Using Game Theory to Model Wireless Networks

UsingGameTheorytoModelWirelessNetworksPartI

LuizDaSilvaProfessorofTelecommunica2ons

Kraków,Poland,17-18September2018

TrinityCollegeDublin,TheUniversityofDublin

TrinityCollegeDublinFounded1592


TrinityCollegeDublin


Whatisgametheory?Andwhyisitrelevantinthecontextofwirelessnetworks?

Asetofanaly2caltoolsfromeconomicsandmathema2cstopredicttheoutcomeofcomplexinterac2onsamongra2onalen22es

Modelsofinterac2onsamongadapta2onsperformedbyautonomousradiosinanetwork

Economicmodelsofspectrummarkets,includinglicensedsharedaccess

Incen2vesforover-the-topserviceproviderstodeploytheirowninfrastructureversuscontrac2ngwithoperators

(…)

inthecontextofwirelessnetworks


BasicsofwirelesscommunicaEonsTheelectromagne2cspectrum


WirelessNetworksinLicense-ExemptSpectrumWhoaretheplayers,whataretheac2onsetsandu2lityfunc2ons?

•  SometechnologiessuchasWiFiaredeployedwithoutfrequencyplanningorcoordina2on:autonomy

•  Opera2oninlicense-exemptspectrum:coexistencewithothernetworksofthesametechnology,differenttechnologies

•  Device-to-devicecommunica2on


WirelessNetworksinLicensedSpectrumWhoaretheplayers,whataretheac2onsetsandu2lityfunc2ons?

•  SometechnologiessuchasLTE(and5G)aredeployedbymul2plecompe2ngoperators

•  Spectrummanagementwithinthelicensedspectrum

•  Spectrumauc2ons

•  Slicingandver2cals•  Interac2onswithover-the-top

services,increasinglyinterestedinalsodeployingnetworks


TrendsWhatischanginginthetelecommunica2onsworld…

OTTprovidersenteringthetelecomspace

IoTbringsnewscalabilitychallenges

Movetowardshigherfrequencies

Operatorslookingfornewrevenuesources

Leveragingofvastamountsofdata

Autonomy,complexdecisions,lotsofdata:AI+GT


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


RelevancetoindustryCONNECTindustrypartners

Normalformgames

{ }, , iG N A u=

N–SetofplayersAi–Setofac2onsavailabletoplayeriA–Ac2onspace{ui}–Setofindividualpayoff(u2lity)func2ons

A= A1 × A2 ×!× An


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


Theu2lityfunc2onisamonotonicallyincreasingfunc2onofthenode’sSIR,forafixedtransmitpower

(Thereisanimplicitassump2onherethatthefunc2onisdifferen2able)

Proper2es:monotonicityinSIR

0,,0),(>∀>

∂

∂ii

i

iii ppUγ

γγ


Theu2lityfunc2onisamonotonicallydecreasingfunc2onofthenode’stransmitpower,forafixedSIR

Proper2es:monotonicityintransmitpower

0,,0),(>∀<

∂

∂ii

i

iii pppU

γγ


Themarginalu2litytendstozeroforhighvaluesofSIR

Proper2es:diminishingmarginalu2lity

0,0),(lim >∀=∂

∂∞→ i

i

iii ppUi γ

γγ


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


Supposeweaoachapricecperunitoftransmitpower

Usersareeffec2velychargedfortheinterferencetheycreateonothersinthenetwork

ü InthiscasetheNashequilibriumiss2llnotParetoop2mal,butitgetsmuchcloserthanintheoriginalformula2on

Pricing

iL

iiii cpe

pERpU i −−= − )1(),( 5.0 γγ


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

ThankYouluizdasilva.wordpress.com

Using Game Theory to Model Wireless Networks

Documents

Transcript of Using Game Theory to Model Wireless Networks