LEADER 05151nam 22007095 450 001 9910957364603321 005 20250801063324.0 010 $a1-4612-4054-9 024 7 $a10.1007/978-1-4612-4054-9 035 $a(CKB)3400000000090681 035 $a(SSID)ssj0001007549 035 $a(PQKBManifestationID)11564924 035 $a(PQKBTitleCode)TC0001007549 035 $a(PQKBWorkID)10950878 035 $a(PQKB)10317559 035 $a(DE-He213)978-1-4612-4054-9 035 $a(MiAaPQ)EBC3077049 035 $a(EXLCZ)993400000000090681 100 $a20121227d1997 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aCompetitive Markov Decision Processes /$fby Jerzy Filar, Koos Vrieze 205 $a1st ed. 1997. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1997. 215 $a1 online resource (XII, 394 p.) 300 $a"With 57 illustrations." 311 08$a0-387-94805-8 311 08$a1-4612-8481-3 320 $aIncludes bibliographical references and index. 327 $a1 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 Stochastic Games via Mathematical Programming -- II Existence, Structure and Applications -- 4 Summable Stochastic Games -- 5 Average Reward Stochastic Games -- 6 Applications and Special Classes of Stochastic 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 Stochastic 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. 330 $aThis 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. 606 $aOperations research 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aAutomatic control 606 $aRobotics 606 $aAutomation 606 $aOperations Research and Decision Theory 606 $aMathematical and Computational Engineering Applications 606 $aControl, Robotics, Automation 615 0$aOperations research. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aAutomatic control. 615 0$aRobotics. 615 0$aAutomation. 615 14$aOperations Research and Decision Theory. 615 24$aMathematical and Computational Engineering Applications. 615 24$aControl, Robotics, Automation. 676 $a519.5/42 700 $aFilar$b Jerzy$4aut$4http://id.loc.gov/vocabulary/relators/aut$0485662 702 $aVrieze$b Koos$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910957364603321 996 $aCompetitive Markov Decision Processes$94431388 997 $aUNINA