Advances in dynamic games: Applications to economics, finance, optimization

699 Pages·2004·4.73 MB·English

by  Andrzej S. Nowak, Krzysztof Szajowski

AnnalsoftheInternationalSocietyofDynamicGames
Volume 7
Series Editor
TamerBas¸ar
Editorial Board
TamerBas¸ar,UniversityofIllinois,Urbana
PierreBernhard,I3S-CNRSandUniversityofNice-SophiaAntipolis
MaurizioFalcone,UniversityofRoma“LaSapieza”
JerzyFilar,UniversityofSouthAustralia,Adelaide
AlainHaurie,HEC-UniversityofGeneva
ArikA.Melikyan,RussianAcademyofSciences,Moscow
AndrzejS.Nowak,Wroc(cid:2)lawUniveristyofTechnology
andUniversityofZielonaGo´ra
LeoPetrosjan,St.PetersburgStateUniversity
AlainRapaport,INRIA,Montpelier
JosefShina,Technion,Haifa
Annals of the International Society of Dynamical Games
Advances in Dynamic Games
Applications to Economics, Finance,
Optimization, and Stochastic Control
Andrzej S. Nowak
Krzysztof Szajowski
Editors
Birkha¨user
Boston Basel Berlin
• •
KrzysztofSzajowski
AndrzejS.Nowak (cid:2)l
(cid:2)l Wroc awUniversityofTechnology
Wroc awUniversityofTechnology
InstituteofMathematics
InstituteofMathematics
WybrzezeWypian´skiego27
WybrzezeWypian´skiego27 ˙ (cid:2)l
˙ (cid:2)l 50-370Wroc aw
50-370Wroc aw
Poland
Poland
and
FacultyofMathematics,ComputerScience,
andEconometrics
UniversityofZielonaGo´ra
Podgo´rna50
65-246ZielonaGo´ra
Poland
AMSSubjectClassifications:91A-xx,91A05,91A06,91A10,91A12,91A13,91A15,91A18,91A20,
91A22,91A23,91A25,91A28,91A30,91A35,91A40,91A43,91A46,91A50,91A60,91A65,91A70,
91A80,91A99
LibraryofCongressCataloging-in-PublicationData
InternationalSymposiumofDynamicGamesandApplications(9th:2000:Adelaide,S.Aust.)
Advancesindynamicgames:applicationstoeconomics,finance,optimization,and
stochasticcontrol/AndrzejS.Nowak,KrzysztofSzajowski,editors.
p.cm.–(AnnalsoftheInternationalSocietyofDynamicGames;[v.7])
Papersbasedonpresentationsatthe9thInternationalSymposiumonDynamicGames
andApplicationsheldinAdelaide,SouthAustraliainDec.2000.
ISBN0-8176-4362-1(alk.paper)
1.Gametheory–Congresses.I.Nowak,AndrzejS.II.Szajowski,Krzysztof.III.Title.
IV.Series.
HB144.I5832000
330’.01’5193–dc22 2004048826
ISBN0-8176-4362-1 Printedonacid-freepaper.
c2005Birkha¨userBoston
(cid:2)
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permissionofthepublisher(Birkha¨userBoston,c/oSpringerScience BusinessMedia,Inc.,Rights
+
andPermissions,233SpringStreet,NewYork,NY,10013,USA),exceptforbriefexcerptsincon-
nectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorage
andretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynow
knownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,evenifthey
arenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare
subjecttoproprietaryrights.
PrintedintheUnitedStatesofAmerica. (KeS/SB)
987654321 SPIN10988183
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . ix
Contributors . . . . . . . . . . . . . . . . . . . . . . xi
PartI RepeatedandStochasticGames
InformationandtheExistenceofStationaryMarkovianEquilibrium 3
IoannisKaratzas,MartinShubikandWilliamD.Sudderth
MarkovGamesunderaGeometricDriftCondition . . . . . . . 21
Heinz-UweKu¨enle
ASimpleTwo-PersonStochasticGamewithMoney . . . . . . 39
PiercesareSecchiandWilliamD.Sudderth
NewApproachesandRecentAdvancesinTwo-PersonZero-Sum
RepeatedGames . . . . . . . . . . . . . . . . . . . . 67
SylvainSorin
NotesonRisk-SensitiveNashEquilibria . . . . . . . . . . . 95
AndrzejS.Nowak
ContinuousConvexStochasticGamesofCapitalAccumulation . . 111
PiotrWiecek
(cid:2)
PartII DifferentialDynamicGames
DynamicCoreofFuzzyDynamicalCooperativeGames . . . . . 129
Jean-PierreAubin
NormalizedOvertakingNashEquilibriumforaClassofDistributed
ParameterDynamicGames . . . . . . . . . . . . . . . . 163
DeanA.Carlson
CooperativeDifferentialGames . . . . . . . . . . . . . . 183
LeonA.Petrosjan
vi Contents
PartIII StoppingGames
SelectionbyCommittee . . . . . . . . . . . . . . . . . 203
ThomasS.Ferguson
StoppingGameProblemforDynamicFuzzySystems . . . . . 211
YujiYoshida,MasamiYasuda,MasamiKuranoandJun-ichiNakagami
OnRandomizedStoppingGames . . . . . . . . . . . . . . 223
ElzbietaZ.Ferenstein
˙
StoppingGames–RecentResults . . . . . . . . . . . . . 235
EilonSolanandNicolasVieille
Dynkin’sGameswithRandomizedOptimalStoppingRules . . . 247
VictorDomansky
ModifiedStrategiesinaCompetitiveBestChoiceProblemwith
RandomPriority . . . . . . . . . . . . . . . . . . . . 263
ZdzisławPorosin´ski
BilateralApproachtotheSecretaryProblem . . . . . . . . . 271
DavidRamseyandKrzysztofSzajowski
OptimalStoppingGameswherePlayershaveWeightedPrivilege . 285
MinoruSakaguchi
EquilibriuminanArbitrationProcedure . . . . . . . . . . . 295
VladimirV.MazalovandAnatoliyA.Zabelin
PartIV ApplicationsofDynamicGamestoEconomics,
FinanceandQueuingTheory
ApplicationsofDynamicGamesinQueues . . . . . . . . . . 309
EitanAltman
EquilibriaforMulticlassRoutingProblemsinMulti-AgentNetworks 343
EitanAltmanandHisaoKameda
EndogenousShocksandEvolutionaryStrategy:Applicationtoa
Three-PlayersGame . . . . . . . . . . . . . . . . . . . 369
EkkehardC.Ernst,BrunoAmableandStefanoPalombarini
Contents vii
RobustControlApproachtoOptionPricing,IncludingTransaction
Costs . . . . . . . . . . . . . . . . . . . . . . . . . 391
PierreBernhard
S-AdaptedEquilibriainGamesPlayedoverEventTrees:AnOverview 417
AlainHaurieandGeorgesZaccour
ExistenceofNashEquilibriainEndogenousRent-SeekingGames 445
KojiOkuguchi
ADynamicGamewithContinuumofPlayersanditsCounterpartwith
FinitelyManyPlayers . . . . . . . . . . . . . . . . . . 455
AgnieszkaWiszniewska-Matyszkiel
PartV NumericalMethodsandAlgorithmsforSolving
DynamicGames
DistributedAlgorithmsforNashEquilibriaofFlowControlGames 473
TansuAlpcanandTamerBas¸ar
ATaylorSeriesExpansionforH ControlofPerturbedMarkovJump
∞
LinearSystems . . . . . . . . . . . . . . . . . . . . . 499
RachidElAzouzi,EitanAltmanandMohammedAbbad
AdvancesinParallelAlgorithmsfortheIsaacsEquation . . . . 515
MaurizioFalconeandPaoloStefani
NumericalAlgorithmforSolvingCross-CoupledAlgebraicRiccati
EquationsofSingularlyPerturbedSystems . . . . . . . . . . 545
HiroakiMukaidani,HuaXuandKoichiMizukami
EquilibriumSelectionviaAdaptation:UsingGeneticProgrammingto
ModelLearninginaCoordinationGame . . . . . . . . . . . 571
Shu-HengChen,JohnDuffyandChia-HsuanYeh
TwoIssuesSurroundingParrondo’sParadox . . . . . . . . . 599
AndreCosta,MarkFackrellandPeterG.Taylor
PartVI Parrondo’sGamesandRelatedTopics
State-SpaceVisualizationandFractalPropertiesofParrondo’sGames 613
AndrewAllison,DerekAbbottandCharlesPearce
viii Contents
Parrondo’sCapitalandHistory-DependentGames . . . . . . . 635
GregoryP.Harmer,DerekAbbottandJuanM.R.Parrondo
IntroductiontoQuantumGamesandaQuantumParrondoGame . 649
JosephNgandDerekAbbott
ASemi-quantumVersionoftheGameofLife . . . . . . . . . 667
AdrianP.FlitneyandDerekAbbott
Preface
Moderngametheoryhasevolvedenormouslysinceitsinceptioninthe1920sinthe
worksofBorelandvonNeumann.Thebranchofgametheoryknownasdynamic
games descended from the pioneering work on differential games by R. Isaacs,
L.S.Pontryaginandhisschool,andfromseminalpapersonextensiveformgames
by Kuhn and on stochastic games by Shapley. Since those early developmental
decades,dynamicgametheoryhashadasignificantimpactonsuchdiversedis-
ciplines as applied mathematics, economics, systems theory, engineering, oper-
ations research, biology, ecology, and the environmental sciences. On the other
hand, a large variety of mathematical methods from differential equations to
stochasticprocesseshasbeenappliedtoformulateandsolvemanydifferentprob-
lems.
Thisneweditedbookfocusesonvariousaspectsofdynamicgametheory,pro-
viding authoritative, state-of-the-art information and serving as a guide to the
vitalityofthefieldanditsapplications.Mostoftheselected,peer-reviewedpapers
arebasedonpresentationsatthe9thInternationalSymposiumonDynamicGames
andApplicationsheldinAdelaide,SouthAustraliainDecember2000.Thiscon-
ference took place under the auspices of the International Society of Dynamic
Games (ISDG), established in 1990. The conference has been cosponsored by
Centre for Industrial and Applicable Mathematics (CIAM), University of South
Australia,IEEEControlSystemsSociety,InstituteofMathematics,WrocławUni-
versityofTechnology(Poland),FacultyofMathematics,ComputerScienceand
Econometrics, University of Zielona Go´ra (Poland), ISDG Organizing Society,
andtheUniversityofSouthAustralia.Everypaperthatappearsinthisvolumehas
passedthroughastringentreviewingprocess,asisthecasewithpublicationsfor
archivaljournals.
Avarietyoftopicsofcurrentinterestarepresented.Theyaredividedintosix
parts:thefirst(fivepapers)treatrepeatedgamesandstochasticgames,andthesec-
ond(threepapers)coversdifferentialdynamicgames.Thethirdpartofthevolume
(nine papers) is devoted to the various extensions of stopping games, which are
alsoknownasDynkin’sgames.Inthefourthparttherearesevenpapersonapplica-
tionsofdynamicgamestoeconomics,finance,andqueuingtheory.Thefinaltwo
partscontainfivepaperswhicharedevotedtoalgorithmsandnumericalsolution
approachesfordynamicgames,andthesectiononParrondo’sgames(fivepapers).
We wish to thank all the associate editors and the referees for their valuable
contributionsthatmadethisvolumepossible.
WrocławandZielonaGo´ra AndrzejS.Nowak
Wrocław KrzysztofSzajowski
Contributors
MohammedAbbad,De´partementdeMathematiquesetInformatique,Faculte´ des
SciencesB.P.1014,Universite´ MohammedV,10000Rabat,Morocco
DerekAbbott,CentreforBiomedicalEngineering(CBME)andDepartmentof
ElectricalandElectronicEngineering,TheUniversityofAdelaide,Adelaide,
SA5005,Australia
AndrewAllison,CentreforBiomedicalEngineering(CBME)andDepartmentof
ElectricalandElectronicEngineering,UniversityofAdelaide,Adelaide,
SA5005,Australia
TansuAlpcan,CoordinatedScienceLaboratory,UniversityofIllinois,1308West
MainStreet,Urbana,IL61801,USA
EitanAltman,INRIA,B.P.93,2004routedesLucioles,06902Sophia-Antipolis
Cedex,France
BrunoAmable,Faculte´ desSciencesEconomies,Universite´ ParisX-Nanterre,
200av.delaRe´publique,92000Nanterre,France
Jean-PierreAubin,CentredeRechercheViabilite´,Jeux,Controˆle,Universite´
Paris-Dauphine,75775Pariscx(16),France
RachidElAzouzi,UniversityofAvignon,LIA,339,chemindesMeinajaries,
AgroparcB.P.1228,84911AvignonCedex9,France
TamerBas¸ar,CoordinatedScienceLaboratory,UniversityofIllinois,1308West
MainStreet,Urbana,IL61801,USA
PierreBernhard,LaboratoireI3S,UNSAandCNRS,2000routedesLucioles,Les
Algorithmes–baˆt.Euclide8,BP.121,106903SophiaAntipolis-Cedex,France
DeanA.Carlson,MathematicalReviews416FourthStreet,P.O.Box8604,Ann
Arbor,MI48107-8604,USA
Shu-HengChen,AI-ECONResearchCenter,DepartmentofEconomics,
NationalChengchiUniversity,64Chi-NanRd.,Sec.2,Taipei11623,Taiwan
AndreCosta,SchoolofAppliedMathematics,UniversityofAdelaide,Adelaide,
SA5005,Australia