Overcoming choice inertia through social interaction: An agent-based study of mobile subscription decision

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. 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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. 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