Competitive Markov Decision Processes / Edition 1

by Jerzy Filar, Koos Vrieze

Overview

This book is intended as a text covering the central concepts and techniques of Competitive Markov Decision Processes. It is an attempt to present a rig­ orous treatment that combines two significant research topics: Shastic Games and Markov Decision Processes, which have been studied extensively, and at times quite independently, by mathematicians, operations researchers, engineers, and economists. Since Markov decision processes can be viewed as a special noncompeti­ tive case of shastic games, we introduce the new terminology Competi­ tive Markov Decision Processes that emphasizes the importance of the link between these two topics and of the properties of the underlying Markov processes. The book is designed to be used either in a classroom or for self-study by a mathematically mature reader. In the Introduction (Chapter 1) we outline a number of advanced undergraduate and graduate courses for which this book could usefully serve as a text. A characteristic feature of competitive Markov decision processes - and one that inspired our long-standing interest - is that they can serve as an "orchestra" containing the "instruments" of much of modern applied (and at times even pure) mathematics. They constitute a topic where the instruments of linear algebra, applied probability, mathematical programming, analysis, and even algebraic geometry can be "played" sometimes solo and sometimes in harmony to produce either beautifully simple or equally beautiful, but baroque, melodies, that is, theorems.

Product Details

ISBN-13:	9781461284819
Publisher:	Springer New York
Publication date:	09/17/2011
Edition description:	1997
Pages:	394
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Introduction.- 1.0 Background.- 1.1 Raison d’Etre and Limitations.- 1.2 A Menu of Courses and Prerequisites.- 1.3 For the Cognoscenti.- 1.4 Style and Nomenclature.- I Mathematical Programming Perspective.- 2 Markov Decision Processes: The Noncompetitive Case.- 3 Shastic Games via Mathematical Programming.- II Existence, Structure and Applications.- 4 Summable Shastic Games.- 5 Average Reward Shastic Games.- 6 Applications and Special Classes of Shastic Games.- Appendix G Matrix and Bimatrix Games and Mathematical Programming.- G.1 Introduction.- G.2 Matrix Game.- G.3 Linear Programming.- G.4 Bimatrix Games.- G.5 Mangasarian-Stone Algorithm for Bimatrix Games.- G.6 Bibliographic Notes.- Appendix H A Theorem of Hardy and Littlewood.- H.1 Introduction.- H.2 Preliminaries, Results and Examples.- H.3 Proof of the Hardy-Littlewood Theorem.- Appendix M Markov Chains.- M.1 Introduction.- M.2 Shastic Matrix.- M.3 Invariant Distribution.- M.4 Limit Discounting.- M.5 The Fundamental Matrix.- M.6 Bibliographic Notes.- Appendix P Complex Varieties and the Limit Discount Equation.- P.1 Background.- P.2 Limit Discount Equation as a Set of Simultaneous Polynomials.- P.3 Algebraic and Analytic Varieties.- P.4 Solution of the Limit Discount Equation via Analytic Varieties.- References.