Problems in Two-person, Zero-sum Stochastic Games
Author: Piercesare Secchi
Publisher:
Published: 1995
Total Pages: 280
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Piercesare Secchi
Publisher:
Published: 1995
Total Pages: 280
ISBN-13:
DOWNLOAD EBOOKAuthor: Alan R. Washburn
Publisher: INFORMS
Published: 2003
Total Pages: 137
ISBN-13: 1877640190
DOWNLOAD EBOOKAuthor: T. Parthasarathy
Publisher: Springer Nature
Published: 2020-12-08
Total Pages: 127
ISBN-13: 9811565775
DOWNLOAD EBOOKThis book discusses stochastic game theory and related concepts. Topics focused upon in the book include matrix games, finite, infinite, and undiscounted stochastic games, n-player cooperative games, minimax theorem, and more. In addition to important definitions and theorems, the book provides readers with a range of problem-solving techniques and exercises. This book is of value to graduate students and readers of probability and statistics alike.
Author: Martino Bardi
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 388
ISBN-13: 1461215927
DOWNLOAD EBOOKThe 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:
Publisher:
Published: 2006
Total Pages: 145
ISBN-13:
DOWNLOAD EBOOKIn this work, two-player zero-sum stochastic games, under imperfect information, are investigated in the discrete-time/discrete-state case. We focus on the case where only one player, Blue, has incomplete or partial information and the other player, Red, has complete state information. In stochastic games with partial information the Information State is a function of a conditional probability distribution. In the problem form here, the payoff is only a function of the terminal state of the system, and the initial information state is a max-plus sum of max-plus delta functions. The Blue player can achieve robustness to the effect of Red's control on its observations. Using the recently established deception-robust theory, we demonstrate that the full state-feedback optimal control applied at the Maximum Likelihood State ('MLS') is not optimal for the Blue player in a partially-observed game and hence the Certainty Equivalence Principle does not hold. An automated deception-enabled control algorithm is derived for the Red player with an assumption that Red can model the Blue algorithm completely. An example game is used to demonstrate that even for the Red player, with complete state information, the optimal control is not the state-feedback optimal control. A future study of deception-enabled Red approach is proposed in the mixed strategy framework. Lastly, some modelling ideas are presented for Urban Warfare. The example cases considered in this study are simple enough to allow an intuitive understanding of optimal strategies, while complex enough to demonstrate real-world difficulties. The theory discussed here is more general than the specific application which has been presented owing to the critical nature of imperfect information and hence its utility in war games.
Author: Serdar Yüksel
Publisher: Springer Nature
Published:
Total Pages: 935
ISBN-13: 3031540719
DOWNLOAD EBOOKAuthor: Tamer Basar
Publisher:
Published: 19??
Total Pages:
ISBN-13: 9783319273358
DOWNLOAD EBOOKRésumé : "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: Eilon Solan
Publisher: Cambridge University Press
Published: 2022-05-26
Total Pages: 279
ISBN-13: 1316516334
DOWNLOAD EBOOKThis book for beginning graduate students presents a course on stochastic games and the mathematical methods used in their analysis.
Author: Tamer Basar
Publisher: SIAM
Published: 1999-01-01
Total Pages: 526
ISBN-13: 089871429X
DOWNLOAD EBOOKAn overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and the role of different information patterns.
Author: Michael Ummels
Publisher: Amsterdam University Press
Published: 2010-12
Total Pages: 174
ISBN-13: 9085550408
DOWNLOAD EBOOKStochastic games provide a versatile model for reactive systems that are affected by random events. This dissertation advances the algorithmic theory of stochastic games to incorporate multiple players, whose objectives are not necessarily conflicting. The basis of this work is a comprehensive complexity-theoretic analysis of the standard game-theoretic solution concepts in the context of stochastic games over a finite state space. One main result is that the constrained existence of a Nash equilibrium becomes undecidable in this setting. This impossibility result is accompanied by several positive results, including efficient algorithms for natural special cases.