Reflexion and Control: Mathematical Models

298 Pages·2014·16.547 MB·English

by  Dmitry A. Novikov, Alexander G. Chkhartishvili

5 5 5
COMMUNICATIONS IN CYBERNETICS, COMMUNICATIONS IN CYBERNETICS,
SYSTEMS SCIENCE AND ENGINEERING SYSTEMS SCIENCE AND ENGINEERING
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This book is dedicated to modern approaches to mathemati cal modeling of refl exive
processes in control. The authors consider refl exive games that describe the game-
theoreti cal interacti on of agents making decisions based on a hierarchy of beliefs
regarding (1) essenti al parameters (informati onal refl exion), (2) decision principles used
by opponents (strategic refl exion), (3) beliefs about beliefs, and so on. Informati onal
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and refl exive equilibria in refl exive games generalize a series of well-known equilibrium
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concepts in noncooperati ve games and models of collecti ve behavior. These models allow
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posing and solving the problems of informati onal and refl exive control in organizati onal,
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economic, social and other systems, in military applicati ons, etc. (the interested reader will
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fi nd in the book over 30 examples of possible applicati ons in these fi elds) and describing i
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uniformly many psychological/sociological phenomena connected with refl exion, viz.,
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implicit control, informati onal control via the mass media, refl exion in chess, art works,

etc. The present book is intended for experts in decision making and control of systems of a
an interdisciplinary nature, as well as for undergraduates and postgraduates. n
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ABOUT THE BOOK SERIES
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Communicati ons in Cyberneti cs, Systems Science and Engineering (CCSSE) is a cross-
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disciplinary book series devoted to theoreti cal and applied research contributi ons, that cater
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to a rapidly growing worldwide interest in a cyberneti c and systemic methodology with an r
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ever-increasing capacity to deal with new challenges in a way that traditi onal science cannot. Dmitry A. Novikov
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The series aims to become a comprehensive reference work on and guide to developments
Alexander G. Chkharti shvili
within the fi eld and strategies required for bett er implementati on of advances, with a view M
to environmental protecti on and sustainable social and economic development. The CCSSE a
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series targets all working in theoreti cal and applied fi elds of cyberneti cs, systems science h
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and engineering, e.g. academics, researchers and consultants, computer and informati on m Refl exion and Control
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scienti sts, development and systems engineers, mathemati cians, management cyberneti cists ti

and systemists, medical scienti sts, and intelligent and manufacturing engineers in industry, ca
as well as leading decision- and policy-makers. l M Mathemati cal Models
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SERIES EDITOR: JEFFREY ‘YI-LIN’ FORREST e
ls
ISSN: 2164-9693
an informa business
Reflexion and Control
Mathematical Models
CommunicationsinCybernetics,SystemsScienceandEngineering
ISSN:2164-9693
BookSeriesEditor:
JeffreyYi-Lin Forrest
InternationalInstituteforGeneralSystemsStudies,GroveCity,USA
SlipperyRockUniversity,SlipperyRock,USA
Volume 5
Reflexion and Control
Mathematical Models
Dmitry A. Novikov &
Alexander G. Chkhartishvili
Trapeznikov Institute of Control Sciences,RussianAcademy of Sciences,
Moscow,Russia
CRCPress/BalkemaisanimprintoftheTaylor&FrancisGroup,aninformabusiness
©2014Taylor&FrancisGroup,London,UK
TypesetbyMPSLimited,Chennai,India
PrintedandBoundbyCPIGroup(UK)Ltd,Croydon,CR04YY
Allrightsreserved.Nopartofthispublicationortheinformationcontained
hereinmaybereproduced,storedinaretrievalsystem,ortransmittedinany
formorbyanymeans,electronic,mechanical,byphotocopying,recordingor
otherwise,withoutwrittenpriorpermissionfromthepublishers.
Althoughallcareistakentoensureintegrityandthequalityofthispublication
andtheinformationherein,noresponsibilityisassumedbythepublishersnor
theauthorforanydamagetothepropertyorpersonsasaresultofoperation
oruseofthispublicationand/ortheinformationcontainedherein.
LibraryofCongressCataloging-in-PublicationData
Novikov,D.A.(DmitryAleksandrovich),1970–author.
Reflexionandcontrol:mathematicalmodels/DmitryA.Novikov&AlexanderG.Chkhartishvili,
TrapeznikovInstituteofControlSciences,RussianAcademyofSciences,Moscow,Russia.
pagescm.—(Communicationsincybernetics,systemsscienceandengineering,
ISSN2164-9693;volume5)
Summary:“Thebookconsidersthebasicsofmathematicalmodelingofreflexiveprocesses
incontrol.Themodelsofinformationalandstrategicreflexionallowdescribingandstudyingthe
behaviorofreflexingsubjects,investigatingtherelationshipbetweenpayoffsgainedbyagentsand
theirreflexionranks,solvingproblemsofinformationalandreflexivecontrolinorganizational,
economic,socialandothersystems,andmilitaryapplicationsamongothers(thebookcontains
over30examplesofpossibleapplicationsinthesefields),describinguniformlymanyphenomena
connectedwithreflexion,viz.,implicitcontrol,informationalcontrolviathemassmediaand
reflexioninpsychology’’—Providedbypublisher.
Includesbibliographicalreferencesandindex.
ISBN978-1-138-02473-1(hardback)—ISBN978-1-315-77554-8(eBookPDF) 1. Gametheory.
2. Controltheory. I. Chkhartishvili,A.G.(AleksandrGedevanovich),author. II.Title.
QA269.N68 2014
515’.642—dc23
2014000188
Publishedby: CRCPress/Balkema
P.O.Box11320,2301EHLeiden,TheNetherlands
e-mail:[email protected]
www.crcpress.com–www.taylorandfrancis.com
ISBN:978-1-138-02473-1(Hbk)
ISBN:978-1-315-77554-8(eBookPDF)
– “Seehowtheminnowscomeoutanddartaroundwheretheyplease!That’swhatfish
reallyenjoy!’’
– “You’renotafish–howdoyouknowwhatfishenjoy?’’
– “You’renotme,sohowdoyouknowIdon’tknowwhatfishenjoy?’’
FromaTaoistparable
– “Well,ofcourse,Archbishop,thepointisthatyoubelievewhatyoubelievebecauseof
thewayyouwerebroughtup.’’
– “That is as it may be. But the fact remains that you believe I believe what I believe
becauseofthewayIwasbroughtup,becauseofthewayyouwerebroughtup.’’
FromD.Myers’book“SocialPsychology’’
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Table of contents
Editorialboard ix
Abouttheauthors xi
Introduction 1
1 Reflexionindecision-making 17
1.1 Individualdecision-making 17
1.2 Interactivedecision-making:Gamesandequilibria 19
1.3 Generalapproachestothedescriptionofinformationaland
strategicreflexion 24
2 Informationalreflexionandcontrol 29
2.1 Informationalreflexionintwo-playergames 29
2.2 Awarenessstructureofgames 32
2.3 Informationalequilibrium 37
2.4 Graphofareflexivegame 40
2.5 Regularawarenessstructures 45
2.6 Reflexionrankandinformationalequilibrium 50
2.7 Stableinformationalequilibria 59
2.8 Trueandfalseequilibria 62
2.9 Thecaseofobservableactionsofagents 64
2.10 ReflexivegamesandBayesiangames 68
2.11 Informationalcontrol 73
2.12 Modelingofinformationalimpact 80
2.13 Set-typeawarenessstructures 89
2.14 Transformationofawarenessstructure 95
2.15 Concordantinformationalcontrol 98
2.16 Reflexioninplanningmechanisms 106
3 Strategicreflexionandcontrol 113
3.1 Strategicreflexionintwo-playergames 113
3.2 Reflexioninbimatrixgamesandgamesofranks 118
3.3 Boundednessofreflexionranks 133
3.4 Reflexivestructuresandreflexivecontrol 134
viii Table of contents
4 Appliedmodelsofinformationalandreflexivecontrol 145
4.1 Implicitcontrol 145
4.2 Themassmediaandinformationalcontrol 153
4.3 Reflexioninpsychology 155
4.3.1 Playingchess 155
4.3.2 Transactionalanalysis 157
4.3.3 TheJohariwindow 159
4.3.4 Ethicalchoice 160
4.4 Reflexioninbélles-léttres 161
4.5 Reflexivesearchgames 167
4.6 Manufacturersandintermediatesellers 171
4.7 Thescarcityprinciple 174
4.8 Jointproduction 176
4.9 Marketcompetition 181
4.10 Lumpsumpayments 183
4.11 Sellersandbuyers 189
4.12 Customersandexecutors 192
4.13 Corruption 194
4.14 Bipolarchoice 195
4.15 Activeexpertise:Informationalreflexion 199
4.16 Thecournotoligopoly:Informationalreflexion 205
4.17 Resourceallocation 207
4.18 Insurance 210
4.19 Productadvertizing 216
4.20 Thehustings 218
4.21 Rank-ordertournaments 219
4.22 Explicitandimplicitcoalitionsinreflexivegames 221
4.23 Activeforecast 231
4.24 Socialnetworks 234
4.25 Mobcontrol 240
4.26 Thereflexivepartitionsmethod 243
4.26.1 Diffusebomb 244
4.26.2 ThecolonelBlottogame 253
4.26.3 TheCournotoligopoly:strategicreflexion 259
4.26.4 Theconsensusproblem 263
4.26.5 Activeexpertise:strategicreflexion 264
4.26.6 Transportflowsandevacuation 266
4.26.7 Astockexchange 268
Conclusion 273
References 275
Subjectindex 283
Editorial board
MichaelC.Jackson,UniversityofHull,UK
JerzyJozefczyk,WroclawUniversityofTechnology,Poland
DonchoPetkov,EasternConnecticutStateUniversity,USA
VladimirTsurkov,RussianAcademyofSciences,Russia
ShouyangWang,ChineseAcademyofSciences,P.R.China
ADVISORY EDITORIAL BOARD
C.L.PhilipChen,UniversityofMacau,P.R.China
ZengruDi,BeijingNormalUniversity,P.R.China
RaulEspejo,SynchoLtd.andWorldOrganizationofSystemsandCybernetics,UK
KeithW.Hipel,UniversityofWaterloo,Canada
BaodingLiu,TsinghuaUniversity,China
NagendraNagarur,StateUniversityofNewYorkatBinghamton,USA
JohnPourdehnad,UniversityofPennsylvania,USA
BrianHowardRudall,InstituteoftheWorldOrganisationofSystemsand
Cybernetics&BangorUniversity,UK
RudolfScheidl,JohannesKeplerUniversityofLinz,Austria
MarkusSchwaninger,InstituteofManagement,UniversityofSt.Gallen,Switzerland