using game theory to model wireless networks
TRANSCRIPT
UsingGameTheorytoModelWirelessNetworksPartI
LuizDaSilvaProfessorofTelecommunica2ons
Kraków,Poland,17-18September2018
TrinityCollegeDublin,TheUniversityofDublin
TrinityCollegeDublinFounded1592
TrinityCollegeDublin,TheUniversityofDublin
TrinityCollegeDublin
TrinityCollegeDublin,TheUniversityofDublin
Whatisgametheory?Andwhyisitrelevantinthecontextofwirelessnetworks?
Asetofanaly2caltoolsfromeconomicsandmathema2cstopredicttheoutcomeofcomplexinterac2onsamongra2onalen22es
Modelsofinterac2onsamongadapta2onsperformedbyautonomousradiosinanetwork
Economicmodelsofspectrummarkets,includinglicensedsharedaccess
Incen2vesforover-the-topserviceproviderstodeploytheirowninfrastructureversuscontrac2ngwithoperators
(…)
inthecontextofwirelessnetworks
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BasicsofwirelesscommunicaEonsTheelectromagne2cspectrum
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WirelessNetworksinLicense-ExemptSpectrumWhoaretheplayers,whataretheac2onsetsandu2lityfunc2ons?
• SometechnologiessuchasWiFiaredeployedwithoutfrequencyplanningorcoordina2on:autonomy
• Opera2oninlicense-exemptspectrum:coexistencewithothernetworksofthesametechnology,differenttechnologies
• Device-to-devicecommunica2on
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WirelessNetworksinLicensedSpectrumWhoaretheplayers,whataretheac2onsetsandu2lityfunc2ons?
• SometechnologiessuchasLTE(and5G)aredeployedbymul2plecompe2ngoperators
• Spectrummanagementwithinthelicensedspectrum
• Spectrumauc2ons
• Slicingandver2cals• Interac2onswithover-the-top
services,increasinglyinterestedinalsodeployingnetworks
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TrendsWhatischanginginthetelecommunica2onsworld…
OTTprovidersenteringthetelecomspace
IoTbringsnewscalabilitychallenges
Movetowardshigherfrequencies
Operatorslookingfornewrevenuesources
Leveragingofvastamountsofdata
Autonomy,complexdecisions,lotsofdata:AI+GT
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Componentsofagame
Asetof2ormoreplayersAsetofac2onsforeachplayerAsetofpreferencerela2onshipsforeachplayerforeach
possibleac2ontupleü usuallyexpressedasau2lityfunc2on
CogniEveadaptaEonsasagame
Availablewaveforms(modula2on,coding,opera2ngfrequency)
ReconfigurableRadio Game
Ac2onsetCogni2veradiosinnetwork Playerset
Objec2vefunc2on(e.g.,increasing,concavefunc2onofSINR)
U2lityfunc2on
Distributedchannelassignmentasagame
Availablechannels
MulE-bandRadio Game
Ac2onsetRadiosinnetwork Playerset
Objec2vefunc2on(e.g.,derivedfromnetworkconnec2vitygraphandconflictgraph)
U2lityfunc2on
Dynamicspectrumaccessasagame
Poten2allyavailablechannels
CogniEveRadio Game
Ac2onsetSecondaryusersinanetwork Playerset
Objec2vefunc2on(e.g.,0ifanyconflictswithprimaryuser,increasingw/#ofchannelsusedotherwise)
U2lityfunc2on
Pricingofspectrumasagame
(bandwidth,bid)
Radio Game
Ac2onsetReal-2mebidders Playerset
Objec2vefunc2on(e.g.,consumersurplus)
U2lityfunc2on
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RelevancetoindustryCONNECTindustrypartners
Normalformgames
{ }, , iG N A u=
N–SetofplayersAi–Setofac2onsavailabletoplayeriA–Ac2onspace{ui}–Setofindividualpayoff(u2lity)func2ons
A= A1 × A2 ×!× An
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NashequilibriumJohnNash(1928-2015)
Apointfromwhichnousercanbenefitbyunilaterallydevia2ng
Anac2ontupleaisaNashequilibriumif,foreveryplayeriinNandeveryac2onbiinAi,
Existenceanduniquenessdependonthestructureofthegame
),()( iaa −≥ iii buu
ParetoopEmality
Aresourcealloca2onsolu2onisParetoop2malifnoplayercanbemadehappierwithoutsacrificingthewelfareofatleastoneotherplayer
– Ameasureofefficiencyinresourcealloca2on
– Inmul2-objec2veop2miza2on,theParetofron2erisogensought
NashequilibriaarenotnecessarilyParetoop2mal
– Theprisoner’sdilemmaisafamousexampleofuniqueNashequilibriumthatisnotParetoop2mal
VilfredoPareto(1848-1923)
PredicEvepowerofNashequilibrium
Aconsistentpredic2onoftheoutcomeofthegame
– IfallplayerspredicttheNE,itisreasonabletoassumethattheywillplayit
– Oncereached,thereisnoreasontobelieveanyplayerwilldeviate,andthesystemwillremaininequilibriumun2lcondi2onschange
Butnotwithoutitsissues…
– Ifplayersstartfromanac2onprofilethatisnotanNE,arewesuretheyeventuallyreachtheNE?(Convergence)
– Whatiftherearemul2pleNEs?Isonemorelikelythantheothers?(RefinementstotheconceptofNE)
– Vulnerabletodevia2onsbyacoali2onofplayers
PredicEvepowerofNashequilibrium
Gamesmodelcoopera2onandcompe22onbetween“intelligentdecisionmakers”
ü Gametheoryismul2-agentdecisiontheory
Mustmodelpreferencerela2onsforthesedecisionmakers,andfromthosederiveu2lityfunc2ons
ü Theu2lityfunc2oncanbethe“weakestlink”inthemodel
ü Thereisnofixedrecipeforhowtodeterminetheappropriateu2lityfunc2on…butforpar2cularapplica2onstheremaybecertainproper2esthatthefunc2onisexpectedtohave
Non-cooperaEvevs.cooperaEvegametheory
• e.g.,powercontrolandinterferencegames
• establishaNashequilibrium
• establishapathtotheNashequilibrium(e.g.,bestresponseforpoten2algames)
• e.g.,spectrumsharingamongequals
• establishabargainingsolu2on
• establishapathtothebargainingsolu2on
ExtendedExample:Powercontrolinwirelessnetworks
Consideranetworkwheremul2plewirelessdevices(radios)havetheautonomytoselecttheirtransmitpower
ü Interference:oneradio’sdecisionsaffectallothersü Reasonabletomodelasagame
Eachplayerisetsitstransmitpower
Aplayer’su2lityisafunc2onofitsselectedpower,pi,anditssignal-to-interferencera2o(SIR),whichwedenoteby
ü NotethattheSIR(orSINR)alsodependsonthepowerlevelsselectedbyothernodes,i.e.,thevector
(…)
Asimplegametoillustrateanapplica2onandassociatedchallenges
),0[ ∞∈ip
iγ
ip−
AuElityfuncEonforthepowercontrolgame
Theu2lityfunc2onisanon-nega2vefunc2onofSIR,and
Asthetransmitpowertendseithertozeroorinfinity,thenode’su2litytendstozero
Proper2es:limitcases
0,0)0,( >∀= iii ppU
0),(lim 0 =→ iiip pUi
γ
0),(lim =∞→ iiip pUi
γ
AuElityfuncEonforthepowercontrolgame
Theu2lityfunc2onisamonotonicallyincreasingfunc2onofthenode’sSIR,forafixedtransmitpower
(Thereisanimplicitassump2onherethatthefunc2onisdifferen2able)
Proper2es:monotonicityinSIR
0,,0),(>∀>
∂
∂ii
i
iii ppUγ
γγ
AuElityfuncEonforthepowercontrolgame
Theu2lityfunc2onisamonotonicallydecreasingfunc2onofthenode’stransmitpower,forafixedSIR
Proper2es:monotonicityintransmitpower
0,,0),(>∀<
∂
∂ii
i
iii pppU
γγ
AuElityfuncEonforthepowercontrolgame
Themarginalu2litytendstozeroforhighvaluesofSIR
Proper2es:diminishingmarginalu2lity
0,0),(lim >∀=∂
∂∞→ i
i
iii ppUi γ
γγ
AuElityfuncEonforthepowercontrolgame
LetEbetheenergyavailableinnodei’sbaoery(inJoules),Rbetherateatwhichinforma2onistransmioed,andLbethelengthofaframeinbits
Doesthisfunc2onmeettheproper2esinthepreviousslides?
Acandidateu2lityfunc2on[Shah,Mandayan,Goodman,IEEEPIMRC’98]
L
iiii
iepERpU )1(),( 5.0 γγ −−=
ExistenceofNashEquilibrium[Shah,Mandayam,andGoodman,iEEEPIMRC’98]
Thestrategyspacesareclosedandbounded(ifweconsiderpowerwithinsomerange[0,pmax])Theu2lityfunc2oniscon2nuousinpTheu2lityfunc2onisquasi-concaveinpi
WhatistheNashEquilibrium?
Iftheproblemisformulatedconsideringradioscommunica2ngwithacommonbasesta2on(singlecell),atequilibriumpthepowerreceivedatthebasesta2onwillbethesameforallplayers
Fortheu2lityfunc2onintheprevioustwoslides
jiphph jjyiiy ,∀=
ü hiyisthechannelgainfromradioitothebasesta2on
Pareto(in)efficiencyoftheNashEquilibrium
TheequilibriumpforthisgameisParetoinefficient
Atequilibrium,thereisavalueα<1suchthatifallusersreduce(mul2ply)theirpowerbythatfactor,thenalluserswillobtainhigheru2lity
This“armsrace”or“shou2ngmatch”resultoccursinseveralsimilarly-formulatedgames
Fortheu2lityfunc2oninthepreviousslides
Dealingwithinefficiency
Whatifweconsiderinsteadthefollowingu2lityfunc2on?
whereisthetargetSINRforradioi
Theresul2nggamehasanequilibriumthatisParetoefficient
ü Simpleadapta2onalgorithmscanbeshowntoconvergetotheNashequilibrium
Adifferentu2lityfunc2on
( )2),( iiiii pU γγγ ⌢−−=
iγ⌢
ThinkingabouttheuElityfuncEonincontext
Isitchea2ngtochangetheu2lityfunc2on?
Posi2vemodelofu2lity–thefunc2onaoemptstorepresentwhatreasonableplayerswouldvalueincoopera2onandcompe22on
Norma2vemodelofu2lity–thefunc2onrepresentshowwedesigntheplayerstobehave
Inwirelessnetworksapplica2ons,eithercanbeused,aslongasyouareclearonwhatyouru2lityfunc2oncaptures
Dealingwithinefficiency
Supposeweaoachapricecperunitoftransmitpower
Usersareeffec2velychargedfortheinterferencetheycreateonothersinthenetwork
ü InthiscasetheNashequilibriumiss2llnotParetoop2mal,butitgetsmuchcloserthanintheoriginalformula2on
Pricing
iL
iiii cpe
pERpU i −−= − )1(),( 5.0 γγ
Dealingwithinefficiency
Anotherwayofdealingwithinefficiencyisthroughrepeatedgames
ü Thiscanbeusedtoestablishaself-enforcingmechanism
Atargetopera2ngpointisselected(e.g.,theequal-received-powerParetoop2malpoint)
ü Ifanyuserexceedsthetargetreceivedpower,theuserispunishedbyrever2ngtotheone-shotNEforseveralrounds
Othertechniquesinthiscategorymaymoreexplicitlytrackreputa2on
ü Userswithpoorreputa2onmaybedeniedserviceorofferedalowergradeofservice
Repe22onandreputa2on
Summary
Recenttrendsinwirelessnetworksmakegametheoryapromisingapproachtobeoermodelanddesignadapta2onsinthenetwork
ü “Intelligence”anddecisionmakingpushedouttothenetworkedgeandtoenddevices
ü Sharingofspectrumandinfrastructure(mul2-tenancy,sharinginlicensedandunlicensedspectrum,mul2-RAT)
Aformula2onofadistributedpowercontrolgamemayyieldaNashequilibriumthatisnotefficient(Paretoop2mal)
ü Approachestodealwiththeinefficiencyincludedefiningadifferentu2lityfunc2on,includingpricingconsidera2ons,andformula2ngtheproblemasarepeatedgame
Itiscrucialtodis2nguishbetweennorma2veandposi2vemodelsofu2lityfunc2on
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