Saha, Ba sha; Ma ínez-Ga cía, Miguel; Bha acha ya, Sha ad Na h; Joshi, Rohi
A icle
O e coming choice ine ia h ough social in e ac ion: An
agen -based s udy o mobile subsc ip ion decision
Games
P o ided in Coope a ion wi h:
MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Saha, Ba sha; Ma ínez-Ga cía, Miguel; Bha acha ya, Sha ad Na h; Joshi, Rohi
(2022) : O e coming choice ine ia h ough social in e ac ion: An agen -based s udy o mobile
subsc ip ion decision, Games, ISSN 2073-4336, MDPI, Basel, Vol. 13, Iss. 3, pp. 1-16,
h ps://doi.o g/10.3390/g13030047
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/329958
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h ps://c ea i ecommons.o g/licenses/by/4.0/
Ci a ion: Saha, B.; Ma ínez-Ga cía,
M.; Bha acha ya, S.N.; Joshi, R.
O e coming Choice Ine ia h ough
Social In e ac ion—An Agen -Based
S udy o Mobile Subsc ip ion
Decision. Games 2022,13, 47.
h ps://doi.o g/10.3390/g13030047
Academic Edi o : Ul ich Be ge
Recei ed: 19 May 2022
Accep ed: 16 June 2022
Published: 20 June 2022
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2022 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
games
A icle
O e coming Choice Ine ia h ough Social In e ac ion—An
Agen -Based S udy o Mobile Subsc ip ion Decision
Ba sha Saha 1,2,* , Miguel Ma ínez-Ga cía3,* , Sha ad Na h Bha acha ya 1and Rohi Joshi 1
1Indian Ins i u e o Managemen Shillong, Shillong 793018, India; [email p o ec ed] (S.N.B.);
[email p o ec ed] (R.J.)
2Cou se a, Moun ain View, CA 94041, USA
3Depa men o Ae onau ical and Au omo i e Enginee ing, Loughbo ough Uni e si y,
Loughbo ough LE11 3TU, UK
*Co espondence: [email p o ec ed] (B.S.); [email p o ec ed] (M.M.-G.)
Abs ac :
Subsc ip ion decision in he elecom ma ke is qui e complex and cumbe some, in oking
decision ine ia in consume s and esul ing in subop imal choices. We implemen ed choice ine ia and
consume in e ac ion as an agen -based model o be e unde s and he p ocess. The model illus a es
ha wi h adequa e pee in e ac ions wi h ac i e consume s, inac i e consume s could o e come
hei ine ia signi ican ly and swi ch o a be e al e na i e. Fu he mo e, he newly con e ed ac i e
consume s in luenced hei ine neighbo s as a ipple e ec . Ac i e consume s con ibu e o i m
p o i s and heal hy ma ke compe i ion. Mo eo e , in en i onmen s wi h low neighbo hood e ec s
and a s onge ine ia h eshold, i ms a e able o main ain p o i s by e aining ine consume s. We
show ha apa om he a ac i eness o ma ke o e ings, i ms can bene i om unde s anding
consume ine ia and de ising means o educe i .
Keywo ds:
consume beha io (ine ia); elecommunica ions; compe i ion; game heo y; agen -based
modelling; homophily; complexi y
1. In oduc ion
The subsc ip ion choice wi h mobile ne wo k ope a o s (MNOs) elies hea ily on
choosing he bes quali y a he lowes p ices. Wi h ad anced echnologies in he pos -
p i a iza ion e a o elecom, he quali y o o e ings ac oss ope a o s is now mo e o less
homogeneous, and se ices a e widely a ailable ac oss he na ional (and some imes in e na-
ional) landscape. As a esul , i ms ace p essu e o educe p ices o main ain hei ma ke
sha e o consume s. The e o e, he game- heo e ic ma ke compe i ion models sugges
ha consume s swi ch o he be e o cheape al e na i e a any gi en ime. Though
many consume s exhibi his expec ed beha io , in eali y, a good p opo ion o he ma ke
de ia es om he ideal scena io. S udies on di e en ma ke s ha e shown ha consume s
o en ail o swi ch o a cheape al e na i e, o , in gene al, hey ail o selec he bes op ion
a ailable o hem [1–3].
The Beha io al Economics li e a u e a ibu es his depa u e om classical a ionali y
assump ions o beha io al biases [
4
], o en mani es ed as consume ine ia. In he con ex
o elecom, he ine ia is no only beha io al bu also due o he complexi y o he a ay
o se ice o e ings which a e di icul o compa e [
5
]. Resea ch on elecom subsc ip ion
decisions epo ed he de ia ion om s anda d expec a ions such as esis ance o swi ching
MNOs [6], bill shocks [7], and selec ion o sub-op imal op ions [8–12].
The de e ence o he ine ia [
13
,
14
] o conside al e na i es and swi ching o a be e
op ion is a combina ion o beha io al biases and associa ed swi ching cos s [
15
]— he
eluc ance o swi ch a ises om he pe cei ed no ion o a cumbe some swi ching p ocess.
Ne e heless, wi h imp o ed echnology and ea u es such as mobile numbe po abili y
Games 2022,13, 47. h ps://doi.o g/10.3390/g13030047 h ps://www.mdpi.com/jou nal/games
Games 2022,13, 47 2 o 16
(MNP), he swi ching p ocess has been made e y e icien [
16
–
19
]. This is eadily ag eed
upon by he consume s who ha e swi ched hei ope a o s [5].
Ne e heless, e en hen, consume s o en de e om seeking ou he be e op ion and
s ick wi h he subop imal choice. Such eluc an consume s may bene i om addi ional
in o ma ion ega ding a ailable o e ings, a ge ed messages, o wo d o mou h om
pee s. The o me wo op ions a e unde he disc e ion o i ms’ ma ke ing and ad e ising
expendi u e. Howe e , he hi d, wo d o mou h o in o mal in o ma ion p opaga ion, may
occu wi hou any explici in luence om i ms.
I is known ha , in complex decision choices, consume s o en conside hei pee
decisions o migh equi e a ce ain amoun o s imulus be o e aking ac ion [
20
]. Telecom
is a ne wo k indus y ha d i es on he olume o subsc ibe s. Fu he mo e, pai ed
wi h i s complex choice p oblem, i is no uncommon o he consume s o eso o
he opinion leade s [
21
] in hei ne wo k o a solu ion. The opinion leade s, in his
con ex , a e he ac i e consume s in one’s pee ne wo k who can in luence o he s’ decisions.
Al e na i ely, he opinion leade s could also u ge hese consume s o o e come hei ine ia
and a ail he bene i s ha come wi h swi ching hei ope a o s. Se e al s udies in di e en
economic con ex s ha e ci ed he in luence o pee e ec s on an indi idual, o example,
die a y beha io and obesi y [22], academic g ades [23], and dis ibu ed ene gy esou ces
adop ion [24].
In his s udy, we explo e he ex en o in o ma ion p opaga ion wi hin consume pee
ne wo ks. The objec i e o he simula ion is o expe imen ally in es iga e he pa e n
o neighbo hood in e ac ion and i s po en ial e ec s on i m bene i s. We implemen a
pa simonious, duopolis ic-p ice compe i ion se ing o he elecom indus y. The agen -
based model (ABM) con ains wo ypes o agen s: i ms and consume s.
The wo i ms ace he demand o he same consume base in each ime pe iod. Assum-
ing he homogenei y o he se ices, he i ms s ic ly compe e in a ac i e
p ice packages
.
On he o he hand, he consume s join he ma ke wi h an exis ing subsc ip ion o
ei he i m. Thei subsc ip ion decisions in subsequen ime pe iods a e based on he p ice
di e ence o he o e ings and hei inhe en ine ia. The consume s espond o he op ion
yielding hem he highes u ili y. Consume ine ia is no s a ic, and he in luence o o he
ac i e consume s can educe i in he pee ne wo k.
We expe imen wi h he p ice compe i ion model by a ying he ine ia and s eng h
o in luence in he social ne wo k. Unde his se ing, we ob ain in e es ing esul s. Fi s ,
he i m o he indus y g ea ly bene i s om ac i e consume s in e ms o p o i by olume.
A low social in e ac ions among he consume s, i ms a e able o e ain p o i s h ough
ine consume s. Second, homophily con ibu es signi ican ly o a consume o o e come
ine ia. Thi d, he s eng h o pee in luence also should be conside ed besides he numbe
o in luence s in he ne wo k. This can be easily ansla ed as he s eng h o he s imulus
equi ed o making a decision depending on i s complexi y and implica ions (pu chasing
candy s. pu chasing insu ance). Ou simula ions con o m o he indings o p io li e a u e
in es iga ing he impac o pee e ec on indi idual decisions. I is challenging o e alua e
consume ine ia nume ically. We con ibu e by eplica ing he in e ac ion as an ABM and
p o iding e idence o he beha io .
In he ollowing sec ion, we build on he heo e ical backg ound. The hi d sec ion
elabo a es on he amewo k and he o mula ion o he ABM. In he ou h sec ion, we
p esen ou esul s o he simula ion and s a is ical analysis. The inal sec ion d aws he
ou comes and gene al conclusions wi h u u e esea ch di ec ions.
2. Rela ed Li e a u e
A ne wo k indus y such as elecom poses complex decision choices o i s consume s.
The consume s need o conside mul iple ac o s such as p icing o he se ices, whe he
he mobile–handse con ac is mo e p o i able han pu chasing hem sepa a ely, he de ice-
o-connec ion compa ibili y (3G/4G de ice wi h 3G/4G-enabled SIM ca ds), compa ing
se ice p o ide s and hei a i s uc u es, and pos pu chase cus ome se ice. The
Games 2022,13, 47 3 o 16
conce ns a e alid o bo h i s - ime consume s and exis ing consume s. Wi h inno a ion
in elecommunica ions echnology, he se ices ha e been ex ensi ely upg aded since hei
incep ion. The ma ke o e ings ha e also e ol ed in andem. The consume s p ocess
and analyze his in o ma ion o a ying deg ees and associa e ce ain psychological and
physical swi ching cos s wi h i . Sophis ica ed consume s, analogous o he ea ly adop e s
in he di usion model, would ake he ini ia i e o analyze he o e ings and ind he
bes i me iculously. This is no necessa ily he case o he naï e consume s o he
imi a o s. Due o he cogni i e o e load and he combina ion o he beha io al biases
men ioned in he p e ious sec ion, hese consume s would main ain a s a us quo wi h
he subop imal choice. The opinion leade s o in luence s in a social ne wo k a e able o
p o ide he s imulus o o he s o o e come hei choice ine ia. In ac , homophily ( he
endency o people o connec wi h o he s simila o hem) plays a ole in seeking ou he
opinion leade s o in luence s in one’s social ne wo k. In his pape , he in e ac ion in
he social ne wo k o a consume is de e mined by i s spa ial neighbo hood in he ABM
en i onmen . The li e a u e on social in e ac ion p o ides e idence o neighbo hood e ec s
(neighbo hoods can be esiden ial, geog aphical, spa ial, o pee g oup) on mic oeconomic
phenomena [25–27].
Agen -based modelling is a popula echnique o s udying mic oeconomic models
o social phenomena h ough simula ion p ocedu es [
27
,
28
]. The ABM li e a u e has con-
ibu ed o s udying socio-economic subjec s such as o ing beha io s [
29
], epidemics [
30
],
spa ial se lemen pa e ns [
31
], ade ne wo ks [
32
], and cus ome beha io [
33
,
34
], among
o he s. In ou pape , we a e in e es ed in s udying he e ec s o social in e ac ion on con-
sume swi ching beha io . The ABM cap u es he ou come o nume ous indi idual-le el
decisions o consume s as he o e all i m and indus y p o i s. I accoun s o he dynamic
indi idual-le el he e ogenei y h oughou he ime ho izon o he p ice compe i ion.
The esul s o he simula ions p o ide e idence o suppo he e ec o neighbo hood
in luence o e indi idual pu chase decisions and how i con ibu es o i ms. We discuss
he model and esul s in de ail in he ollowing sec ions.
3. P oposed Model
To illus a e he e ec o pee in luence on consume decisions, we p opose an agen -
based model ha s udies consume decision pa e ns in esponse o an exogenously se p ice
compe i ion. The agen s’ decisions e ol e o e ime based on neighbo hood in e ac ions.
3.1. Analy ical F amewo k o P ice Compe i ion unde Consume Ine ia
We implemen he p ice compe i ion model o Spiegle , 2011 [
35
], including he con-
sume ine ia (modi ica ion o S ahl, 1989 and Va ian, 1981 [
36
,
37
]) in ou ABM. The model
assumes a duopoly o MNOs wi h he homogeneous p oduc . The in e ac ion be ween
i ms is expec ed o con inue o a ini e ime ho izon un il
p(i,j)=c(i,j)+δ
. Fo any
consume belonging o Fi m i, he decision unc ions a e gi en by:
Di =hβindi . −βIi−pi
Dj =−pj
and
βindi . =ϕβindi . −1
, whe e
ϕ
= cumula i e ep esen a ion o neighbo hood in luence
βindi .∈(0, 1)deno es consume ine ia
βI= h eshold o o e come ine ia
I , Di >Dj , consume s s ay wi h Fi m i
Dj >Di , consume s swi ch o Fi m j
Di =Dj
, consume s a e indi e en be ween choices and s ay wi h hei exis ing
se ice p o ide s.
F om he classical Be and duopoly p ice compe i ion model, he p o i ea ned by a
i m is gi en by Πi=piqi−ci. Consume s hold a p e e ence o he cheape o e ing.
Games 2022,13, 47 4 o 16
When
pi>pj
,
qi=
0, he eby ende ing
Πi=
0 (assuming he i ms ope a e a ze o
cos , ci=0) and Fi m j accumula es he en i e ma ke sha e.
Now, wi h he in oduc ion o consume ine ia, he model modi ies in o,
Πi=piqi(1−β)−ci
when
pi>pj
. Unlike he classical model,
Fi m i
is able o
main ain some o i s o iginal consume s. The exis ence o
β
in oduces he di e ence in
consume beha io om he Be and p ice compe i ion. Fo
βindi
.
<βI
, a consume
will no swi ch a he p ospec o he a ailabili y o a cheape al e na i e, con a y o he
assump ion o he neoclassical model.
A
β
= 1, he model con e ges o he Be and p ice compe i ion. In he ABM,
β
is
inhe en o each agen o consume , and hey a e una ec ed by any ex e nal ac o a he
ini ia ion o he p ice compe i ion.
3.2. Agen -Based Model
The agen -based model e lec s he duopoly p ice compe i ion s a ed in he p e ious
sec ion. The model assumes compe i ion be ween wo exis ing mobile ne wo k ope a o s
wi h simila se ices. The e o e, each o he MNOs al eady holds a ce ain numbe o
consume s wi h simila p ices, since he i m i= 1, 2 o e ings a e homogeneous, and he
consume s di e en ia e be ween hem only by he p ice packages o e ed. Consume s
p e e he lowe p ice as he be e al e na i e. We ollowed he guidelines o Rand and
Rus , 2011 and Twomey and Cadman, 2002 [
38
,
39
] in designing he agen -based model.
The ABM ca e s o wo ypes o agen s: he wo i ms and he indi idual consume s.
3.3. Fi m Beha io
Mobile elecom o e ings became exceedingly complex o compa ison. The a i a es
no longe speci y he cha ges only o calling, bu hey en ail a bundle o calling, messaging,
and da a se ices wi h di e en alidi y pe iods. Consume s ace decision ine ia due o
he cogni i e load pe cei ed om he ask o compa ing se ice bundles. Wi h imp o ed
echnology, he o e ings ac oss MNOs a e o simila quali y. The e o e, he ma ke is le
o compe e on p ices and in angible o e ings ( ee ex ended subsc ip ion o OTT se ices
and cus omiza ion op ions). Fo simplici y, we es ic he i m-side ac ion o eplica e p ice
compe i ion as long as ac i e consume s a e p esen in he ma ke . Ou ocus is on he
consume decision in he p esence o social in e ac ion, whe e he p ice compe i ion ac s as
he igge o he decision ask.
In each ime pe iod, he i ms a e designed o engage in p ice compe i ion. They e-
spond o hei compe i o by educing hei p ice pby a small amoun
δ
, i.e.,
pi =Pj −1−δ
whe e is he ime pe iod. A ime + 1, he en i e compe i i e p ocess epea s. The i ms
con inue he p ice compe i ion un il ei he i m eaches
pi ≥ci+δ
. Fo simplici y, we
assume a ixed cos
ci
. The elecommunica ions indus y is an in as uc u e-hea y en-
i y. I equi es ample in es men in in as uc u al suppo and con inuous R&D. The
game- heo e ic model assumes ha each i m has su icien bandwid h o se e he whole
ma ke independen ly, wi hou a compe i o . The e o e, ixed cos aids i ms in deciding
whe he i is p o i able o ope a e in he ma ke o no . The i ms a e expec ed o ace a
olume–ma gin ade-o wi h p ice educ ion in each i e a ion. The lowcha o he p ice
compe i ion is shown in Figu e 1.
The o al numbe o consume s q emains cons an h oughou he p ice compe i ion
game. The consume base is spli be ween wo i ms in each p ice-compe i i e i e a ion
depending on he p ice se by hem, indi idual ine ia, and he esul an decision o each
consume . Wi h he a o emen ioned compe i i e se ing, he consume s a e expec ed o
lock owa d he cheape o e ing in each i e a ion. In eali y, wi h he mani es a ion o
ine ia due o he easons men ioned in Sec ion 2, consume s o en de e om ampan
swi ching. We simula e he same beha io in ou model by p o iding he consume agen s
wi h inhe en ine ia. Fo simplici y, we do no explici ly accoun o he collusion scena io
in modelling i ms’ ac ion space. The consume decision unc ion al eady accoun s o he

Games 2022,13, 47 5 o 16
collusion case (bo h i ms a a s alema e wi h he same p ice) wi h no eac ion (i.e., hey
con inue wi h hei choice in he p e ious pe iod).
Games 2022, 13, x FOR PEER REVIEW 5 o 17
Figu e 1. Flowcha o he ABM p ocess.
Figu e 1. Flowcha o he ABM p ocess.
Games 2022,13, 47 6 o 16
3.4. Consume Social Ne wo k
In he Ne Logo en i onmen [
40
], he consume s a e ep esen ed by a ini e se o
agen s
N={1, . . . , n}
. The agen s ha e a ying deg ees o connec ions o neighbo s. Fo
his s udy, he connec ions a e s ic ly de e mined by he Moo e neighbo hood, e e ing o
he cellula au oma a li e a u e. The Moo e neighbo hood su ounding a gi en cell, say
(x0,y0), is gi en by,
NM
(x0,y0)={(x,y):|x−x0|≤ ,|y−y0|≤ }[41].
Fo Moo e neighbo hood ange = 0, 1, 2, 3,
. . .
he numbe o cells in he neighbo hood
is gi en by
(2 +1)2=
1, 9, 25, 49, 81
. . .
. In ou s udy, we conside = 1, such ha each
cell can ha e a maximum o 9 – 1 = 8 neighbo s, and hey can in e ac wi h each o he .
The diag am abo e (Figu e 2a) illus a es he neighbo hood schema ( = 1) used in
he ABM. The su ounding 8 whi e cells (o agen s) a e he neighbo s o he blue cell (o
agen ) in he middle. Consume s wi h
β≥
h eshold a e capable o in luencing consume s
wi h
β
< h eshold wi hin hei ne wo k. Fo a isual ep esen a ion (Figu e 2b), we use he
do ed lines o show he ac i e consume s in a neighbo hood. The weigh o he do ed
lines di ec ly ansla es in o hei lack o ine ia o p opensi y o swi ch in he p esence o a
be e al e na i e. Among all he neighbo s, he agen s wi h simila subsc ip ions s ongly
in luence he ine pee . This se up is o induce homophily among he agen s. Mo eo e ,
he in e ac ion is unidi ec ional, i.e., only he ac i e agen s can in luence he ine agen s.
Games 2022, 13, x FOR PEER REVIEW 6 o 17
The o al numbe o consume s 𝑞 emains cons an h oughou he p ice compe i-
ion game. The consume base is spli be ween wo i ms in each p ice-compe i i e i e a-
ion depending on he p ice se by hem, indi idual ine ia, and he esul an decision o
each consume . Wi h he a o emen ioned compe i i e se ing, he consume s a e expec ed
o lock owa d he cheape o e ing in each i e a ion. In eali y, wi h he mani es a ion o
ine ia due o he easons men ioned in Sec ion 2, consume s o en de e om ampan
swi ching. We simula e he same beha io in ou model by p o iding he consume agen s
wi h inhe en ine ia. Fo simplici y, we do no explici ly accoun o he collusion scena io
in modelling i ms’ ac ion space. The consume decision unc ion al eady accoun s o he
collusion case (bo h i ms a a s alema e wi h he same p ice) wi h no eac ion (i.e., hey
con inue wi h hei choice in he p e ious pe iod).
3.4. Consume Social Ne wo k
In he Ne Logo en i onmen [40], he consume s a e ep esen ed by a ini e se o
agen s 𝑁=󰇝 1,…,𝑛󰇞. The agen s ha e a ying deg ees o connec ions o neighbo s. Fo
his s udy, he connec ions a e s ic ly de e mined by he Moo e neighbo hood, e e ing
o he cellula au oma a li e a u e. The Moo e neighbo hood su ounding a gi en cell, say
(𝑥,𝑦
), is gi en by,
𝑁(

,

)
=󰇝
(𝑥,𝑦):|𝑥−𝑥
|𝑟,|𝑦−𝑦
|𝑟󰇞 [41].
Fo Moo e neighbo hood ange 𝑟 = 0, 1, 2, 3, … he numbe o cells in he neighbo -
hood is gi en by (2𝑟 + 1)= 1, 9, 25, 49, 81 … . In ou s udy, we conside 𝑟=1, such ha
each cell can ha e a maximum o 9−1=8 neighbo s, and hey can in e ac wi h each
o he .
The diag am abo e (Figu e 2a) illus a es he neighbo hood schema (𝑟=1) used in
he ABM. The su ounding 8 whi e cells (o agen s) a e he neighbo s o he blue cell (o
agen ) in he middle. Consume s wi h 𝛽≥ h eshold a e capable o in luencing consum-
e s wi h 𝛽< h eshold wi hin hei ne wo k. Fo a isual ep esen a ion (Figu e 2b), we
use he do ed lines o show he ac i e consume s in a neighbo hood. The weigh o he
do ed lines di ec ly ansla es in o hei lack o ine ia o p opensi y o swi ch in he p es-
ence o a be e al e na i e. Among all he neighbo s, he agen s wi h simila subsc ip ions
s ongly in luence he ine pee . This se up is o induce homophily among he agen s.
Mo eo e , he in e ac ion is unidi ec ional, i.e., only he ac i e agen s can in luence he
ine agen s.
(a) (b)
Figu e 2. (a) No mal neighbo hood s uc u e. (b) Neighbo hood o agen s wi h a ying deg ees o
ine ia.
3.5. Decision Rule
Indi idual ine ia is no s a ic in na u e. The e o e, consume beha io may change
o e ime in esponse o exogenous ac o s. Pee in luence, wo d o mou h [42], ad e ise-
men , and communica ion play a ole in modi ying consume decisions. In ou case, his
modi ica ion is basically he agen s o e coming hei ine ia o seek a be e al e na i e.
We conside he e ec o pee beha io o wo d o mou h o he pee g oup o in luence
he ine consume s o e ime un il hey o e come hei ine ia.
Figu e 2.
(
a
) No mal neighbo hood s uc u e. (
b
) Neighbo hood o agen s wi h a ying deg ees
o ine ia.
3.5. Decision Rule
Indi idual ine ia is no s a ic in na u e. The e o e, consume beha io may change
o e ime in esponse o exogenous ac o s. Pee in luence, wo d o mou h [
42
], ad e ise-
men , and communica ion play a ole in modi ying consume decisions. In ou case, his
modi ica ion is basically he agen s o e coming hei ine ia o seek a be e al e na i e. We
conside he e ec o pee beha io o wo d o mou h o he pee g oup o in luence he
ine consume s o e ime un il hey o e come hei ine ia.
The decision o an ine consume o swi ch is de e mined by he s eng h o he pee
in luence and he numbe o pee s who ha e swi ched o he be e al e na i e. The ole
o he ine s and in luence s a e analogous o he imi a o s and adop e s in he di usion
model, espec i ely [
43
,
44
]. The model assumes ha only he in luence s can a ec he
ine ia o he ine consume s. Addi ionally, he decision ule also dic a es ha , once he
ine consume s o e come hei ine ia, hey will no e e o hei ine sel es again. The
p ocess con inues un il he p ice compe i ion e mina es. This design inco po a es he
in o ma ion p opaga ion o pee e ec in a social ne wo k [45,46].
Figu e 3illus a es he in e ac ion and change in ine ia. Figu e 3a shows he basic
Moo e neighbo hood se up used in his s udy. In Figu e 3b, he wo colo s indica e he
indi idual subsc ip ions o he consume s o wo MNOs. The indi idual-le el ine ia o
he consume s is p esen ed in Figu e 3c. The weigh o he solid lines is p opo ional o
he s eng h o ine ia, and he same logic holds o he ac i e consume s iden i ied by
do ed lines. A
pi>pj
, he ini ial se up in Figu e 3d ans o ms in o 3 ou o 5 consume s
o
Fi m i
swi ching o
Fi m j
as in Figu e 3e. The ine ia o he es o he 2 consume s is
Games 2022,13, 47 7 o 16
educed bu no su icien o he swi ch. The exac condi ions con inue o bo h i ms un il
he p ice compe i ion e mina es. The same p ocess is ollowed in he ABM.
Games 2022, 13, x FOR PEER REVIEW 7 o 17
The decision o an ine consume o swi ch is de e mined by he s eng h o he pee
in luence and he numbe o pee s who ha e swi ched o he be e al e na i e. The ole
o he ine s and in luence s a e analogous o he imi a o s and adop e s in he di usion
model, espec i ely [43,44]. The model assumes ha only he in luence s can a ec he
ine ia o he ine consume s. Addi ionally, he decision ule also dic a es ha , once he
ine consume s o e come hei ine ia, hey will no e e o hei ine sel es again. The
p ocess con inues un il he p ice compe i ion e mina es. This design inco po a es he in-
o ma ion p opaga ion o pee e ec in a social ne wo k [45,46].
Figu e 3 illus a es he in e ac ion and change in ine ia. Figu e 3a shows he basic
Moo e neighbo hood se up used in his s udy. In Figu e 3b, he wo colo s indica e he
indi idual subsc ip ions o he consume s o wo MNOs. The indi idual-le el ine ia o
he consume s is p esen ed in Figu e 3c. The weigh o he solid lines is p opo ional o
he s eng h o ine ia, and he same logic holds o he ac i e consume s iden i ied by
do ed lines. A 𝑝>𝑝
, he ini ial se up in Figu e 3d ans o ms in o 3 ou o 5 consume s
o 𝐹𝑖𝑟𝑚 𝑖 swi ching o 𝐹𝑖𝑟𝑚 𝑗 as in Figu e 3e. The ine ia o he es o he 2 consume s
is educed bu no su icien o he swi ch. The exac condi ions con inue o bo h i ms
un il he p ice compe i ion e mina es. The same p ocess is ollowed in he ABM.
(a) (b) (c) (d) (e)
Figu e 3. (a) Gene al se up, (b) Blue and ed cells ep esen subsc ip ion o i ms i and j, espec i ely.
(c) Di e en ypes o cell bo de s deno e a ying deg ees o ine ia (de ails below). (d) P ice
compe i ion a 𝑝

>𝑝

and (e) esul ing changes in consume ine ia and subsc ip ion due o
neighbo hood in e ac ion e ec .
4. Resul s
4.1. Simula ion
The agen -based model is se o simula e he p ice compe i ion unde dynamic con-
sume ine ia. We expe imen ed wi h he neighbo hood e ec s by manipula ing he h ee
model pa ame e s: (a) neighbo hood in luence, (b) he numbe o nonine pee s, and (c)
ine ia. Fo simplici y, we men ion hem as he ‘neighbo hood in e ac ion’ pa ame e s.
Consume s compa e he al e na i es based on hei decision unc ions. They can ei he
swi ch in he p esence o a be e al e na i e o main ain he s a us quo i hei cu en
choice yields maximum ou pu . We conduc ed egula code walk h oughs wi h a p o es-
sional p og amme o e iew he ABM p og am. The model is examined ac oss se e al
es cases o ensu e he alidi y, eliabili y, and e iciency o he coding p ocess and also
o scan o any po en ial bugs. A sample o he Ne Logo p og am ins ance is shown in he
ollowing 2 igu es.
Figu e 4 shows he isual ep esen a ion o he ABM on i s g aphical in e ace. I
p o ides in e ac i e bu ons and slide s o dynamic con ol o he simula ions (as op-
posed o he ha d-coding o pa ame e s). Figu e 5 cap u es a snap o he In o window,
which allows p og amme s o main ain he documen a ion o he p og am in b ie .
The models we e es ed o low, medium, and high le els o neighbo hood in luence
wi h se en le els o in luence g oup in he Moo e neighbo hood se up. The inhe en in-
e ia is simula ed in nine dis inc le els (low–high). The combined e ec o he a iables
de e mines he pee e ec o educe he ine ia o ine consume s loca ed a ound he ac-
i e consume s. We used he Beha io Space ool in Ne Logo o conduc he simula ions
10 imes o each combina ion o inpu pa ame e s.
Figu e 3.
(
a
) Gene al se up, (
b
) Blue and ed cells ep esen subsc ip ion o i ms iand j, espec i ely.
(
c
) Di e en ypes o cell bo de s deno e a ying deg ees o ine ia (de ails below). (
d
) P ice compe i-
ion a
pi>pj
and (
e
) esul ing changes in consume ine ia and subsc ip ion due o neighbo hood
in e ac ion e ec .
4. Resul s
4.1. Simula ion
The agen -based model is se o simula e he p ice compe i ion unde dynamic con-
sume ine ia. We expe imen ed wi h he neighbo hood e ec s by manipula ing he h ee
model pa ame e s: (a) neighbo hood in luence, (b) he numbe o nonine pee s, and (c)
ine ia. Fo simplici y, we men ion hem as he ‘neighbo hood in e ac ion’ pa ame e s. Con-
sume s compa e he al e na i es based on hei decision unc ions. They can ei he swi ch
in he p esence o a be e al e na i e o main ain he s a us quo i hei cu en choice
yields maximum ou pu . We conduc ed egula code walk h oughs wi h a p o essional
p og amme o e iew he ABM p og am. The model is examined ac oss se e al es cases
o ensu e he alidi y, eliabili y, and e iciency o he coding p ocess and also o scan o
any po en ial bugs. A sample o he Ne Logo p og am ins ance is shown in he ollowing
2 igu es.
Figu e 4shows he isual ep esen a ion o he ABM on i s g aphical in e ace. I
p o ides in e ac i e bu ons and slide s o dynamic con ol o he simula ions (as opposed
o he ha d-coding o pa ame e s). Figu e 5cap u es a snap o he In o window, which
allows p og amme s o main ain he documen a ion o he p og am in b ie .
Games 2022, 13, x FOR PEER REVIEW 8 o 17
Figu e 4. Ne Logo window o he ABM p og am.
Figu e 5. Ne Logo In o window.
Table 1 shows he indi idual a iable le el manipula ion and he esul an numbe
o combina ions o he simula ion expe imen . The expe imen al uns o aled 1890. The
esul s a e ex ac ed and abula ed o u he s a is ical analysis.
Table 1. ABM expe imen a ion pa ame e s.
Neighbo hood In lu-
ence
Numbe o Nonine
Pee s Ine ia Unique Combina ions To al
3 7 9 3 × 7 × 9 = 189 189 × 10 = 1890
(low, medium, high) (7 le els o neighbo s) (low o high, inc eased
in 9 s eps)
(10 uns o each com-
bina ion)
Figu e 4. Ne Logo window o he ABM p og am.
Games 2022,13, 47 8 o 16
Games 2022, 13, x FOR PEER REVIEW 8 o 17
Figu e 4. Ne Logo window o he ABM p og am.
Figu e 5. Ne Logo In o window.
Table 1 shows he indi idual a iable le el manipula ion and he esul an numbe
o combina ions o he simula ion expe imen . The expe imen al uns o aled 1890. The
esul s a e ex ac ed and abula ed o u he s a is ical analysis.
Table 1. ABM expe imen a ion pa ame e s.
Neighbo hood In lu-
ence
Numbe o Nonine
Pee s Ine ia Unique Combina ions To al
3 7 9 3 × 7 × 9 = 189 189 × 10 = 1890
(low, medium, high) (7 le els o neighbo s) (low o high, inc eased
in 9 s eps)
(10 uns o each com-
bina ion)
Figu e 5. Ne Logo In o window.
The models we e es ed o low, medium, and high le els o neighbo hood in luence
wi h se en le els o in luence g oup in he Moo e neighbo hood se up. The inhe en
ine ia is simula ed in nine dis inc le els (low–high). The combined e ec o he a iables
de e mines he pee e ec o educe he ine ia o ine consume s loca ed a ound he
ac i e consume s. We used he Beha io Space ool in Ne Logo o conduc he simula ions
10 imes o each combina ion o inpu pa ame e s.
Table 1shows he indi idual a iable le el manipula ion and he esul an numbe
o combina ions o he simula ion expe imen . The expe imen al uns o aled 1890. The
esul s a e ex ac ed and abula ed o u he s a is ical analysis.
Table 1. ABM expe imen a ion pa ame e s.
Neighbo hood In luence Numbe o Nonine Pee s Ine ia Unique Combina ions To al
3 7 9 3 ×7×9 = 189 189 ×10 = 1890
(low, medium, high) (7 le els o neighbo s) (low o high, inc eased
in 9 s eps)
(10 uns o each
combina ion)
4.2. Model Ou pu
We es ed ou models in wo aspec s. Fi s , o es o he ine ia dynamics, and second,
he changing esponse o he p ice compe i ion game.
The ine ia dynamics we e es ed by analyzing he in luence o he neighbo hood
in e ac ion pa ame e s on he esul an numbe o ac i e consume s a he end o he game.
The numbe o o al ac i e consume s deno es he sum o he inhe en ly ac i e consume s
and hose who o e came ine ia h oughou he game. The eg ession equa ion is gi en by:
Yac i e =β0+β1(non −ine )+β2(in luence)+β3(ine ia)+β4(non −ine pee s)+ε
The ela ionship was ound o be s a is ically signi ican wi h a sa is ac o y R-squa ed
alue (Table 2). The esul indica es ha he numbe o ac i e consume s pa icipa ing in
he p ice compe i ion is de e mined by he in e play o he independen a iables.
The numbe o ac i e consume s a he end o he p ice compe i ion game is plo ed
acco ding o he in luence le el, he numbe o nonine consume s in he pee ne wo k,
and he h eshold o ine ia o o e come. The h ee g aphs show he a e o con e sion o
ine consume s in he p esence o he neighbo hood pa ame e s.
The ou pu o he Beha io Space expe imen s was hen u he analyzed wi h an
o dina y leas squa e (OLS) es ima e o s udy he i m side o he model beha io . The linea
eg ession s udies he e ec o he in e play be ween consume ine ia and pee in luence
Games 2022,13, 47 15 o 16
Re e ences
1.
B ennan, T. Consume p e e ence no o choose: Me hodological and policy implica ions. Ene gy Policy
2007
,35, 1616–1627. A ail-
able online: h ps://econpape s. epec.o g/RePEc:eee:enepol: :35:y:2007:i:3:p:1616-1627 (accessed on 15 May 2022). [C ossRe ]
2.
Giulie i, M.; P ice, C.W.; Wa e son, M. Consume Choice and Compe i ion Policy: A S udy o UK Ene gy Ma ke s. Econ. J.
2005
,115, 949–968. A ailable online: h ps://econpape s. epec.o g/RePEc:ecj:econjl: :115:y:2005:i:506:p:949-968 (accessed on
15 May 2022). [C ossRe ]
3. Wilson, C.M.; P ice, C.W. Do consume s swi ch o he bes supplie ? Ox . Econ. Pap. 2010,62, 647–668. [C ossRe ]
4. Della Vigna, S. Psychology and Economics: E idence om he Field. J. Econ. Li . 2009,47, 315–372. [C ossRe ]
5. Lunn, P.D. Telecommunica ions Consume s: A Beha io al Economic Analysis. J. Consum. A . 2013,47, 167–189. [C ossRe ]
6.
Xa ie , P.; Ypsilan i, D. Swi ching cos s and consume beha iou : Implica ions o elecommunica ions egula ion. In o
2008
,10,
13–29. [C ossRe ]
7.
Xa ie , P. Beha io al Economics and Cus ome Complain s in Communica ions Ma ke s; Aus alian Communica ions and Media
Au ho i y: Melbou ne, Aus alia, 2011.
8. Ba -Gill, O.; S one, R. Mobile Mispe cep ions. Ha . J. Law Technol. 2009,23, 49–118.
9.
Ge po , T.J. Biased choice o a mobile elephony a i ype:: Explo ing usage bounda y pe cep ions as a cogni i e cause in
choosing be ween a use-based o a la a e plan. Telema . In o m. 2009,26, 167–179. [C ossRe ]
10. G ubb, M.D. Selling o O e con iden Consume s. Am. Econ. Re . 2009,99, 1770–1807. [C ossRe ]
11.
Lamb ech , A.; Skie a, B. Paying Too Much and Being Happy abou I : Exis ence, Causes, and Consequences o Ta i -Choice
Biases. J. Ma k. Res. 2006,43, 212–223. [C ossRe ]
12.
Ge po , T.J.; Meine , P. Choosing a w ong mobile communica ion p ice plan: An empi ical analysis o p edic o s o he deg ee o
a i mis i among la a e subsc ibe s in Ge many. Telema . In o m. 2017,34, 303–313. [C ossRe ]
13.
Poli es, G.L.; Ka ahanna, E. Shackled o he S a us Quo: The Inhibi ing E ec s o Incumben Sys em Habi , Swi ching Cos s, and
Ine ia on New Sys em Accep ance. MIS Q. 2012,36, 21–42. [C ossRe ]
14. Samuelson, W.; Zeckhause , R. S a us quo bias in decision making. J. Risk Unce ain. 1988,1, 7–59. [C ossRe ]
15.
Ga cía-Ma iñoso, B.; Suá ez, D. Swi ching mobile ope a o s: E idence abou consume s’ beha io om a longi udinal su ey.
Telecommun. Policy 2019,43, 426–433. [C ossRe ]
16.
Lunn, P.D.; Lyons, S. Consume swi ching in en ions o elecoms se ices: E idence om I eland. Heliyon
2018
,4, e00618.
[C ossRe ]
17.
Lyons, S. Measu ing he E ec s o Mobile Numbe Po abili y on Se ice P ices. J. Telecommun. Manag.
2010
,1, 2. A ailable online:
h p://hen ys ewa .me ap ess.com/link.asp?id= 5 3gw5528262u51 (accessed on 15 May 2022).
18.
Use o Sánchez, B.; Asimakopoulos, G. Regula ion and compe i ion in he Eu opean mobile communica ions indus y: An
examina ion o he implemen a ion o mobile numbe po abili y. Telecommun. Policy 2012,36, 187–196. [C ossRe ]
19.
Une , M.M.; Gu en, F.; Ca usgil, S.T. Chu n and loyal y beha io o Tu kish digi al na i es: Empi ical insigh s and manage ial
implica ions. Telecommun. Policy 2020,44, 101901. [C ossRe ]
20.
Jackson, M.O.; Ya i , L. Chap e 14—Di usion, S a egic In e ac ion, and Social S uc u e. In Handbook o Social Economics;
Benhabib, J., Bisin, A., Jackson, M.O., Eds.; No h-Holland: Ams e dam, The Ne he lands, 2011; Volume 1, pp. 645–678.
[C ossRe ]
21.
Ka z, E.; Laza s eld, P.F. Pe sonal In luence: The Pa Played by People in he Flow o Mass Communica ions; F ee P ess: New Yo k, NY,
USA, 1955.
22.
Gwozdz, W.; Nie, P.; Sousa-Poza, A.; DeHenauw, S.; Fels˝o, R.; Hebes ei , A.; Iguacel, I.; Lissne , L.; Lau ia, F.; Page, A.; e al. Pee
E ec s on Weigh S a us, Die a y Beha iou and Physical Ac i i y among Adolescen s in Eu ope: Findings om he I.Family
S udy. Kyklos 2019,72, 270–296. [C ossRe ]
23.
Goldsmi h-Pinkham, P.; Imbens, G.W. Social Ne wo ks and he Iden i ica ion o Pee E ec s. J. Bus. Econ. S a .
2013
,31, 253–264.
[C ossRe ]
24.
Moncada, J.A.; Tao, Z.; Valke ing, P.; Meinke-Hubeny, F.; Dela ue, E. In luence o dis ibu ion a i s uc u es and pee e ec s on
he adop ion o dis ibu ed ene gy esou ces. Appl. Ene gy 2021,298, 117086. [C ossRe ]
25.
Blume, L.; Du lau , S. The In e ac ions-Based App oach o Socio-Economic Beha io ; (Wo king Pape s, Issue 1); Wisconsin Madison—
Social Sys ems: Madison, WI, USA, 2000. A ailable online: h ps://econpape s. epec.o g/RePEc:a :wimass:20001 (accessed on
15 May 2022).
26. B ock, W.A.; Du lau , S.N. Disc e e Choice wi h Social In e ac ions. Re . Econ. S ud. 2001,68, 235–260. [C ossRe ]
27. Manski, C.F. Economic Analysis o Social In e ac ions. J. Econ. Pe spec . 2000,14, 115–136. [C ossRe ]
28. Ake lo , G.A. Social Dis ance and Social Decisions. Econome ica 1997,65, 1005–1027. [C ossRe ]
29. Kollman, K.; Mille , J.H.; Page, S.E. Adap i e Pa ies in Spa ial Elec ions. Am. Poli ical Sci. Re . 1992,86, 929–937. [C ossRe ]
30.
Eps ein, J.M.; Ax ell, R. G owing a i icial socie ies: Social science om he bo om up. In G owing A i icial Socie ies: Social Science
om he Bo om Up; The MIT P ess: Camb idge, MA, USA, 1996.
31.
Dean, J.; Gume man, G.; Eps ein, J.; Ax ell, R.; Swedlund, A.; Pa ke , M.; Mcca oll, S. Unde s anding Anasazi Cul u e Change
h ough Agen -Based Modeling; Wo king Pape s; San a Fe Ins i u e: San a Fe, NM, USA, 1998.
32.
Tes a sion, L. A T ade Ne wo k Game wi h Endogenous Pa ne Selec ion. In Compu a ional App oaches o Economic P oblems;
Sp inge : Bos on, MA, USA; New Yo k, NY, USA, 1997; pp. 249–269. [C ossRe ]

Games 2022,13, 47 16 o 16
33.
England, R.; Owadally, I.; W igh , D. An Agen -Based Model o Mo o Insu ance Cus ome Beha iou in he UK wi h Wo d o
Mou h. J. A i . Soc. Soc. Simul. 2022,25, 2. [C ossRe ]
34.
Gibson, M.; Po ugal Pe ei a, J.; Slade, R.; Rogelj, J. Agen -Based Modelling o Fu u e Dai y and Plan -Based Milk Consump ion
o UK Clima e Ta ge s. J. A i . Soc. Soc. Simul. 2022,25, 1–3. [C ossRe ]
35. Spiegle , R. Bounded Ra ionali y and Indus ial O ganiza ion; Ox o d Uni e si y P ess: Ox o d, UK, 2011.
36. S ahl, D.O. Oligopolis ic P icing wi h Sequen ial Consume Sea ch. Am. Econ. Re . 1989,79, 700–712.
37. Va ian, H. A Model o Sales. Am. Econ. Re . 1981,71, 517. [C ossRe ]
38. Rand, W.; Rus , R.T. Agen -based modeling in ma ke ing: Guidelines o igo . In . J. Res. Ma k. 2011,28, 181–193. [C ossRe ]
39.
Twomey, P.; Cadman, R. Agen -based modelling o cus ome beha iou in he elecoms and media ma ke s. In o
2002
,4, 56–63.
[C ossRe ]
40.
Wilensky, U.; Rand, W. An In oduc ion o Agen -Based Modeling: Modeling Na u al, Social, and Enginee ed Complex Sys ems wi h
Ne Logo; MIT P ess: Camb idge, MA, USA, 2015.
41.
Weiss ein, E.W. Moo e Neighbo hood; Ma hWo ld—A Wol am Web Resou ce. 2021. A ailable online: h ps://ma hwo ld.
wol am.com/Moo eNeighbo hood.h ml (accessed on 15 May 2022).
42.
Fa ow, K.; G olleau, G.; Mzoughi, N. Wha in he Wo d! The Scope o he E ec o Wo d Choice on Economic Beha io . Kyklos
2018,71, 557–580. [C ossRe ]
43. Bass, F.M. A New P oduc G ow h o Model Consume Du ables. Manag. Sci. 1969,15, 215–227. [C ossRe ]
44. Roge s, E. Di usion o Inno a ions; F ee P ess: New Yo k, NY, USA, 2003.
45. Du lau , S. Neighbo hood e ec s. Handb. Reg. U ban Econ. 2004,4, 2173–2242. [C ossRe ]
46.
Eps ein, J.M. Agen -based compu a ional models and gene a i e social science. In Gene a i e Social Science; P ince on Uni e si y
P ess: P ince on, NJ, USA, 2012; pp. 4–46. [C ossRe ]
47.
O’Donoghue, T.; Rabin, M. Choice and P oc as ina ion. Q. J. Econ.
2001
,116, 121–160. A ailable online: h p://www.js o .o g/
s able/2696445 (accessed on 15 May 2022). [C ossRe ]
48.
Gabaix, X.; Laibson, D. Sh ouded A ibu es, Consume Myopia, and In o ma ion Supp ession in Compe i i e Ma ke s. Q. J.
Econ. 2006,121, 505–540. [C ossRe ]
49. G ubb, M.D. Failing o Choose he Bes P ice: Theo y, E idence, and Policy. Re . Ind. O gan. 2015,47, 303–340. [C ossRe ]
50.
Del e, S.A.; Panico, C.; Wie enga, B. Compe i i e s a egies in he mo ion pic u e indus y: An ABM o s udy in es men decisions.
In . J. Res. Ma k. 2017,34, 69–99. [C ossRe ]
51.
Rand, W.; He mann, J.; Schein, B.; Vodopi ec, N. An Agen -Based Model o U gen Di usion in Social Media. J. A i . Soc. Soc.
Simul. 2015,18, 1. [C ossRe ]
52. Cye , R.; Ma ch, J. Beha io al Theo y o he Fi m; Wiley-Blackwell: Hoboken, NJ, USA, 1992.