B daeUiveiyfTe h

On Priing, Inentives and Congestion

Control in Heterogeneous Networks

Gergely Bizók

PhDDissertation

Advisor:

Dr. Tuan A.Trinh

High Speed NetworksLab

Departmentof Teleommuniations andMedia Informatis

Budapest University of Tehnology andEonomis

Budapest, Hungary

2010.

Heterogeneity is inherently present in multiple aspets of thewired and wireless Internet. Un-

derstanding, overomingoreven exploitingthisheterogeneityatdierentlevelsarefundamental

goals for researhersinomputernetworks. Thisdissertation presentsresults on Internet aess

priing, wireless ommunity networks and ongestion ontrol. All proposed approahes share

one thing in ommon: they intend to help a diverse set of network providers, e.g., Internet

Servie Providers, ommunity wireless operators, miro-operators (end-users themselves) and

mobile operators, to addressthe hallenges stemmingfromthe heterogeneity of theirrespetive

networks.

First, I quantify the impat of ustomer loyalty on the priing ompetition between net-

work providers. Ithen proposea priingmehanismfor Internet aess, whih enables network

providers to plantheir revenues, while users an diretlyinuene the implemented billing pol-

iy. Seond, I analyze the eonomi interations in wireless ommunity networks. I show that

properinentivedesignanduserheterogeneityfailitatestheemergeneofatrulyglobalwireless

ommunity, where both users andnetwork providersprot fromthenetwork. Third, Ishowthe

limitationsofexistingTCPversionsindynamimobileenvironments,partiularlyafterasudden

apaityinrease. Motivatedbytheselimitations, Iproposeasimple,end-to-endnon-ongestion

detetion mehanismfor TCP whih solvesthis problemeetively.

AvezetékesésvezetéknélküliInternetalapvet®tulajdonságaasokszín¶ség. Ennekasokszín¶ség-

nek a megértése, legy®zése,s®t, akár kihasználása különböz® szervezésiszinteken aszámítógép-

hálózatokterületén tevékenyked® kutatókegyiklegfontosabb élja. Eza disszertáióaz Internet

hozzáférés árazásával, vezetéknélküli közösségi hálózatokkal és torlódáskezeléssel foglalkozik. A

javasolt megoldásoknak közös a élja, segíteni a különböz® hálózati szolgáltatóknak, ideértve

az internetszolgáltatókat, vezetéknélküli közösségi operátorokat, mikrooperátorokat (magukat a

felhasználókat) és mobilszolgáltatókat hogy a saját hálózatuk heterogenitása miatt felmerül®

m¶szaki éstársadalmi-gazdasági problémákat orvosolnitudják.

Az els® részben a felhasználói h¶ség hatását számszer¶sítem a hálózati szolgáltatók ár-

versenyére vonatkozóan. Egy olyan árazási mehanizmus is kidolgozásra kerül, amely lehet®vé

teszi, hogya hálózatiszolgáltatók megtervezzék bevételüket, míg afelhasználók közvetlenülbe-

folyásolhatjákazalkalmazottszámlázásimódszerkiválasztását. Amásodikrészbenavezetéknél-

küli közösségi hálózatokban fellép® gazdasági kölsönhatásokat elemzem. Megmutatom, hogy

az ösztönz® mehanizmusok helyes tervezése és a felhasználók sokfélesége el®segíti egy valóban

globális vezetéknélküli közösség kialakulását, miközben mind a felhasználók, mind a hálózati

szolgáltatók jól járnak. A záró részben a létez® TCP verziók teljesítménykorlátait vizsgálom

dinamikus mobilhálózatokban, a hirtelen kapaitás-növekedés esetére konentrálva. Továbbá,

mivelazeredményekkedvez®tlenek,egyúj,egyszer¶,végpont-végpont jelleg¶,ahirtelenkapai-

tásváltozástjól kezel®mehanizmust(TCPkiterjesztést) dolgozokki.

Thisdissertation marks the end ofa longjourney (and thestart of another), thereforeIwould

like to pay myrespets to anumberof peoplewhohelped mereah thesummit.

First,Iwould liketo thank myadvisor,Dr. Tuan A.Trinh (HSNLab),for hisguidane and

perseverane. Without hishelpthis dissertation wouldhave neverbeen ompleted.

Myspeialthanksgoesto Dr. András Veres (Erisson Researh). Having aresearhdisus-

sion withhimhasalways been inspiring andfun.

Iowe a greatdeal ofgratitude to Prof. AleksandarKuzmanovi (Northwestern University).

He hastaught menevertoaim low.

I would also like to thank Dr. Róbert Szabó (Head of HSNLab) for being supportive with

this dissertation.

Thanks to the olleagues and fellow students I have worked/rested/suered together with.

Espeially Sándor Kardos, László Toka, Dr. András Gulyás, Balázs Sonkoly, Felíián Németh,

Dr. Zalán Heszberger, Dr. Attila Vidás and Prof. József Bíró at HSNLab; Kristóf Fodor,

Miklós Aurél Rónai, MátéCsorba, Dr. Sándor Palugyai, Ákos Kovás, Zoltán Turányi, Gábor

Németh, Feren Kubinszky, Péter Tarján, Ágoston Szabó, Dr. Balázs Kovás and Dr. András

Valkó at Erisson Researh; and Ionut Trestian, Amit Mondal, Karl Deng and Ao-Jan Su at

Northwestern University.

At last,but foremost,mydeepestthanksaredueto myfamilyfor their ontinuoussupport.

To Mother,for heraring. ToFather, forbeingarole model. ToZsuzsi,forherloveand endless

patiene. Ilove you all.

1 Introdution 1

1.1 Researh Objetives . . . 3

1.2 Methodology . . . 3

1.2.1 Basinotions of gametheory . . . 4

1.3 Struture . . . 6

2 Priing InternetAess under User Inuene 9 2.1 Bakground . . . 10

2.1.1 Interneteonomis . . . 10

2.1.2 Brand loyalty . . . 11

2.2 PriingInternet aessinthe preseneofuser loyalty . . . 12

2.2.1 Motivation . . . 12

2.2.2 Assumptions . . . 14

2.2.3 Inentive to ooperate . . . 16

2.2.4 Dierentiated reservation pries . . . 19

2.2.5 Enhaned modelsof userloyalty . . . 22

2.2.6 Experimental evaluation . . . 24

2.2.7 Disussion onserviebundling . . . 33

2.3 User-inuenedpriing for Internet aessproviders. . . 36

2.3.1 User-inuened priing . . . 36

2.3.2 The votinggame model . . . 37

2.3.3 Equilibrium solutions. . . 40

2.3.4 Distribution of power. . . 44

2.3.5 Disussion onfeasibility . . . 46

2.4 Conlusion. . . 47

3 Inentives for Wireless Community Networks 49 3.1 Bakground . . . 51

3.1.1 Wireless ommunitynetworks . . . 51

3.2.1 Assumptions . . . 54

3.2.2 The mediator . . . 56

3.2.3 The user. . . 57

3.2.4 The Internet Servie Provider . . . 57

3.2.5 Tehnology penetration . . . 58

3.3 Equilibrium analysis . . . 60

3.3.1 One-shot usergame withhomogeneouspayments . . . 60

3.3.2 Evolutionary usergamewith homogeneouspayments . . . 63

3.3.3 One-shot usergame withheterogeneous payments. . . 65

3.3.4 The ISPgame. . . 67

3.3.5 Mediator: anoptimization problem . . . 69

3.4 Experimental evaluation . . . 70

3.4.1 Modeling usermobilityand relevane. . . 71

3.4.2 The evolutionarygame . . . 73

3.4.3 Simulationresults . . . 73

3.5 Conlusion. . . 77

4 Congestion Control in Dynami Mobile Environments 79 4.1 Bakground . . . 81

4.1.1 TCP variants for high-speed networks . . . 81

4.1.2 TCP performaneinwireless mobilenetworks . . . 82

4.2 Measuringhigh-speed TCP performaneduring mobilehandovers . . . 83

4.2.1 Emulationtestbed . . . 83

4.2.2 Handovermodel . . . 84

4.2.3 Measurement results . . . 87

4.2.4 Bueroverow probability at handovers . . . 91

4.3 SpeedDetet: handling suddenapaityinrease . . . 96

4.3.1 The SpeedDetet algorithm . . . 98

4.3.2 Parametertuning . . . 102

4.3.3 Measurement results . . . 104

4.3.4 Simulationresults . . . 107

4.4 Disussion onFAST . . . 109

4.5 Conlusion. . . 110

5.1.1 Contribution . . . 113

5.1.2 Appliation possibilities . . . 114

5.2 Inentivesfor wireless ommunitynetworks . . . 114

5.2.1 Contribution . . . 114

5.2.2 Appliation possibilities . . . 114

5.3 Congestion ontrol indynamimobile environments . . . 115

5.3.1 Contribution . . . 115

5.3.2 Appliation possibilities . . . 116

2.1 Demand funtionsfor

G ₁

G ₂

2.2 Bestresponsefuntionsof

G ₁

2.3 Referene senario: pries, prots andmarket sharesfor 2,3 and10 ISPs (deter-

ministi loyalty, fullyinformed,

L = 1

2.4 Pries,prots andmarketsharesfor2(

L = 0.05

L = 0.05

L = 0.15

10 ISPs (

L = 0.05

L = 0.15

L = 0.15

L = 1.0

10 ISPs (

L = 0.15

2.6 Pries,protsandmarketsharesfor3ISPs(

L = 0.05, 0.20, 0.35, 1.0

2 entrants, deterministi loyalty . . . 30

2.7 Pries, prots and market sharesfor 3 ISPs with fullyinformed (

L = 0.05, 0.35

and partiallyinformed users (

L = 0.05, 0.35

istiloyalty . . . 32

2.8 Total individual prots for 2 ISPs (

L = 0.05, 0.30, 1.0

deterministi loyalty . . . 33

2.9 Overallumulative protsof 2 ISPsat dierent loyaltylevels . . . 33

2.10 User-Inuened Priingmehanism (UIP) . . . 37

3.1 Interationsamongusers,ISPsandmediator(strutureoftheStakelbergmodel).

Solidlinesdenotediretinput(ost parameters andrevenue shares),dashedlines

denoteimpliit feedbak(outome ofsubgames, for subgame perfet design) . . . 55

3.2 Expetedrevenueforusersundervariousparameterssettings(defaultparameters:

c _o = 10, c _i = 5, α = 0.3, ρ = 2

3.3 Expeted revenue for users: heterogeneous vs. homogeneous payment struture

(all otherparameters xed) . . . 67

3.4 Expeted revenue for ISPs: lowand highrevenue shares(

β

3.5 Mediator payos: greedy vs. soial welfare (xaxis: revenue shares

(α, β)

ost parameters

(c _i , c _o )

3.6 Geographi distribution ofFON users inBerlin . . . 71

(u = 4, c o = 3, c i = 3, α = 0.5, µ = 0.001)

3.8 Evolutionofthe userpopulationandtheaverageinsiderrelevaneunderdierent

initial onditions (default parameters:

u = 4, c _o = 3, c _i = 3, α = 0.5, µ = 0.001

4.1 Measured round-trip timesduring ahandover . . . 80

4.2 Throughput of various TCP variants during intra-system handover (left), inter- systemup-swith (middle) and down-swith (right).. . . 88

4.3 NewReno reeiver-side time-sequene graph of data pakets. There is a bursty lossof pakets around10.14s,whih later areretransmitted. . . 89

4.4 A simplied TCP ontrol loop as seen by the sender. Data pakets leaving the senderS rstgetqueued(andpossiblydropped)atthebottleneklink,thenarrive at thelient C. There,ACK paketsaretriggered that travelbakto thesender. Base propagationdelay(

RT T

T _p

4.6 Buer oupation growth around thepeaks. Dashed linesmark buer growth in ase ofno linkoutages. Non-zerogrowth rates arealsonoted. . . 95

4.7 Buer overow probability of NewReno. (Note: Lowest value for

B

µT = 2

= 250

P (B p ) = 1

4.8 Measured buerdynamis (NewReno) . . . 97

4.9 Blok diagramofSpeedDetet . . . 100

4.10 Congestion windows duringhandover . . . 106

4.11 SD versus PNCD:

N = 20, K = 2

4.12 SD vs. PNCD:distribution ofdetetion time . . . 108

4.13 Throughputomparison withNewRenoasreferene . . . 109

4.14 RTT-fairness(lean run) . . . 110

4.15 Inter-protool fairnesswithNewRenoasreferene . . . 110

2.1 Payomatrix for thebasi game (inthousanddollars) . . . 13

2.2 Payomatrix for thebrand loyaltygame (inthousand dollars) . . . 13

2.3 Charateristi funtion for the user-inuened priing game (

w ₁

t ₁

w 3

t 3

2.4

ψ

3.1 Notationusedinthemodel . . . 54

3.2 ISPgame payos . . . 58

3.3 Simplied payomatrix for theISPgame . . . 68

4.1 Link parameters of radioaesstehnologies . . . 85

4.2 Emulated systemparameters . . . 86

Introdution

Designing the next-generation global network is a omplex task. What was one onsidered

a pure engineering problem has beome ross-disiplinary: engineers, eonomists, soiologists

and legal experts ooperate to propose eient methods for future networked systems. While

performane enhaning tehniques like ongestion ontrol are still very important as the

popularityof bandwidth-hungry andreal-time appliations andservies (lesharing, streaming

video, et.) isever-growing, soio-eonomi aspetsarebeominginreasinglysigniant [1℄.

Onthe otherhand, heterogeneity isinherently present inmultiple aspets of the wiredand

wireless Internet. Asaesstehnologies, network-enabled devies and end-usersthemselvesare

moreandmorediversied,heterogeneitywillonlygainevenmoremomentuminfuturenetworks.

Therefore, understanding, overoming or even exploiting this heterogeneityat dierent levels is

a fundamental goalfor researhers.

Heterogeneous networks aremanaged bya diverse olletion ofnetwork operators: Internet

ServieProviders,ommunitywirelessproviders,miro-providers(end-usersthemselves),ellular

mobile operators, et. Theseoperatorsfaevarious hallenges bothat thesoio-eonomialand

tehnial levels. This work fouses on a subset of these hallenges. First, the dissertation aims

to quantify the impat of user-behavior on Internet aess priing, and to propose a diretly

user-inuened priing mehanism. Seond, inentive shemes are studied whih enable the

global proliferationofa ommunitywireless network. Third,a novelTCP extension isproposed

and analyzed; this extension enables mobile operators and ontent providers to utilize eient

ongestion ontrolin dynamimobileenvironments.

Starting with the emergene of ommerial Internet Servie Providers (ISPs), ontinuing

in the dotom era, ulminating in today's feature-rih, appliation-driven, multimedia servies

network, prot-making is the single most-important driving fore behind the evolution of the

Internet. Understanding the eonomi proessesof theInternet is thereforeessential [2℄. There

is broad literature in the area of modeling interations between ISPs, most of these employ

game-theoretial tools [3℄ [4℄ [5℄. While these papers introdue and analyzeomplex models on

the interation of ISPs at dierent levels of the hierarhy, they mostly assume a very simple

user behavior model when investigating the market for last-mile ISPs: end-users hoose the

heapest provider assuming that the quality of the servie is the same. This assumption ould

beplausible inertainsenarios, butitouldbemisleadingifthereareloyalustomer segments

present inthemarket. Ontheotherhand, eonomistsarewell aware ofthenotion of onsumer

or brand loyalty, whih is very muh existing in realisti markets [6℄. Pratially speaking, a

ustomerisloyaltoabrand ifshepurhases theprodutofthatbrand,even ifthereareheaper

substitutions onthe market. Ifuser loyalty isgiven onsideration whenpriing Internet aess,

higher prots an be ahieved by the servie providers. Also, the ongoing network neutrality

debate [7℄ is driving a hange in priingshemes used by players of the Internet eosystem [8℄.

AessISPs arethinking abouttaxingontent providersfor arrying their ontent to end-users,

furthermore, they want to ap user's datatra inorder to operate protably. While ertainly

advantageous for aess ISPs, these shemes may not be optimal or even aeptable for users

and ontent providers. Furthermore, the global eonomi risis left providers worrying about

their revenues and users trying to utdown on their osts. Given theirumstanes, designing

a priing mehanism, whih lets ISPs plan their inome and gives users the possibilityto save

some money,is highlyrelevant.

User-provided networking hasseen its stok risingreently. While some see this onept as

aninterestingbut onlymoderatelyviablealternativetothetraditionalInternetServieProvider

entri paradigm, others believe ithasthe potential toindue aomplete shift inInternet om-

muniation patterns. The latter view an be justied by four important disruptive aspets of

user-provided networking. First, sine the end-user an share or sell her own resoures (e.g.,

onnetivity), thedistintion between end-user devie and network devie disappears. Seond,

thenatureofwirelessmedia,humanmobility[55℄andtheriseofmiro-operatorsreatetheneed

forprotoolsthatinherentlyhandleintermittent onnetivity,opportunistirelayingandsmooth

roaming. Third,user-provided serviesrequire traditionaltrustrelationships to be transformed:

soial networksoftrust shouldbeformedto ensurethewillingnessto ooperateandto maintain

network growth. And last, swift adoption of new tehnologies is possible as adopters are the

end-users themselves. Itis reasonable tobelieve thatthese novelharateristis andfuntional-

ities ould enable user-provided wireless networking to be the foundation of thefuture wireless

Internet. Existingworkon wirelessommunity networksfouses onuserpartiipation andom-

munity priing [56℄ [57℄ [58℄. Although FON [59℄ and wireless ommunity networks in general

show great promise, their ultimate suess dependson properly designed inentive mehanisms

for both users and ISPs. Thesenetworksshould be asmuh user-provided asISP-endorsed: a

dualsupport isessential to ahieve global wireless onnetivity.

With the proliferation of wireless ellular and ommunity networks, and more speially

evenmoredominant. High-speedwirelesstehnologieslikeUMTS,HSPA,LTE[80℄andWiMAX

are beoming reality, bringing broadband experiene to mobile users. The data rates of these

tehnologieswerealreadyrealizedandsurpassedinwirednetworksadeadeago,eventriggering

a urry of researh for making TCP (thedominant transport protoolof the Internet) apable

of utilizing high-bandwidth, high-delay network onnetions [81℄ [82℄ [83℄ [84℄. Also, there is a

signiantamountofworkonmakingTCPwireless-friendly[85℄[86℄[87℄[88℄[89℄. However,sine

new, broadbandwirelessnetworksaredeployedinanisland-likemanner,inter-systemhandovers

are beoming ommonplae. A handover between a GPRS and an LTE network means a link

apaity inrease of several orders of magnitude. This ould signiantly impat a number of

appliations, e.g., multimedia streaming over TCP [90℄ [91℄. Understanding the limitations of

existingTCP variants andproposing anewmehanismwhihan handlethese senarios well is

important,beauseuserexperieneansuerfromineienttransportprotools,drivingpeople

away from using mobile Internet. Mehanisms with expliit signaling introdue the need for

network support and additional overhead, and also have a low hane of deployment [92℄. In

order to ensure deployability and failitate adoption, the proposed sheme should be a simple,

easily implementable,server-side algorithm, adhering to theend-to-enddesign priniple.

1.1 Researh Objetives

The objetive ofmy researhis threefold.

(1) Quantify theimpat ofustomer loyalty onthepriingompetitionbetween Internet Ser-

vie Providers. Propose a priing mehanism for Internet aess, whih enables network

providerstoplanetheirrevenues,whileusersandiretlyinuenetheimplementedbilling

poliy.

(2) Understandthe eonomiinterations inwireless ommunitynetworks. Show thatproper

inentive design failitatestheemergene ofatrulyglobal wireless ommunity,whileboth

users and network providers protfrom the network.

(3) Understand the limitations of existing TCP versions in senarios of sudden apaity in-

rease. Propose a simple non-ongestion detetion mehanism whih solves this problem

eetively.

1.2 Methodology

TheresultspresentedinChapter2wereobtainedmainlybygame-theoretialanalysis[9℄. Quan-

tiationoftheimpatofustomerloyaltyonInternetaesspriingwasdonebyapplyingnono-

perfet equilibrium, Nash reversion). For proving the properties of the novel user-inuened

priing mehanism, I used ooperative game theory (transferable payos, ore,

ψ

Shapley value).

Eonomiinterations inglobalwirelessommunitynetworks(Chapter3)werealsomodeled

and evaluated with the help of nonooperative (one-shot game, Nash equilibrium, Stakelberg

game, subgame-perfet equilibrium,bakwardindution) andevolutionarygametheory(tness,

mutation, evolutionarily stable strategies) [60℄. Probability theory was used for modeling the

geographi relevanes of users. Extensive simulations were utilized for evaluating the extended

modelinludingusermobility,heterogeneouspaymentsandtemporalevolution. Real-worlddata

setswereusedasinputtothe simulations,e.g.,GPSoordinatesoftheusers'homes,population

densityand user mobility behavior.

ThemainresultsofChapter4werederivedfromtestbedmeasurementswithaworkingLinux

kernelimplementationoftheproposedmethods. ThelowerboundforFAST,andthemethodfor

SpeedDetet parameter tuning was derived byanalytial alulations. Larger sale throughput

and fairness evaluation was done by simulations in the well-known ns-2 framework using the

exat kernel implementation ode.

Sine we use game theoryextensively throughout the dissertation, we introdue some basi

onepts inthefollowing.

1.2.1 Basi notions of game theory

Here we present elements of lassial non-ooperative (players behave rationally and selshly,

i.e., maximize their individual prots) and evolutionary (in the biologial sense) game theory

we build upon throughout the dissertation. Note that onepts of ooperative game theory

used inSetion 2.3 aredened there to failitate understanding and the ow of reading. For a

omprehensive materialon gametheoryplease refer to [9℄and [10℄.

One-shot game

Also known as a stage game, this type of game assumes that players at at the same time

instant, therefore there is no ausality. A gamein strategi (normal) form an be desribed by

three elements:

•

i ∈ I

{ 1, 2, . . . , I }

•

s _i ∈ S _i

i

s _i

i

•

π _i

i

π _i (s)

s = (s ₁ , . . . , s _I )

A mixed strategy

σ i

i

− i

AgeneralsolutiononeptforgamesofeonomiinterestistheNashequilibriumsolution. A

Nashequilibriumisaproleofstrategiessuhthateahplayer's strategyisanoptimalresponse

to theother players' strategies.

Denition 1 (Nash equilibrium) A mixed strategy prole

σ ^∗

i

π i (σ _i ^∗ , σ ^∗ _{− i} ) ≥ π i (s i , σ ^∗ _{− i} ) ∀ s i ∈ S i .

A pure-strategy Nash equilibrium is a pure-strategy prole that satises the same onditions.

Pratially speaking, a strategy prole is a Nash equilibrium point, when no individual player

an geta higherpayobyunilaterallydeviating from it.

Note,thatweassumegamesofompleteinformation inthiswork,meaning thateveryplayer

knows the exat payofuntionsof otherplayers.

Stakelberggame

Also known asa leader-follower game, it introdues multiple stages. The leader ommits itself

rst,hoosesitsstrategy,thenthefollowersrespondsequentially. Note,thatweassumeobserved

ationsthroughout thedissertation.

TheStakelbergmodelanbesolvedtondthesubgame perfetNashequilibrium or equilib-

ria, i.e. thestrategy prolethatserveseahplayerbest,giventhestrategiesoftheotherplayers

and thatentailseveryplayer playing ina Nashequilibrium inevery subgame.

Denition 2 (Subgame-perfet equilibrium) Astrategy prole

s

Theusual method to ompute thisequilibrium isalledbakward indution.

Repeated game

Themostwidelystudied repeatedgametypeiswhenastagegameisrepeatedapossiblyinnite

number of times. An important feature of a repeated game is the way in whih a player's

preferenesmaybemodeled. Weusedisountedpayostomodelthatthevaluationofthegame

diminishes with time depending on the disount parameter

Θ

optimal strategysetisthesameasinDenition2,however, bakward indutionannotbeused

to derive it.

Onmany oasions, it isfound that the optimal method of playing a repeated game is not

optimum strategy. This an be interpreted as a soial norm. An essential part of innitely

repeatedgamesispunishingplayerswhodeviatefromthisooperativestrategy. Thepunishment

may be something like playing a strategy whih leads to redued payo to both players for the

rest of thegame (alleda triggerstrategy). Ifthepunishment strategy isa Nashequilibrium of

thestage game, the ation isreferredto asNash reversion.

Evolutionary game

Maynard Smith's evolutionary theoryoriginates from the appliation of the mathematial the-

oryofgamesto biologialontexts, arisingfromtherealizationthatfrequenydependenttness

introduesastrategi aspetto evolution. Reently,however, evolutionarygametheory hasbe-

omeofinreasedinteresttoeonomists,soiologists,andomputersientists,sineevolutionary

games an be adaptedto their domains. Themain dierenes inan original evolutionary game

ompared to a lassialgame are:

•

•

•

Pratially speaking,evolutionarygame theoryanalyzes theompetitionof strategies, with-

out emphasizingtheindividualplayers. Heneitssolution onept,evolutionarilystable strategy

(ESS).

Denition 3 (Evolutionarily stable strategy) A strategy

s _i

who adopts anotherstrategy

s _j

j 6 = i

Alongthelinesofpureandmixedstrategies, theonept ofamixed ESS emerges. However,

inthisaseithastwodierentinterpretations. EitheritisanESSinmixedstrategies,i.e.,every

individual plays the same mixed strategy; or the population is partitioned to groups playing

pure strategies, and relative group sizes represent the probability distribution assignedto pure

strategies. Thisseond interpretationis usedinthiswork.

1.3 Struture

Thebodyofthisdissertationisdividedintothreehapters. Thetopisoveredinthisdissertation

are somewhat heterogeneous from a related work and methodology point of view, hene we

Chapter 2 presents our eorts in quantifying user-inuene with regard to priing in the

Internet. We introdue basi game-theoretial onepts and relatedwork on Internet priingin

Setion 2.1. Setion 2.2 presents the impat of ustomer loyalty on theompetition of Internet

ServieProviderssellingaessto end-users. Afterharaterizingthisimpliiteet,wepropose

andevaluateanexpliitlyuser-inuenedpriingshemeinSetion2.3. Weonludethehapter

inSetion 2.4.

Chapter3 desribesinentive design inuser-provided and ISP-endorsedwireless ommunity

networks. We briey introdue evolutionarygame theory, and surveyexisting work on wireless

ommunity networks in Setion 3.1. We onstrut a Stakelberg game inSetion 3.2 modeling

the three levels of the deision hain in building wireless ommunities. We analyze the user

andISPgames,and givenumerial solutionstothe StakelberggameinSetion3.3. Wefurther

supportouranalytiresultswithdata-drivensimulationsinSetion3.4. Weonludethehapter

inSetion 3.5.

Chapter4 introduesourresults onTCPbehaviorindynamienvironments;furthermore, it

proposes and evaluates theend-point-only SpeedDetet extension to TCP thathandles sudden

apaityinreaseinasimpleandeientmanner. Setion4.1givesanoverviewonTCPversions

for high-speed andmobile environments. We present ameasurement study on high-speed TCP

performane during mobile handovers in Setion 4.2. Based on the ndings of this study, we

proposeandevaluatetheSpeedDetetextensiontoTCPinSetion4.3. Weonludethehapter

inSetion 4.5.

Finally, we summarize the ndings of this dissertation and outline their possible pratial

appliations inChapter5.

Priing Internet Aess under User

Inuene

Advanesinnetworkingtehnologyandaordableserviepriesareontinuingtomake Internet

aess available for billions of ustomers. To provide end-to-end network onnetion, Internet

Servie Providers (ISPs) form a hierarhy that spans from loal ISPs who sell aess to end-

users, through regional ISPs who onnet loal ISPs to the Internet bakbone, to Tier-1 ISPs

who form the bakbone, and are peering with eah other. The eonomi interations among

servie providers of dierent levels and end-users have been in the fous of interest for several

years. Furthermore, these interations will ontinue to get speial attention, sine initiatives

like theNSFFIND [1℄and EURO-NF[19℄ promote eonomiinentivesasarst-order onern

in future network design. Also, deision-makers trying to work out a plausible solution for the

reentlysurfaednetneutralitydebate[7℄wouldgreatlybenetfroman in-depthunderstanding

of eonomiproessesinside theuser-ISP hierarhy.

On the other hand, the net neutrality debate has shed light on some problems of Internet

ServieProviders(ISPs). Sineat-ratebillingisdominantandusertrakeepsongrowing[17℄,

ISPsgetlowerprots perdataunitarried. Aninreasing numberofnewsandstudiesreporton

thetehniquesISParebeginning tolookat andusetokeep themselvesprotable: theseinlude

tra disrimination, introduing download aps and experimenting with alternative priing

shemes (e.g., usage-based priing, three-part taris and harging ontent providers) [18℄. In

parallel,thereisanongoingglobaleonomirisisofunseenproportionsfoldingout inthereent

months. This downturn makes people think twie about spending more than they absolutely

have to. Consequently,ISPs may have to faethefatof dereasing popularityof their servies

among users. Sine eonomianalystsannot really preditthelength of theglobal risis,ISPs

have to preparefor a userdemand-driven market resulting indiminishingprots, andsimilarly,

ustomershave to minimizetheir Internet aessostsforan extendedperiod oftime.

The above developments indiate a lear need for the better understanding of the impat

of user-inuene on Internet aess priing. In this hapter we deal with two aspets of this

issue. In Setion 2.2, we investigate the impat of ustomer loyalty on thepriing ompetition

between loal ISPs who sellInternet aess to end-users, both qualitatively and quantitatively,

using game-theoretial models and simulation. We assume a single-servie setting, where ISPs

sell Internet aessas astandalone produt; we also disussthe importane of serviebundling

and its relevane to user loyalty. In Setion 2.3 we develop an expliitly user-driven priing

mehanism,and showhowuser-inuened priingan providetheISPwithalulable revenues,

whilegivingtheusers ahaneto lowertheir ostsvia votingfor theirpreferredpriingsheme.

Furthermore,wemodelthemehanismasaooperativeweightedvotinggame,deriveequilibrium

solutions,andinvestigate thedistribution ofpower. Weshowthatuserswithmediumgenerated

travolumearepivotaltotheoutome. Wealsodisussthepratialfeasibilityoftheproposed

mehanism. Setion 2.4onludes thehapter.

Resultspresentedinthis hapter arepublishedin[C6℄, [C5℄ and[J2℄.

2.1 Bakground

Here we give a briefoverviewon Internet eonomis and brand loyalty.

2.1.1 Internet eonomis

There isasigniant bodyofworkonInternetpriingmehanisms. Someof thepaperspropose

sophistiated priing models for ISPs to extrat onsumer surplus [20℄ [21℄ [22℄. Others argue

that simplepriing plansare theonlyviable ones, sine there isa learuser preferenetowards

them[2℄[23℄.ATCP-sessionbasedpriingshemeisproposedin[24℄. Bypresentingtheuserwith

ost andprie information,theproposedsysteman be usedforost reovery andto enourage

eient use of network resoures. In another paper [25℄, authors propose a responsive priing

method based on the urrent utilization of network resoures. They show how this method

puts ontrol of network servie bak to the users. A simple solution for priing dierentiated

serviesisproposedin[26℄. Asmart-marketmehanism,whereusersbidfortheusageofnetwork

resouresisintrodued in[27℄. Authorsof[20℄ritiquethewelfare-optimizing paradigmonthree

grounds: marginalostpriesmaynotproduesuientrevenuetofullyreoverostsandsoare

perhaps of limitedrelevane, ongestion ostsare inherently inaessible to thenetwork and so

annotreliablyformthe basisfor priing,andthatthereareothermorestrutural goalsbesides

optimality. In [28℄ authors establish the Prie of Simpliity (PoS) referring to the dierene

in revenues between a simple priing sheme (at-rate) and the maximum ahievable revenue.

Furthermore, they haraterize a rangeof environments, where PoS islow, i.e., at-rate priing

ThereisalsobroadliteratureintheareaofmodelingeonomiinterationsbetweenISPswith

game-theoretial means [3℄ [4℄ [5℄. While these papers introdue and analyze omplex models

for the interation of ISPs atdierent levels of thehierarhy,they mostlyassumeaverysimple

userbehaviormodelwheninvestigatingthemarketforloalISPs: end-usershoosetheheapest

provider assuming that the quality of the ertain servies is the same. Thisassumption ould

beplausible inertainsenarios,but itouldbemisleadingifthereareloyalustomer segments

present inthe market.

2.1.2 Brand loyalty

Eonomists are well aware of the notion of onsumer or brand loyalty, whih is very muh

existing in realisti markets. Pratially speaking, a ustomer is loyal to a brand, when she

purhases the produt of that brand, even if there are heaper substitutions on the market.

Brand loyalty is rooted in both satisfation towards a given brand and ustomers' relutane

to try substituteproduts. Moreover, the often-debated endowment eet [29℄ ouldalso be in

play; losing something you have owned hurts more than it feels good to gain something new.

Thisovervaluation ofsomeone'sownproperty ouldbea fatorinbrand loyalty.

There is existing work dealing with lassiation of buyers into loyalty groups [30℄, and a

reent study develops and empiriallytests amodel ofanteedents of onsumerloyaltytowards

ISPs [31℄. In [6℄ authors use a game-theoreti framework to prove that if loyalty inreases

withmarketshareand penetration,ustomer retention strategiesseem tobeonsequently more

eient for market leaders. An other study [11℄ analyzes a duopolisti prie setting game in

whih rms have loyal onsumer segments, but annot distinguish them from prie sensitive

onsumers. Theydemonstrate thatonsumerloyaltyplaysanimportant roleinestablishingthe

existene andidentityof aprie leader.

The latter two papers provide valuable insight to the impat of brand loyalty on ertain

markets, butalso inspireforfurtherinvestigations. Firstofall,howdoesustomer loyaltyaet

the dynami market of Internet aess? Seond, authors of [11℄ only onsider perfetly inelas-

ti demand and a single reservation prie for the whole ustomer population. While these two

assumptionsmayholdinertainsenarios, arethey validifonsidering theInternetaessmar-

ket in developing ountries or an eonomially dierentiated Internet user population? Third,

are there inentivesfor ooperative priingregarding loalInternet Servie Providers ina mar-

ket where user loyalty is present? And last, is the simple model, whih is ommonly used in

game-theoreti frameworks,a good representation ofreal-world brand loyalty? Can thereal-life

behaviorof ustomers(suh as sensitivity to the prie dierene between providers and uner-

taintyintheirdeisions)beinorporatedintoabetterusermodel? Wearguethatndinganswers

tothese questionsan bringuslosertotheunderstanding ofeonomiinterations amongISPs

involving ustomer loyalty intheir future investigations.

2.2 Priing Internet aess in the presene of user loyalty

Soio-eonomi aspets of future ommuniation networks suh as priing models for network

providers, network neutrality, and Quality of Experiene (QoE) are beoming more and more

important as the onvergene of networks is inprogress. All the above areas share a ommon

interest: the deeper understanding of user behavior. As a step towards a more realisti user

model, we investigate ustomer loyalty and its impat on the priing ompetition of Internet

Servie Providers(ISP) whosellInternet aess toend-users.

Themainontributionofthis setionistwofold. First,we analyzetheimpatofuserloyalty

withgame-theoretial meansmotivatedbytheBertrand game. Weshowhowloyaltyintrodues

anewequilibriuminarepeatedgamesettingresultingintheooperationofISPs. Furthermore,

we investigate thease of a dierentiated ustomer population by introduing dualreservation

values,and showhow itleads tonew, purestrategy Nashequilibria indiating thatISPsshould

makethemostoutoftheirrespetiveloyaluserbase. Seond,we onstruttwo novelmodelsfor

ustomer loyalty inorporating two important aspets of the users' purhasing deisions: prie

sensitivityandinherentunertainty. Weevaluatetheimpatofuserloyaltythroughthesemodels

byextensivesimulationsinanumberofrelevantsenarios. Inpartiular,weshowhowthehigher

levelofloyaltyinthe userpopulationleadstolarger protsforISPs. Wearguethatourndings

an motivate network researhers to inorporate a ner-grained user behavior model in their

investigations on priingmodels ofnetwork servies andother soio-eonomi issues.

2.2.1 Motivation

First, we showan example on the eet of loyalustomers througha simple game, and seond,

we justifythe existeneofa loyaluser segment inthe Internet aessmarket.

Brand loyalty

To illustrate theeet of brand loyalty we onsider the following game [32℄. Suppose there are

tworestaurantssellingpizzainapartiulargeographimarket. Supposetheyeahonsiderthree

possible priesfor pizzas: a highprie (H), amedium prie (M)anda low prie(L). The prot

per produtisknowntobe$12,$10 and$6 foreah rmregardlessofthevolume ofsales. Also

let us assume a perfetly inelasti demand funtion,

D(p) = 10000

pizzas without regard to its prie. The game is similar to the Bertrand game as if the pries

of the two rms are dierent all demand goes to the lower pried rm, and if the pries are

equal, rms split the market evenly. It is easy to see that

(p ^∗ ₁ , p ^∗ ₂ ) = (L, L)

Table2.1: Payo matrixfor thebasi game (inthousanddollars)

H M L

H

(60, 60) (0, 100) (0, 60)

M

(100, 0) (50, 50) (0, 60)

L

(60, 0) (60, 0) (30, 30)

Table 2.2: Payomatrix for the brand loyalty game(inthousand dollars)

H M L

H

(60, 60) (36, 70) (36, 42)

M

(70, 36) (50, 50) (30, 42)

L

(42, 36) (42, 30) (30, 30)

Now, we hange the game a little bit, and introdue brand loyalty, suh as the rm with

thehigher prie losessome but not all of itsustomers to thelower pried ompetitor. Assume

that eah rm has a loyal ustomer base that buys

3000

for the remaining demand of

4000

(p ^∗ ₁ , p ^∗ ₂ ) = (M, M )

underuttheprieoftheotherrminordertostealmarketshare. Thegameabovedemonstrates

qualitativelyhowtheexisteneofbrandloyaltyanaettheoutomeofthepriingompetition,

byhangingthe equilibriumpoint.

Loyalty in the ISP market

A reent empirial surveybythe Walkerompanydemonstrates theexistene ofuser loyaltyin

thewiredandwirelessISPmarket[13℄. First,itpointsouttheexisteneofatrulyloyalustomer

segment (around 38%) whih tolerates higher pries, and is likely to pay for new servies and

looks for along-term business relationship. Onthe otherhand, there arehigh risk ustomers

(around 30%)who arewillingto swithproviders at theearliestopportunity,andare drivenby

both lower pries and individual behavior. Seond, while 78% of the ustomers are satised

withtheserviethey get, only theabove-mentioned 38%aretruly loyal, henethere ismore to

loyaltythan beingsatised (again, behavioral patterns). Third, it is shownthat ISPs with the

most loyal ustomers (loyalty leaders) an expet signiantly larger revenues, faster growth

and higher stokprie performanethan their ompetitors. Inaddition, a numberof otherISP

surveys agree on the existene of loyal user bases in various geographi regions, suh as the

United States, the United Kingdom and Taiwan [31℄ [33℄ [34℄. They point out that the most

importantfatorsinhoosingaservieproviderisprie,pereivedvalueandserviesatisfation.

priingInternetaess. However,theexistingliteratureassessingthepriingompetitionamong

Internet aess providers (loal ISPs) does not take brand (or user) loyalty into onsideration

resulting in an overly simplied user model. This may lead to impreise statements regarding

equilibrium properties. But what is the partiular quantitative impat of user loyalty on loal

ISP priing ompetition? We apply the simple, stati loyalty modelused both in the pizza

game and [11℄ to the senario of multiple loal ISPs ompeting in prie to attrat ustomers

(users) to showhowloyalty ouldintrodue new equilibria, and how ooperation between ISPs

ould emergeinthe preseneof loyalty. Later inSetion 2.2.5, we addressseveralshortomings

ofthestatiloyaltymodelandintrodue twonovelmodels,whihenableusto inorporatemore

realisti user behavior to priing ompetition. These new models are inspired by the above

empirialsurveys: theyapturetheeetofpriedierene andongenitaluserbehavioronthe

loyaltyoftheuserpopulation. Weshowtheimpliation ofthesemodelsto aesspries,market

sharesand long-term prots bymeans of simulation inSetion 2.2.6.

2.2.2 Assumptions

Before gettinginto thedetails,we herebyjustifyour assumptionsusedinthegames throughout

this work. Notethat the loyaltymodel used inthegames below is similarin nature to theone

used inSetion 2.2.1. There isa xedloyal user base for eah ompeting servieprovider, and

there is anadditional group ofpotential users, not tied to anyrm, seekingthelowestprie on

themarket.

Flat-rate subsriptions

There are repeating patterns in the history of ommuniation tehnologies, inluding ordinary

mail, the telegraph, the telephone, and the Internet. In partiular, the typial story for eah

servieis thatqualityrises, pries derease, andusage inreases to produe inreased total rev-

enues. At thesame time,priingbeomessimpler [2℄. Solutions aimingtoprovide dierentiated

servielevelsand sophistiatedpriingshemes areunlikelyto be widelyadopted. Ontheother

hand, prie and quality dierentiation are valuable tools that an provide higher revenues and

inrease utilization eieny of a network, and thus in general inrease soial welfare. It is

also shown that at-rate priingwastesresoures, requires light users to subsidize heavy users,

and hinders deployment of broadband aess [35℄. However, it appears that as ommuniation

servies beome less expensive and are used more frequently, those arguments lose out to us-

tomers' desire for simpliity, so ISPs oer at rates, even if it is not revenue-maximizing [28℄.

Until there is widespread network-level arhitetural support for dierentiated priing in the

Internet, a signiant hange in these patterns is not foreseen. Additionally, mobile network

KDDI'sat-rateplanfortheirCDMA2000(CodeDivisionMultipleAess)system[36℄andNTT

DoCoMo'sfortheirhigh-speedFOMA-based(FreedomofMobileMultimediaAess)i-modeser-

vie [37℄. Nowadays, thanks in a large part for multimedia ontent, mobile at-rate plans are

availableworldwide. Furthermore,non-at ratebillingisalsoresoureonsumingfromaservie

provider'sviewpoint [38℄. Alloftheabove,andthefatthatmostInternetaessprovidersoer

at-rate subsriptions for end-users today, motivates us to assume a at-ratepriing sheme in

our models.

Consumer demand for Internet aess

Theprie elastiity ofdemandfor apartiular demandurveisgreatly inuenedbythedegree

ofneessityorluxury: luxuryprodutstendto have greater elastiitythanneessities. Thepro-

portionofinomerequiredtopurhaseaserviealsoplaysakeyrole: produtsrequiringalarger

portion of the onsumer's inome tend to have greater elastiity [39℄. These two observations

suggest that ina developed ountry, where inomes are high, Internet aess is ubiquitousand

peopletendto lean onthe Internet bya great degree(in their work andalso duringtheir spare

time), almost every household has Internet aess, so the demand an be modeled asonstant

(perfetly inelasti)[40℄. Onthe otherhand,marketsindeveloping regionsarehighlypriesen-

sitive, sine people have lower inomes, and thenumber of Internet subsriptions wouldgreatly

benetfromlowerpries. Therefore,the demandfor Internet aessinsuhregionsan bebest

modeled aselasti. We usetheinelasti modelinSetion 2.2.3 to omplywiththeassumptions

of [11℄,while weinvestigate both ofthem inthegames ofSetion 2.2.4.

Reservation priesof ustomers

Consumer population is heterogeneous in the sense that ertain groups are willing to pay dif-

ferent amounts of money for the same servie. In thedream world ofISPs, in whih they were

able to perfetly identify thereservation prie of eah ustomer in themarket, they ouldoer

individually dierentiated pries, thus squeezing o every ent from the users. Suh a perfet

identiation of reservation priesis not likely inthereal world. However, thereservation prie

ofexistingustomersisgenerallyhigherthan thatofnewustomers, beauseexistingustomers

tend to exhibit higher swithing osts and also higher brand preferene for that produt [41℄.

Furthermore, most oftheanalytial literature on prie disrimination hasfound that itis opti-

mal to penalize loyals withhigher priesthan swithers [12℄ [42℄. While we do not introdue

targetedpriingtoour models,westillassumethatloyalusersinherently tolerateahigherprie

than swithers, who are only interested in disount pries. This way, we usedual reservation

values inSetion 2.2.4 to represent the heterogeneity of the user population. In Setion 2.2.3,

In allases, reservationpries areassumedto be ommon knowledge.

Quality of servie and apaity expansion

Network apaity and the user's demand for bandwidth are related to the qualityof servie in

omputer networks. A signiant inrease of a singleISP's userbase might auseongestion in

the ore network thus reduing the quality of experiene for other users. Suh a degradation

in servie quality might results in theloss of ustomer satisfation and so it an aet loyalty.

Throughout this work, we assume homogeneous quality of servie levels among all ISPs. For

analytial tratability,we assumethat theabove-dened ongestion isnegligible, and swithing

usersexperienethesamepereivedserviequalityaftertheswith. Furthermore,inthissetion

we make theassumptionthat every singleISPisprepared to handlethewholeuser population,

i.e., they have the infrastruture and apability to servie the entire market without loss of

quality. In Setion 2.2.6 we relax this assumption and integrate the need for network apaity

expansion into themodel.

Additionally, we assume that the marginal ost of apaity is onstant (zero) for all ISPs.

This roots inthe previous assumption: ISPs have built up enough apaityto handle all users

at one. Setting the marginal ost to a onstant is reasonable for alarge rangeof demand, but

growsinstepsafterreahingsomeritiallimit[39℄. Basially,weassumethatthesystemalways

operatesintherangewhere the marginal ost isonstant.

Although the payo funtions of ISPs are pretty simple in this work, they are inline with

at-rate priing, onsumer demand elastiity and reservation values disussed above, and thus

they suit ourneeds.

2.2.3 Inentive to ooperate

Herewepresentasingle-shotgameofuserloyaltywhihwasintroduedin[11℄. Later,weextend

thisgametoaninnitelyrepeatedgame,andshowhowaooperativemaximumanbeenfored,

where the long-term prot of ISPs are higher than that of playing the equilibrium strategy of

thestage gamein eah round.

The stage game

Consider a market with two loal ISPs ompeting in pries for a xed number of ustomers.

Customers aresplit into three partitionsupon their brand loyalty: the rst group onsistsof

l ₁

ustomerswho areallloyal to ISP

1

1

p ₁

reservationvalue

α

₁

Internet aess. The seond grouponsists of

l ₂

₂

ontains

n

α

(p 1 = p 2 < α)

ISP

1

2

simultaneously,thenustomersmaketheir hoies. Thisgameisreferred toas

G ₀

Note, that though values

l ₁ > 0

l ₂ > 0

α > 0

bership of a given ustomer annot bedetermined, so there is no prie disrimination possible.

Furthermore, forsimpliitywe assumeaonstant unitostofzeroforbothrms,and thatISP

1

hasthelargerloyal userbase,

l ₁ > l ₂

Given the above andthat

p ₁ ≤ α

p ₂ ≤ α

₁

π ₁ (p ₁ , p ₂ ) =



 



 



(l ₁ + n)p ₁ p ₁ < p ₂ (l 1 + 0.5n)p 1 p 1 = p 2

l ₁ p ₁ p ₁ > p ₂

(2.1)

Itanbeshown(see[11℄and[12℄)thatthisgamehasauniqueNashequilibriuminmixedstrate-

gies. In this ase, equilibrium prots are

π 1 = l 1 α

π 2 = ^l _l ² ₁ ⁺ⁿ _+n l 1 α.

equilibriumhasshiftedompared tothe simpleBertrandgamewithoutonsumerloyalty(whih

is (0,0)inase ofzero produtionosts), both partieshaving apositivepayoinequilibrium.

The repeated game

Now, we extend the previous model, and show that the innitely repeated

G ₀

perfet equilibrium, whih an be enfored by a threat strategy, namely the Nash equilibrium

strategy of the stagegame

G ₀

In the following we onstrut

G _r

G ₀

ounted at step

k

Θ < 1

disountedpayoinanystepisboundedby

α(l ₁ +n)

priniple to prove sub-gameperfetionof agiven strategy set.

Now,ifthetwoprovidersooperateandsettheirpriesequaltothereservationvalue

α

willshare"swithers"equally,inadditiontokeepingtheirownloyalusers. Thiswaytheirpayos

(

π

π

π ₁

= (l ₁ +0.5n)α > π ₁

= l ₁ α

and

π

₂ = (l ₂ + 0.5n)α > π ₂

= ^l _l ^{2 +n}

1 +n l ₁ α

n > l ₁ − 2l ₂

of thetwo ISPsis themaximumahievable

(n + l 1 + l 2 )α

for both parties. Ifsomehow one ISPtries to grab thewholefree marketina singlestep

k

otherISPan ounterat fromstep

k + 1

G ₀

on,whihresults ina dereasedpayofor thetraitor. We showthatthisNashreversionassures

sub-game perfetion forthe following strategy prole under thestated onditions.

Proposition 1 The strategy prole Cooperate until the other player deviates and then play

aordingto theequilibrium in

G ₀

G _r

n > l ₁ − 2l ₂

Θ > ¹ ₂ + ^{l 1 −}

n+l 1 n+l 2 l 2

2n

Proof: A strategy prole issub-gameperfet,ifthefollowing holds:

π _i

(k, ∞ ) > π _i

(k) + π _i

(k + 1, ∞ ),

meaning that the sum prot is greater if there is no deviation from theagreed strategy. If we

assumethat ISP

2

X ∞

i=k

Θ ⁱ π

₂ > Θ ^k π ₂

+ X ∞

i=k+1

Θ ⁱ π ₂

.

After solving (2.3)for

Θ

Θ > π

₂ − π

₂

π ₂

− π ₂

.

The one-stepdeviation at step

k

ǫ > 0

and harging a prie of

α − ǫ

π

₂ = (l ₂ + n)(α − ǫ)

substitutedierent payos for ISP

2

Θ ₂ > 1

2 + l ₁ − ^n+l _n+l ¹ ₂ l ₂

2n .

If ISP

1

Θ ₁ > ¹ ₂

l ₁ > l ₂

Θ ₂ > Θ ₁

Θ > ¹ ₂ + ^{l 1 −}

n+l 1 n+l 2 l 2

2n

The optimal deision of ISPs lies in evaluating the assumption inequalities. For Player 1

(larger loyal userbase) it isalways better to ooperateand try to ahieve sub-game perfetion.

For Player 2it is a matterof loyal user basesize: if

n > l ₁ − 2l ₂

If not, thenshe will play the

G ₀

the

G ₀

While expliit ooperation may be illegal, this inentive may lead to disussions between

servie providers. Note, that a two-ISP setting may seem artiial, it is ertainly not, e.g., a

large fration of Internet users in the US an only hoose between the loal able and phone

ompany. Moreover, there is some speulation about a artel-like ooperation among large

players in the US Internet market [43℄. Wu mentions that in the United States and in most

of the world, a monopoly or duopoly ontrols the pipes that supply homes with information.

These ompanies, primarily phone and able ompanies, have a natural interest in ontrolling

supply to maintain prie levels and extrat maximum prot from their investments, similar to

how OPEC sets prodution quotas to guarantee high pries. While this phenomena is rooted

innetneutralityandprotetinginfrastrutural investment,sine itinvolvessettingmanipulated

2.2.4 Dierentiated reservation pries

Here we onstrut and analyze single-shot games modeling the priing ompetition between

loal ISPs ghting for ustomers with dierent reservation pries. First, we deal with thease

of inelastidemand, and later,we introdue elasti demand.

Inelasti demand

Weneedtohangethesingle-shotgame

G ₀

We onstrut

G ₁

α ₁

α ₂

α ₁ < α ₂

α

funtion for

G 1

D(p) =



 



 



n + P _N

j=1 l j 0 ≤ p ≤ α 1

P _N

j=1 l _j α ₁ < p ≤ α ₂

0 p > α 2

(2.6)

where

p

N

funtion an be seen in Figure 2.1(a). From that, we an dene the payo funtion

Π _i (p _i )

ISP

i

Π _i (p) =



 



 



p _i l _i + _m ⁿ

p _i = min _j p _j ≤ α ₁ p _i l _i min _j p _j < p _i ≤ α ₂ 0 p _i > α ₂

(2.7)

where

m

equally.

Proposition 2 Consider

G 1

N = 2

A = nα 1

B i = (α ₂ − α ₁ )l _i

i = 1, 2

1.

(p 1 , p 2 ) = (α 2 , α 2 )

A < B 1

A < B 2

2.

(p ₁ , p ₂ ) = (α ₂ , α ₁ )

A < B ₁

A > B ₂

3.

(p ₁ , p ₂ ) = (α ₁ , α ₂ )

A > B ₁

A < B ₂

4. There isno pure strategy Nash equilibrium if

A > B 1

A > B 2

Proof:

1)If

A < B ₁

A < B ₂

α ₂

is noinentive to inreasetheir priessine anyinrease will resultinzeroprot. Furthermore,

there is no inentive to derease their pries, sine their prot at

p = α ₂

α ₁ < p < α ₂

0 ≤ p ≤ α ₁

p = α ₁