Experimental evaluation - Priing Internet aess in the presene of user loyalty

2.2 Priing Internet aess in the presene of user loyalty

2.2.6 Experimental evaluation

We have developed a simulator to study the impat of the novel loyalty models. Simulations

analyze the behavior of ompeting loal ISPs. Eah ISP has some end users, a share of the

market. We suppose that the overall demand funtion for their servies is onstant: no users

enter or leave the market. This model is relevant to a saturated market, where everybodyan

aordtohaveInternetonnetivity,andInternetonnetivityisamust(seetheinelastiasein

Setion2.2.4fordetails). Wesupposethattheusermarketisinnitelydividableamongthexed

number of ISPs. The total end user market is normalized to 1,e.g., if there aretwo ISPs with

equal market share,thenboth ofthem have a marketshare of 0.5. ISPs ompetefor ustomers

bysettingtheir aesspriesineahround. Thepriingshemeusedis at-rateandwe assume

ahomogeneoususerpopulation(single,ommon reservationprie). ThelowestprieanISPan

set for a round is 0, while the highest prie is 100, whih orresponds to the reservation value

ommon to allusers. Note, that these priesaresymboli, representing thepossible lowestand

highestprie an ISPwould onsider.

Before the rst round, the loyalty model, the threshold

L

^, ^the ^disount ^fator

θ

^for ^future

prots and initial market shares are set. In eah round, end users may migrate from their

respetive provider with regard to the applied loyalty model (see Setion 2.2.5). Swithers

hoose their next ISP aording to two possible migration poliies: informed and greedy. The

ISP.For simpliity weassumethat ifthere aretwominimally-pried ISPs, halfofthemigrating

users joins one and the other half joins the other one. The greedy poliy represents a

partly-informeduserbase,whereusersswithtosome heaperISPtheyknowof. ThiswayalltheISPs

who announeaprie lower than their urrent ISPdraw someusers away.

Ineahround theISPs tryto maximizetheirinstant prot. Every ISPusesthesamesimple

andgreedystrategy. Theysupposethatthepriesoeredlastbytheirompetitionstaythesame

for the next round. Withthis in mind,they alulate their projeted marketshare hange and

prot by probing all possible priesthey an set, and nally, they hoose theprie thatwould

maximize their protinthe next round andthen playit.

The results presented in this setion are intended to point out some interesting issues

on-erning the impat of user loyalty on the priing ompetition of ISPs in dierent senarios. In

senarios where the stohasti loyalty model was used, every data point represents an average

of 10 simulation runs. Furthermore, parameter

σ

^(standard^deviation) ^was ^set ^to

0.5

^; ^this ^way

variations due to the stohasti behavior an be visualized eetively. The simulator ode is

availablefor download [45℄.

Referene senario

First, we lay down a referene senario whih serves as a baseline for theupoming

investiga-tions. Theparameter settings are: deterministi loyaltymodel, fully-informed migration poliy,

threshold

L = 1

(zero-level user loyalty and no administration onstraint for the ISPs), equal initial market sharesand disount fator

θ = 0.995

^. ^Results^for ^two, ^three ^and ^ten^ISPs ^an ^be

seenin Figure2.3.

Inthe aseof two ISPs,theplayers donot dare toinrease their pries, beause theywould

lose all of their ustomers if they did so. On the other hand, it is not worth dereasing the

pries, beause the prot inrease aused by gaining a larger portion of the user base does not

ompensate for the loss aused by dereasing the prie. Therefore, pries, prots and market

sharesstay thesameduring the game.

However,withthree ISPs,the situationhanges. Astwothirdsofthemarketbelongsto the

ompetition, itlooks promising to derease the prie,and grab alarger market share.

Unfortu-nately, allthe players think the same,whih leads toa prie war, andpriesfall quikly.

WithtenISPs,weseeasimilarproess. Whatseemssurprising, isthatthedereaseofpries

isslowerthan in the 3-player ase. Onewouldexpetthatlarger ompetitionleads to aquiker

prie war. However, withmore ISPs,the users attrated from eah ofthem add up,soyou an

grabthe same total numberof users witha smallerdierene inprie. On theother hand,you

ISP1 ISP2 ISP3 ISP4 ISP5 ISP6 ISP7 ISP8 ISP9 ISP10

(i)

Figure2.3: Referene senario: pries, protsandmarketsharesfor2,3and10ISPs

(determin-isti loyalty, fullyinformed,

L = 1

^,^equal ^initial ^market^share)

beause of at-rate priing; we hoose to depit both in the following senarios to failitate

understanding.

Degree of loyalty/swithing osts

Now, we set

L

^below

1

^introduing ^user ^loyalty ^and administrative onstraints to the system.

Comparing the results inFigure2.4 to thereferene senariothere aremajor dierenes.

First, looking at the 2-player ase, ISPs inrease their respetive pries to the maximum

in the rst round, and this prie stabilizes. This is beause users move muh slower now, so

whatever theprie dierene is, ISPs make more money by getting the most out of their loyal

0 20 40 60 80 100 120

Prices

Round

ISP1 ISP2 ISP3

(d)

0 20 40 60 80 100

0 20 40 60 80 100 120

Profits

Round

ISP1 ISP2 ISP3

(e)

0 0.2 0.4 0.6 0.8 1

0 20 40 60 80 100 120

Market shares

Round

ISP1 ISP2 ISP3

0 20 40 60 80 100 120

Prices

Round

ISP1 ISP2 ISP3 ISP4 ISP5 ISP6 ISP7 ISP8 ISP9 ISP10

(j)

0 20 40 60 80 100

0 20 40 60 80 100 120

Profits

Round

ISP1 ISP2 ISP3 ISP4 ISP5 ISP6 ISP7 ISP8 ISP9 ISP10

(k)

0 0.2 0.4 0.6 0.8 1

0 20 40 60 80 100 120

Market shares

Round

ISP1 ISP2 ISP3 ISP4 ISP5 ISP6 ISP7 ISP8 ISP9 ISP10

(l)

Figure 2.4: Pries, prots and market sharesfor 2 (

L = 0.05

^), ³ ⁽

L = 0.05

^and

L = 0.15

⁾ ^and

10 ISPs (

L = 0.05

^),deterministi loyalty

Althoughtheproess startsthesamewaywiththreeISPs and asmallthreshold, itisworth

starting to dereaseyour pries fromthe maximumprie to grab a larger marketshare. When

all the players reah a relatively low prie, they see that they an make the highest prot by

taking advantage of their loyal userbase, and it is worth inreasing theprie to the maximum.

This proess is repeated periodially resulting in a sawtooth pattern. With a larger threshold

(meaninglessloyalusers),alargeruserbaseanbeattratedwithasinglederease. Thisenfores

larger dereases, and also brings the ruial prie lower. Note that the main harateristis of

theurvesremainthe same.

WithtenISPs(due tothesamereasonsaslistedinthereferenesenario)asmallerderease

inprieisenoughtoattratthesamenumberofusers,thereforethepriedereaserateisslower.

Stohastiloyalty

Letushange theloyaltymodeltothestohastitypewithstandarddeviationxedat

0.5

^. ^Now

wesetparameter

L

^to^dierent^values^and^observe^the^simulation ^results^presentedⁱⁿ^Figure^2.5.

Notie how pries utuate wildly beause of the random-like number of swithers: the

sawtooth patternan still be reognized,but priesarenot drivento thehighestpossiblevalue.

This phenomenon has two reasons: rst, inany given round it may be more beneial for the

ISP to emphasize milking its loyal users than lowering its pries to attrat newustomers, and

vie versa; seond, every data point in Figure 2.5 is an average of ten simulation runs whih

smoothsout theurves,but is absolutelyneededto identify harateristi behavior.

Inthe ases, where

L

^is ^low, ^pries, ^prots ^and ^market ^shares^utuate ^around ^their

deter-ministi ounterparts (see Figure 2.4). However, when we assoiate zero administrative ost to

swithingISPs(

L = 1.0

⁾ ^things^hange. ^There ^is^randomnessⁱⁿ^pries^and^market^sharesⁱⁿ^the

rst few rounds, but priesfall to their minimumand staythere making market sharesfreeze

at a given level. This level is lose to the fair share, but ISP

1

^has ^some ^disadv^antage. ^What

happenshereisthatthe stohastiityofuserloyaltyisnotsigniant enoughto movethepries

from their minimum, sothe marketonserves itsstate after theinitial utuations.

Inumbent vs. entrants

In an attempt to study an inumbent-newomer ISP setting we set theinitial market share of

ISP

1

^to

1.0

^. ^W^e ^get ^bak ^to ^the deterministi loyalty model, and investigate how the loyalty level impats the prie war between the inumbent and the two entrants. Results are depited

inFigure 2.6. ISP

1

^is^the^inumbent ^provider.

It an be seen generally that entrant ISPs start grabbing the market from ISP

Round

ISP1 ISP2 ISP3 ISP4 ISP5 ISP6 ISP7 ISP8 ISP9 ISP10

(l)

Figure 2.5: Pries, prots and marketsharesfor 2(

0 20 40 60 80 100 120

Profits

Round

ISP1 ISP2 ISP3

(b)

0 0.2 0.4 0.6 0.8 1

0 20 40 60 80 100 120

Market shares

Round

ISP1 ISP2 ISP3

0 20 40 60 80 100 120

Prices

Round

ISP1 ISP2 ISP3

(g)

0 20 40 60 80 100

0 20 40 60 80 100 120

Profits

Round

ISP1 ISP2 ISP3

(h)

0 0.2 0.4 0.6 0.8 1

0 20 40 60 80 100 120

Market shares

Round

ISP1 ISP2 ISP3

Figure 2.6: Pries, protsand market sharesfor 3 ISPs (

L = 0.05, 0.20, 0.35, 1.0

^), ¹ ^inumbent,

2 entrants, deterministiloyalty

dierent ompetition patterns. A highly loyal user population result in a low amplitude prie

utuationand fairlong-timemarketsharesfor allthree providers. A slightly moremobileuser

baseresults insharperpriehanges andperiodially evolvingmarketshares.

L = 0.35

^,^prie^utuations^are^at^the^extreme,alternatingbetweenveryhighandverylow pries. Thisis dueto thefatthat

L

^multiplied^by^the^number^of ^ISPs^is^larger ^than

1

^meaning

that the market an be ompletely redistributed in a single round. This results in a highly

unstable system. One would expet something similar in the ase when loyalty is non-existent

(

L = 1.0

^). ^However, ⁱⁿ ^this ^ase, ^a ^very ^quik ^prie ^war ^leads ^to ^very ^low ^and homogeneous pries. Note that beause the inumbent reahed the minimum prie last, its market share

beame zero(refer to theformulaof prie sensitive loyalty inSetion 2.2.5).

Note that the stohasti loyalty model produes very similar ompetition in this senario

(resultsarenot shown).

Informed vs. uninformed users

In this senario we studied the dierene in market dynamis indued by fully and partially

informedusers. We usedthe stohastimodelwithstandarddeviation setto0.5,an

inumbent-newomersetting withthreeISPs. We ompare theresultsprodued withtheinformedand the

greedy migration modelinFigure2.7. ISP

1

^is^the^inumbent ^provider.

The lessons from these results arethe following. First, for a highly loyal market (rst and

third row), there is no big dierene in prie dynamis when omparing fully and partially

informed users. However, when users move easily (seond and fourth row), partially informed

users ausemore stablepriesand marketsharesonvergeswiftly toequilibrium. Thishappens

beausenotonlytheheapestISPgetsalltheusers,sothebenetofpriingbelowalltheothers

is lowerthan inthe fullyinformedase.

Prot in the long run

UserloyaltyalsoaetstheoverallprotofISPs. Here,weusethedeterministiloyaltymodelin

an inumbent-entrant setting andwedisount prots overtime witha disount fator of

0.995

ISP

1

^is^the ^inumbent ^provider. ^W^e ^an ^observe ⁱⁿ^Figure^2.8 ^that^both^ISPs ^do ^better^overall,

whenthereisahigh-levelofloyaltyamongusers. Furthermore,inFigure2.8(),asthetotallak

ofloyaltyandadministration onstraintsdrivesthe priestozeroinashorttime, both ISPsfail

to earnanyprotafter afew rounds.

In Figure 2.9, overall sum prots of two ISPs an be seen in time. Dierent lines denote

0 20 40 60 80 100 120

Prices

Round

ISP1 ISP2 ISP3

(g)

0 20 40 60 80 100

0 20 40 60 80 100 120

Profits

Round

ISP1 ISP2 ISP3

(h)

0 0.2 0.4 0.6 0.8 1

0 20 40 60 80 100 120

Market shares

Round

ISP1 ISP2 ISP3

Figure2.7: Pries,prots andmarketsharesfor 3ISPs withfullyinformed(

L = 0.05, 0.35

⁾ ^and

Round

ISP1 ISP2

()

Figure 2.8: Total individual prots for 2 ISPs (

L = 0.05, 0.30, 1.0

^), ¹ ^inumbent, ¹ ^entrant,

deterministi loyalty

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

0 20 40 60 80 100 120

Total profits

Round Threshold=0.1

Threshold=0.2 Threshold=0.3 Threshold=0.4

Figure2.9: Overall umulative prots of 2ISPs at dierent loyaltylevels

beingloyal to them,sine stronger loyalty results inhigher overallprots. Thisresultis inline

withreent empirialsurveys onuser loyalty [13℄.

In document B daeUiveiyfTe h (Pldal 40-49)