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Competitive Markov Decision Processes

  • Textbook
  • © 1997

Overview

Authors:
  1. Jerzy Filar

    1. School of Mathematics, University of South Australia, Adelaide, Australia

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  2. Koos Vrieze

    1. Department of Mathematics, University of Limburg, Maastricht, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    1. Introduction

      • Jerzy Filar, Koos Vrieze
      Pages 1-6

  3. Mathematical Programming Perspective

    1. Front Matter

      Pages 7-7
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    2. Markov Decision Processes: The Noncompetitive Case

      • Jerzy Filar, Koos Vrieze
      Pages 9-84

    3. Stochastic Games via Mathematical Programming

      • Jerzy Filar, Koos Vrieze
      Pages 85-151

  4. Existence, Structure and Applications

    1. Front Matter

      Pages 153-153
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    2. Summable Stochastic Games

      • Jerzy Filar, Koos Vrieze
      Pages 155-234

    3. Average Reward Stochastic Games

      • Jerzy Filar, Koos Vrieze
      Pages 235-300

    4. Applications and Special Classes of Stochastic Games

      • Jerzy Filar, Koos Vrieze
      Pages 301-341

  5. Back Matter

    Pages 343-393
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Keywords

About this book

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: Stochastic Games and Markov Decision Processes, which have been studied exten­ sively, 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 stochastic 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 program­ ming, 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.

Authors and Affiliations

  • School of Mathematics, University of South Australia, Adelaide, Australia

    Jerzy Filar

  • Department of Mathematics, University of Limburg, Maastricht, The Netherlands

    Koos Vrieze

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