polystochastic game when one player controls transitions, S.R. Mohan et al.
by "Nielsen BookData"