©CopyrightJASSS

KeeheonLee,ShintaeKim,ChangOukKimandTaehoPark(2013)

AnAgent-BasedCompetitiveProductDiffusionModelfortheEstimationandSensitivityAnalysisofSocialNetworkStructureandPurchaseTimeDistribution

JournalofArtificialSocietiesandSocialSimulation 16(1)3<http://jasss.soc.surrey.ac.uk/16/1/3.html>

Received:02-Nov-2011Accepted:04-Aug-2012Published:31-Jan-2013

Abstract

Tomaximisethepossibilityofsuccessforanewproductandminimisetheriskandopportunitycostofafailedproduct,firmsmustunderstandthediffusiondynamicsofcompetingproducts.Thediffusiondynamicsofcompetingproductsemergefromtheaggregationofconsumers'decisions.Attheindividuallevel,aconsumer'sdecisionconsistsof"whichproducttobuyamongtheavailableproducts"and"whentobuyaproduct".Individualproductchoicesareaffectedbylocalandglobalsocialinteractionsamongconsumers.Itwouldbehelpfulforfirmstobeabletodeterminethecharacteristicsoftherelevantsocialnetworkfortheirtargetmarketandhowchangesinthissocialnetworkinfluencetheirmarketshares.Inaddition,determiningthedistributionofproductpurchasetimesofconsumersandhowtheirvariationaffectsmarketsharesareinterestingissuesforfirms.Inthisstudy,therefore,weproposeanagent-basedsimulationmodelthatgeneratesthemarketsharepaths(marketsharesovertime)ofcompetingproducts.WeapplythemodeltoestimatethesocialnetworkandpurchasetimedistributionoftheKoreannetbookmarket.OurobservationisthatKoreannetbookconsumerstendtobuyaproductwithouthesitation,andtheirsocialnetworkisratherregularbutsparse.Wealsoconductsensitivityanalyseswithrespecttothesocialnetworkandthepurchasetimedistribution.

Keywords:Agent-BasedProductDiffusionModel,IndividualPurchaseTime,SocialNetworkStructure,Estimation,SensitivityAnalysis

Introduction

1.1 Today'sproductmarketsarecompetitive.Becausehigh-techfirmsusuallyhavesimilarlevelsoftechnologyandutilisesimilarmarketingresearchmethodsfortheelicitationofconsumerneeds,itishighlyprobablethatthereexistsimultaneousinnovations(GoldenbergandEfroni2001).Insuchmarketsituations,productswithsimilarfunctionscompetewitheachothertoexpandtheirmarketshares,andasignificantpercentageofnewproductsdisappearfromstoreshelvesaftertheirlowsales.Therefore,tomaximisethepossibilityforthesuccessofanewproductandminimisetheriskandopportunitycostofafailedproduct,firmsmustunderstandthediffusiondynamicsofcompetingproducts.

1.2 Thediffusiondynamicsofcompetingproductsemergefromtheaggregationofconsumers'decisions.Attheindividuallevel,aconsumer'sdecisioniscomposedof"whichproducttobuyamongtheavailableproducts"and"whentobuyaproduct".Individualproductchoiceisaffectedbysocialinteractionsamongconsumers.Withintheirsocialnetwork,consumerscommunicatetheirevaluationsofproductstotheirfriendsandinfluencetheirfriends'purchases.Thisphenomenoniscalledthenetworkeffect,orword-of-moutheffect.

1.3 Productfamilieshavedifferentlogicalsocialnetworkstructures,evenwithinasinglephysicalsocialnetwork,consistingofonlineandofflinesocialconnections.Forexample,apersonasksdifferentfriendsforsuggestionswhenconsideringhigh-techproductsversusclothes.Therearetwostructuralfeaturesofasocialnetworkthataffectthenetworkeffect.Onefeatureistherewiringprobability,whichaffectsthenumberofshortcutsamongconsumers.Theshortcutsareknowntoreducethenumberofstepsbetweenconsumersbylinkingpeoplewhosefriendsdonotknoweachother(Granovetter1973).Becausetheseshortcutshelpconsumerstransferinformationtodistantconsumers,wemaysaythattherewiringprobabilitycontributestothediffusionofinformationaboutproductsinaglobalmanner.Theotherfeatureisthedegreeofconnectivity,whichdeterminesthedegreeofclusteredtiesinanetwork,i.e.,thenumberofneighbours.Agreaterdegreeofclusteredtiesinanetworkisknowntoprovidestrongersocialreinforcementforbuyinganewproduct(CentolaandMacy2007).Becausetheclusteredtieshelpconsumersreceiveinformationonproductsfromtheirneighbours,wemaystatethatthedegreeofconnectivitycontributestothediffusionofproductinformationinalocalmanner.

1.4 Productpurchasetimingcanbemodelledasaprobabilitydistribution,anddifferentproductfamilieshavedifferentpurchasetimedistributions.Forexample,consumerstendtobuyinformationtechnologyproductsearlierintheproductcycle,and,asaresult,theirpurchasetimedistributioncanbeapproximatelymodelledasanexponential-likedistribution.Incontrast,expensivedurablessuchasautomobilesandrefrigeratorshavepurchasetimedistributionsintheshapeofnormaldistributions.Peopletendtotaketheirtimeandcontemplateadoptingsuchdurablesbecausetheseproductsarecostlyandhavelonglifespans.Thisdeliberationresultsinasmallnumberofpeoplebuyingthedurablesearlyintheproductcyclefollowedbyalargenumberofpeoplebuyingthedurableslater.EmpiricalstudiesbyRogers(2003)showusthattheprocessofadoptionovertimeistypicallyillustratedasanormaldistribution.

1.5 Basedontheseconditionsoftheconsumers'socialnetworkandproductpurchasetimes,weareinterestedintheproblemofhowafirmcandeterminethesocialnetworkandthepurchasetimedistributionappropriateforatargetproductmarket.Inaddition,weareinterestedinasensitivityanalysisthatpredictswhatwilloccurwhenthesocialnetworkstructureorthepurchasetimedistributionchangesfromthecurrentmarketconditionsandhowafirmcangainmarketshare.Weaddresstheseproblemsusinganovelexperimentalapproachcalledagent-baseddiffusionmodellingandsimulation,whichiscapableofpredictingthefuturemarketsharepaths(i.e.,marketsharesovertime)ofcompetingproducts.Intheagent-basedsimulationmodel,aconsumer-agentsimulatesthepurchasebehaviourofaconsumer,andasetofconsumer-agentswiththeirinteractionstructurecorrespondstothesocialnetworkofconsumers.Thenodesofthesocialnetworkareconsumer-agents,andeachlinkrepresentsafriendshipbetweentwoconsumer-agents.Thesocialnetworkcanbemodelledasanartificialmarket.Eachconsumer-agentchoosesproductsbasedontheirindividualevaluationsandtheirneighbours'evaluations(i.e.,thenetworkeffect)oftheproducts.Weproposeafuzzymulti-attributeutilitymodeltoformalisetheirproductchoice.Theproductchoicemodelalsoconsiderstheheterogeneouspropensityofconsumers—consumersplacedifferentweightsontheimportanceofproductattributesandvaryingdegreesofsensitivitytothenetworkeffect.Somepeoplewithstrongpersonalitiesmaynotbesusceptibletothenetworkeffect,whereasotherswhoareverysensitivetothetrendsofpublicopinionaccommodatethemselvestothedecisionsofearlyproductadopters.

1.6 Wechoosetousesmall-worldnetworkmodelforthesocialnetworkofconsumer-agents.Rewiringasmallfractionofconnectionsinaringlatticeform,whereeverynodeislinkedtoitsneighbourswithafixeddegreeofconnectivity,resultsinasmall-worldnetwork(WattsandStrogatz1998).Inthisnetwork,nodesarehighlyclustered,andtheinformationtransfertimebetweennodesisshort.Itiswellknownfromempiricalevidencethatthesmall-worldnetworkrepresentsmanytypesofrealsocialnetworks(AlkemadeandCastaldi2005).Normally,therewiringprobabilityofasmall-worldnetworkiswithintherangeof0.01and0.1.AsillustratedinFigure1,ahighrewiringprobabilityleadstorapidproductinformationtransferbetweenclustersofnodes,causingtheglobalnetworkeffecttoincrease.Thedegreeofconnectivitynormallyhasavaluebetween4and20(Kimetal.2011).Whenthenumberofnetworkconnectionsiszero,individualschooseproductsbasedonlyontheirownproductevaluations,withoutinteractionswithneighbourstoobtainproductevaluationinformation.AsshowninFigure1,ahighdegreeofconnectivityleadstorapidproductinformationtransferwithinclusteredties,causingthelocalnetworkeffecttoincrease.Therefore,wecanobservelocalandglobalnetworkeffectsbyvaryingtherewiringprobabilityandthedegreeofconnectivityfromzerotopositivevalues.

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Figure1.Examplesofsmall-worldnetworkswithrespecttotheirrewiringprobabilityanddegreeofconnectivitywhenthenumberofnodesis8

1.7 Consumers'productpurchasetimesareassignedrandomlyusingtheshiftedGompertzdistribution.Thisdistributionisawell-knownpurchasetimedistributionwithvariousshapes(BemmaorandLee2002).Equation(1)givesthegeneralformoftheshiftedGompertzdistribution:

(1)

1.8 Figure2plotsshiftedGompertzdistributionswhentheshapeparameter,η,is0.01,0.1,1,and10.Thescaleparameter,b,isfixedat0.4,followingBemmaor(1994).Customers'tendencytobuyfashionableproductscanbemodelledbytheshiftedGompertzdistributionwithη=0.01,whichresemblesanexponentialdistribution.However,theshiftedGompertzdistributionwithη=10hasashapesimilartoanormaldistributionandsatisfactorilyexplainsthepurchasetimesofexpensivedurables.Thus,asmallershapeparameter,whichrepresentsconsumersbuyingproductsearlierinthecycle,leadstoahigherrateofproductdiffusion.Theshape,determinedbyη,ofashiftedGompertzdistributiondeterminesthediffusionspeedofaproductbecauseconsumerspurchaseproductsaccordingtothedistribution.Therefore,wecanobservehowthemarketsharesofcompetingproductsdifferwhenwechangetheshapeparameter.

Figure2.ExamplesofshiftedGompertzdistributions:(a)whentheshapeparameteris0.01andthescaleparameteris0.4,(b)whentheshapeparameteris0.1andthescaleparameteris0.4,(c)whentheshapeparameteris1andthescaleparameteris0.4,and(d)whentheshapeparameteris10andthescaleparameteris0.4.

1.9 Tonarrowourscope,weapplytheagent-basedsimulationmodeltothecaseoftheKoreannetbookmarket.Inthisstudy,ourcontributionsarethreefold.First,wecomparethemarketsharepathsgeneratedbythesimulationwiththerealsalesdataobtainedfromaKoreane-commercecompanytoestimatetherewiringprobabilityandthedegreeofconnectivityofthesocialnetworkandtheshapeparameteroftheshiftedGompertzdistributionmostappropriatefortheKoreanconsumers.Afterestimatingthethreeparameters,weconductsensitivityanalyseswithrespecttotheseparameters.Asstatedabove,therewiringprobabilitydeterminesthespeedofinter-clusteredproductinformationtransfer,thedegreeofconnectivitydeterminesthespeedofintra-clusteredproductinformationexchange,andtheshapeparameterfixesproductdiffusionspeed.Thus,wecontroltheparametersindividuallytogeneratedifferentglobalandlocalnetworkeffectsanddifferentdiffusionspeeds.Basedontheobservedresults,wesuggeststrategicimplicationsforfirmsdesiringtoincreaseormaintainmarketshareineachcase.

1.10 Theremainderofthispaperisorganisedasfollows.Section2explainsrelatedagent-basedsimulationmodelsforproductdiffusion.Section3introducesthedetailsofourproposedmodel.Section4presentstheempiricalstudyandsensitivityanalyseswithmarketingimplications.Finally,Section5presentsadiscussionandconcludingremarks.

LiteratureSurvey

2.1 Simulationmodelsforproductdiffusioncanbedividedmainlyintocellularautomatamodels(GoldenbergandEfroni2001;Goldenbergetal.2001;MoldovanandGoldenberg2004;GuseoandGuidolin2009;SchwarzandErnst2009)andagent-basedsocialnetworkmodels(JanssenandJager2001;JanssenandJager2003;Delreetal.2007a;Delreetal.2007b;Kimetal.2011;Guntheretal.2011).Acellularautomatamodeliscomposedofcellsinaregulargrid.Eachcellhasafinitenumberofstatesandbelongstooneofthestates(e.g.,'0'fornon-adoptionand'1'foradoption).Ateachtimestepofsimulation,thestateofanysinglecellisdeterminedbytheneighbouringcells'previousstatesandatransitionfunctionthatspecifiesanidenticalruleactingoneachoftheadjacentcells.Transitionfunctionscanbedefinedaseithersimplerulesorprobabilityfunctions.Usingaverysimpletransitionfunction,GoldenbergandEfroni(2001)soundlydemonstratedthepropagationofawarenessofemergentneedsinthemarket.Goldenbergetal.(2001)furtherproposedaprobabilistictransitionfunctionforcellsinconsiderationofinterpersonalfactorsandexternalfactorstoexploretheunderlyingprocessofword-of-mouthcommunications.MoldovanandGoldenberg(2004)laterinvestigatedhowtheadverseeffectsofnegativeword-of-mouthandconsumerresistancetochangemaydecreasemarketsize.GuseoandGuidolin(2009)focusedonthestatetransitionsofacellularautomatanetworkratherthanthestatetransitionsofthecellsthemselves.Theyfocusedonthestatetransitionsofedgesamongcellsundertheassumptionthatmarketpotentialisassociatedwiththecollectiveknowledgeinthecommunicationnetwork.Thestateofanedgebetweentwonodesisdeterminedbythestatesofotheredgesconnectedtothetwonodes,andthemarketpotentialisdeterminedbythenumberofactiveedges.Themarketpotentialisappliedtotheadoptionprocessofcells.However,SchwarzandErnst(2009)indicatedthatcellularautomatamodelsyieldspatiallyexplicitresultsbutmerelyusethestatesoftheircellsforthesimulationwithoutcapturingtheheterogeneityofthecellswheresuchheterogeneityexists.

2.2 Theagent-basedsocialnetworkmodelhasrecentlydrawnattentionfromresearchersinvestigatingcollectivemarketdynamics.JanssenandJager(2001)studiedthedynamicsofmarketsfromapsychologicalperspectiveanddefinedfourcognitiveprocessesforbehaviouraldecisions,relyingonthelevelofuncertaintyandthelevelofsatisfaction,andshowedthatthesebehaviouralrulesdeterminetheartificialconsumer'sdecisionmaking.Inasubsequentstudy,JanssenandJager(2003)exploredtheeffectsofthedifferentsocialnetworkstructuresoftheagentsandshowedthatamarketorganisesitselfviainteractionsamongagents'decision-makingprocesses,productcharacteristics,andthenetworkstructureoftheagents.Delreetal.(2007a)studiedtheeffectofsocialprocessesondiffusiondynamicsandtheeffectsofconsumerheterogeneityandconsumers'networkstructureondiffusionspeed.Delreetal.(2007b)alsoinvestigatedtheeffectivenessofdifferentpromotionalstrategiesforthelaunchofaproduct.However,theagent-basedsocialnetworkmodelsinthesestudiesconsideronlyasingleproductcategory.Thesemodelsdonotconsidercompetitivemarketconditionsunderwhichaconsumerchoosesaproductamongcompetingproducts.Concerningthepurchasetimeoftheagent,thesemodelsalloweveryagenttocomparetheutilityofaproductwithathresholdvaluethatisgivenrandomlyandadopttheproductwhentheutilityexceedsthethreshold.Thethreshold-basedmodelofproductadoptioniseasytoimplementandappropriateforthediffusionmodellingofasingleproductcategorybecauseitinvolvesonlybinaryoptions,suchasadoptionornon-adoption(Granovetter1978).However,whenseveralproductscompeteinamarket,thethreshold-basedmodelisdifficulttoapplybecausetheremaybeseveralproductsthatsimultaneouslyexceedthethresholdofaparticularconsumer.Kimetal.(2011)proposedanagent-basedsimulationforestimatingthediffusionofcompetingproductsinanautomobilemarket.Intheirsimulation,anagentchoosesacarusingamulti-attributedecision-makingheuristiccalledfuzzyTOPSIS(TechniqueforOrderPreferencebySimilaritytoIdealSolution).Underthisheuristic,eachagentselectsthebestcar

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fromamongcompetingmodelsasbeingtheclosesttothepositiveidealsolutionandthefarthestfromthenegativeidealsolution.Theauthorsassumeauniformdistributiontomodelconsumers'purchasetimes.Additionally,ourstudypositsthatconsumers'purchasetimeshavedifferentdistributionsaccordingtoproducttype.Guntheretal.(2011)proposedamodelforassessingmarketingactivitiessuchaslaunchtiming,markettargeting,andpricingforbiomass-basedfuelthatwillbeusedinAustriainthenearfuture.Inthisstudy,anagentadoptseitherbiomass-basedfuelorfossilfuelonthebasisofthreshold-basedadoptionrules.

TheAgent-BasedSimulationModel

3.1 Thismodelhasthreeinputvariables:theexperts'ratingsofproductattributes,theagents'weightsforproductattributes,andtheagents'degreesofsensitivitytothenetworkeffect.Weassumethatallconsumer-agentssharetheexperts'opinionsthroughmassmediainthebeginningofproductdiffusionandfollowtheexperts'opinions.Thus,aconsumer-agent'sevaluationisinitiallysettotheexperts'ratingsofproductattributeswithaconsiderationoftheagent'sownweightsforproductattributes.Inaddition,intherealworld,theextenttowhichconsumersareinfluencedbythenetworkeffectdiffersaccordingtoindividualcharacteristics.Thus,eachagenthasadegreeofsensitivitytothenetworkeffectthatrepresentstheindividual'ssensitivitytohisorherneighbours'opinions.

3.2 WeassumethatthethreeinputvariablesareassessedusingthefivelinguistictermslistedinTable1.Becauselinguisticassessmentisimprecise,modellingusingafuzzysetisaneffectiveapproachtoquantifyingtheseterms.ThevaguenessofeachterminthisstudyischaracterisedasavaluesetwithatriangularmembershipfunctionsshowninFigure3-(a)(Zimmermann2001).AsillustratedinFigure3-(b),avaluesetdefinedas(a,b,c)iscalledatriangularfuzzynumber,andthecorrespondingmembershipfunctionindicatesthedegreeofcertaintythatavalueinthesetbelongstothelinguisticterm.Inparticular,wescaledtriangularfuzzynumberswithintherangeof[0,100],assuggestedbyYehandKuo(2003),downtotherangeof[0,1].Itisalsopossibleforaspecificapplicationdomaintoinducetriangularfuzzynumbersusingsurvey(orexperimental)data(HongandLee1996),butthisworkremainsalargeandchallengingresearchissue.

Table1.Linguisticvariablesandtriangularfuzzynumbers

Figure3.(a)ThefuzzymembershipfunctionsofthefivelinguistictermsinTable1;(b)adepictionofatriangularfuzzynumber

3.3 Thediffusionsimulationconsistsofaninitialisationstageandanexecutionstage.Intheinitialisationstage,weconstructasocialnetworkofconsumer-agentswithaspecificrewiringprobabilityandadegreeofconnectivityandassigneachagentthreepersonalproperties:aproductpurchasetime,weightsforproductattributes,andadegreeofsensitivitytothenetworkeffect.Weassigneachagent'spurchasetimebyusingashiftedGompertzdistributionwithaspecificshapeparametervalue.Forthelasttwoproperties,weconductaquestionnairesurveywiththefivelinguisticterms,buildempiricaldistributions,andassigneachagentrandomlychosenvaluesfromthedistributions.

3.4 Theexecutionstageproceedsasfollows.Weassumethattherearemproductspi(i=1,…,m)inanartificialmarket,andeachproducthasnobservableattributesdj(j=1,…,n).Lettheexperts'ratingsoftheproductswithrespecttotheattributesbegivenasfollows:

(2)

Inthismatrix,r*ijisthetriangularfuzzynumberthatcorrespondstotheexperts'linguisticevaluationofattributedjofproductpi(seeTable1).

3.5 Atthebeginningoftheexecutionstage,eachconsumer-agentacceptstheexperts'opinionswithaconsiderationoftheattributeweights.LetW*k=(w*

1k,…,w*nk)betheattributeweightvectorofconsumer-agent

k,inwhichtheelementsofthevectorarealsodenotedbythetriangularfuzzynumbersinTable1.TheagentmultipliestheattributeweightvectorW*kbytheexperts'productratingmatrixE*.Theresultis

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consumer-agentk'spersonalisedfuzzydecisionmatrixD*k,whichisdefinedas

(3)

wherex*kij=r*ij⊗w*jk.LetA*1=(a1,b1,c1)andA*2=(a2,b2,c2)betwotriangularfuzzynumbers.Themultiplicationoperator⊗ofthetwotriangularfuzzynumbersisthendefinedasA*1⊗A*2=(a1a2,b1b2,

c1c2)(Zimmermann2001).Thenewfuzzynumber,x*kij,canberegardedasthepartialutilityofproductpiwithrespecttoattributedjevaluatedbytheconsumer-agentkwithoutconsideringthenetworkeffect.

3.6 Fortheconsumer-agentktochooseaproduct,itisrequiredthattheattribute-levelfuzzyutilitiesx*ij(i=1,…,m;j=1,…,n)beaggregatedforeachproductandcomparedamongproducts.However,thisfuzzy,multi-attributedecision-makingapproachsuffersfromvariousdrawbackssuchasalackofsensitivitywhencomparingsimilarfuzzynumbers,counterintuitiveoutcomesinsomecircumstances,andcomplexcomputationalprocesses(DengandYeh2006).Toavoidthedrawbacksintheproductchoiceprocess,weemployacommonandusefuldefuzzificationtechniquecalledthecentre-of-gravity(COG)approach(WangandLuoh2000).Infuzzysettheory,defuzzificationhasbeenusedasaneffectivemeansofinterpretingthemembershipdegreeofatriangularfuzzynumberasaspecificcrispvalue.TheCOGisan

expectedgeometriccentreofmass.Givenafuzzynumberx*kij,denotedas(xk(1)ij,xk(2)ij,xk(3)ij),itsCOG,xkij,isdefinedas

(4)

whereSUPijisthesupportofx*kijandμ(x)isthemembershipfunctionofx*kij.Byapplyingthedefuzzificationmethodinequation(4)tothepersonalisedfuzzydecisionmatrixD*kinequation(3),weobtaina

personaliseddecisionmatrixDkthatiscomposedofcrispvalues(equation(5)).Thismatrixcontainsconsumer-agentk'spersonalisedutilitieswithrespecttoproductattributes.

(5)

3.7 Consumersalsoreflectontheproductratingsoftheirneighboursinmakingpurchasedecisions.Tomodelnetworkeffectsinproductchoice,weaveragetheproductattributeratingsforwardedfromneighbours.Theutilityofconsumer-agentkwithrespecttotheattributedjofproductpiisthendefinedastheweightedaverageofapersonalisedcomponentandanetworkeffectcomponent:

(6)

whereLkisthesetofconsumer-agentk'sneighbours,AkisthesetofadoptersinLk,andαkisthedefuzzifiedsensitivitydegreeofconsumer-agentktothenetworkeffect(0≤αk≤1).Whenaconsumerismoreinnovative,thepersonalisedcomponentisweightedmoreheavily.Incontrast,whenaconsumerislessinnovative,thenetworkeffectcomponentisweightedmoreheavily.Byincorporatingthenetworkeffect

componentintoequation(5),acompleteattributeutilitymatrix,Sk,isobtainedas

(7)

3.8 Fromthebeginningofthesimulation,consumer-agentkupdatestheattributeutilitymatrixSkwiththeattributeratingsforwardedbyneighbouringadopters(seeequation(6)).Whenthesimulationtimereachesthe

givenpurchasetimeoftheagent,theagentchoosesacertainproductwithacertainprobability,Pk(i),usingapopularchoicerulecalledthemultinomiallogitrule(Train2009),whichisdefinedbyequation(8):

(8)

3.9 Whenusingindividualpurchasetimedistributionsasinthesimulationmodel,allconsumer-agentseventuallybuyproductsattheendofthesimulationbecauseeveryagentisassignedapurchasetime.Ingeneral,however,allagentsdonotadoptnewproductsinreal-worldmarkets.Forthiscase,weaddadummyproduct(i.e.,itisnotarealproductbutrepresentsnoadoption)tothesimulationmodel.Becausethedummyproductisequivalenttotheproductinuse,itsutilityiscalculatedbyassumingthattheratingsofalltheproductattributesare"fair".Suchamodificationenablesourmodeltoincorporatenoproductadoptioninequation(8).

3.10 Thefollowingstepssummarisethesimulationprocess:

Initialisation

Step1.Createaconsumer-agentnetworkwitharewiringprobabilityandadegreeofconnectivity.

Step2.Assignweightstoproductattributesandthedegreeofsensitivitytothenetworkeffecttoconsumer-agentsusingempiricaldistributions.

Step3.Generateconsumer-agents'purchasetimesusingashiftedGompertzdistributionwithashapeparameter.

Step4.Establishexperts'linguisticratingsoneachcompetingproduct.

Execution

Step5.Atsimulationtimet=0,introducetheexperts'ratingsofcompetingproductstoallconsumer-agents,whoeachcreatethepersonaliseddecisionmatrixDkinequation(5)usingtheirindividualweightsfortheproductattributes.

Step6.Allconsumer-agentsupdatetheattributeutilitymatrixSkinequation(7)byrequestinginformationfromneighbourswhopurchasedanyproductsbeforethecurrenttimet.Thosewhosepurchasetimesareequaltothecurrenttimetselectproductsusingthemultinomiallogitrule.

Step7.Sett=t+1.Ifthesimulationtimereachestheterminationtime,stopthediffusion;otherwise,returntoStep6.

ExperimentalDesign

Koreannetbookmarket

4.1 NetbooksareafamilyofnotebooksfocusingonmobilityandInternetuse.Netbookproductswerereleasedinonlineshoppingmallsinthefirsthalfof2008inKorea.Theproductsofsixproducersmakeupthe

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netbookmarket,andthreeproductsfromtwoproducersoccupied60percentofthetotalmarket.Thesethreeproductshadsimilarreleasetimes(twoofthethreeproductswereintroducedtwoweeksearlierthantheother,butweignorethistimedifferenceinthisexperiment)andwereintroducedapproximatelythreemonthsearlierthantheotherproducts,forwhichthemarketsharesandvariationsweresmall.

Datadescription

4.2 Productattributeslistedasmajorbuyingcriteriaincommercialexpertreviewwebsites(e.g.,PCWorld)includeCPUperformance,datastoragesize,memorysize,displaysize,batterylife,weight,andprice.ThewebsitesprovidedgradedratingsofthethreenetbooksinJuly2008,justbeforetheproducts'releaseontheKoreanmarket.Weaveragedtheratingsoftheproductsforeachattribute;theresultsaresummarisedinTable2.TheCPUperformance,memorysizes,andpricesofthethreeproductsarethesame.Basedontheratingresults,itwasnoteasytopredictwhichproductwouldbeawinnerinthemarket.

Table2.Experts'productattributeratingsforthethreeproducts

4.3 Weconductedaquestionnairesurveytoobtainindividualconsumers'weightsfortheattributesofanetbookandtheirsensitivityleveltothenetworkeffect.Of153respondents,therewere100validresponsesincludedinouranalysis.ThesurveyresultsaresummarisedinTables3and4.Table3showsthatCPUperformance,weight,andpriceareimportantattributes(i.e.,approximately30%ormoreoftherespondentsratedtheseattributesas"veryhigh").AsshowninTable4,norespondentswereverystronglysensitivetothenetworkeffect;41%oftherespondentsratedthemselvesas"stronglyornormally"sensitivetothenetworkeffect,and59%oftherespondentswere"weaklyorveryweakly"sensitivetothenetworkeffect.

Table3.Consumers'weightsforthenetbookattributes

Table4.Consumersensitivitytonetworkeffects

Descriptionoftheexperiment

4.4 UsingtheNetlogosoftware(http://ccl.northwestern.edu/netlogo),wecreatedasmall-worldnetworkof5,000consumeragentstorepresenttheKoreannetbookmarket.Theexperimentconsistsofanempiricalstudyandasensitivityanalysis.Intheempiricalstudy,weadjustedtherewiringprobabilityandthedegreeofconnectivityoftheconsumer-agentnetworkandtheshapeparameterofindividualpurchasetimedistributionsappropriatefortheKoreannetbookmarket.Wetestedfourrewiringprobabilities(0.01,0.0.5,0.1,and0.25)andfivedegreesofconnectivity(4,6,8,10,and20)fortheconsumer-agentnetwork.Wealsoevaluatedfourshapeparameters(0.01,0.1,1,and10)fortheshiftedGompertzdistributionthatgeneratedfourdifferentindividualpurchasetimedistributions.Thetotalnumberofparametercombinationswas80.Foreachcombination,100simulationrunswerereplicatedsothataperformancemeasureatthelevelofthe95%confidenceintervalwasobtainedbyChebyshev'stheorem(Shannon1975).Theperformancemeasureusedintheempiricalstudywasthemarketsharepathofeachproduct.Themarketshareofaproductatatimewascalculatedasitscumulativesalesvolumedividedbythetotalsalesvolumeatagiventime,anditsmarketsharepathissimplythemarketshareovertime.Inthesensitivityanalysis,wecontrolledthethreeparameters(thedegreeofconnectivity,therewiringprobability,andtheshapeparameter)toobservethechangesinthemarketsharepathsofthethreeproducts.Themeansandthevariancesofthemarketsharepathswereusedasmetricsfortheanalysis.

4.5 Inthisexperiment,wedidnotconsider"noproductadoption"fortworeasons.First,therespondentsofthequestionnairesurveywerewillingtobuyanewproduct,andtheyhadusedproductswithsimilarfunctions.Second,wecomparedoursimulationresultwiththerealmarketsharepathsbasedonthesalesvolumesofonlythreeproducts.Themarketshareofaproductisdefinedastheproportionofthesalesvolumeoftheproducttothetotalsalesvolumeofsimilarproductsinmarket.Buyingnoproductoraproductotherthanthethreestudiedproductswaspreviouslyexcludedfromtherealmarketsharepaths.Therefore,wedidnotincludeanoptionfor"nopurchase".

Notation

Thetermsbelowareusedfrequentlyinthefollowingsections:

T:theentiresalesintervalR:thenumberofsimulationreplicationsyij(·):thesimulatedmarketsharepathofproductioverT,generatedbythejthreplicationzi(·):therealmarketsharepathofproductioverT

Empiricalstudy

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5.1 Wedefinedthedistancebetweentwopathsincomparison(i.e.,thesimulatedmarketsharepathofaproductandthecorrespondingrealmarketsharepath)astheEuclidiandistanceevaluatedbythedynamictimewarping(DTW)technique(SakoeandChiba1978).Thistechniqueisoftenappliedtomeasuretwotime-seriespatternsofdifferentlengthsandpossiblywithdifferenttimescales.Weusedthistechniquebecausethetimelinesbetweentherealmarketsharepath(inweeks)andthesimulationresult(insimulationtimesteps)aredifferent.Thedistance(disti)betweenthesimulatedmarketsharepaths(yij(·))andtherealmarketsharepath(zi(·))ofproductiinRreplicationsisdefinedbyequation(9),inwhichthefunctionDTW(a,b)givesthedifferencebetweentwosequencesaandbasaEuclidiandistance:

(9)

5.2 Becausethereismorethanoneproduct,wedefinetheaggregateddistance(dist)ofmproductsbyequation(10):

(10)

Figure4.Euclidiandistancesbetweensimulation-generatedandrealmarketsharepaths

5.3 Figure4summarisesourresults,depictingthedistancesbetweenthesimulation-generatedmarketsharepathsandtherealmarketsharepathsofthethreenetbooksinKorea.Inthisfigure,asmallaggregateddistanceindicateshighsimilarity.Theresultmostsimilartotherealdataoccurredwhentheshapeparameterofthepurchasetimedistributionwas0.01.ThefigurealsoshowsthatoursimulationresultbecomessimilartotheactualnetbookdiffusioninKoreawhentheshapeparameterissmaller.ThisresultimpliesthatKoreannetbookbuyersarelikelytopurchasenetbooksearlyasfashionableandtrendyproducts.Demandforhigh-techproducts,e.g.,netbooks,notebooks,andsmartphones,isvolatile(Wuetal.2005),andtheproductsexperienceconsiderableup-frontexpenditurefollowedbyrapidobsolescence(PangburnandSundaresan2009).Forexample,thesalesvolumeofeverynewmodelofiPadoriPhonewasveryhighatthebeginningofproductlaunch.Wemayextendourinferencethatconsumers'rapidpurchasesatthebeginningofproductreleaseenticefirmstoprovidenewproductswithshortlifecycles.

5.4 ThediffusionofnetbooksintheKoreanmarketcanbeexplainedbytwostructuralfeaturesofasocialnetwork:therewiringprobabilityandthedegreeofconnectivity.InFigure4,theresultmostsimilartotherealdatawasfoundwhentherewiringprobabilitywas0.05andthedegreeofconnectivitywas4.ThisfindingindicatesthatthesocialnetworkofKoreannetbookconsumersisaregularnetwork,andeachconsumerhasasmallnumberofneighbours.Thatis,thesocialnetworkislogicallywellorganisedbutsparse.Becauseasmall-worldnetworkisdefinedwitharewiringprobabilityrangingbetween0.01and0.1,therewiringprobabilityoftheKoreannetbookconsumernetwork(0.05)appearstobehigh.However,thedegreeofconnectivityoftheKoreannetbookconsumernetwork(4)islow.Thisvalueimpliesthat,inKorea,netbooksarelikelytodiffusenotbyreinforcementfrommanylocalsources(CentolaandMacy2007;Centola2010)butratherbysimplecontactwiththehelpofshortcuts(Granovetter1973).Thatis,anetworkwithmanysmallclustersrepresentsthesocialnetworkofKoreannetbookconsumers.

5.5 Figure5illustratestherealmarketsharepathsandthemarketsharepathssimulatedwithascaleparameterof0.4,ashapeparameterof0.01,arewiringprobabilityof0.05,andadegreeofconnectivityof4.Inthisfigure,therealmarketsharepathsaftert=3inFigure5(a)andthesimulatedmarketsharepathsaftert=0inFigure5(b)aresimilarintermsofrelativedominance.However,wecanobservethatthedifferenceinmarketsharepathsfromt=0tot=3andthedifferenceinthemarketsharepathsofProduct1andProduct2aftert=3.Inthesimulation,wemayhavelostsomefactorsthatcontrolmarketsharepaths.Wesuspecttwofactorsaremissed:

a. Coercivesynchronisationofproductreleasetimes:wehavealignedthereleasetimesofthethreeproductstostartdiffusionatthesametime.Wehavetruncatedthedataofthefirsttwoweeksoftwoproductsthatwerereleasedtwoweeksbeforetheotherone.Wemayhavelostsocialinfluencehappenedinthetwoweeks.Thismayleadtotheresultofthedifferenceinthemarketsharepathsfromt=0tot=3.

b. Noexternalshockfromthemarket:wemayhavemissedexternalshocksthathappenunevenlyinreallife.Theexternalshockscouldbemarketingstrategies(e.g.,pricediscountandpromotion)andchangesintheexperts'opinions.TheabsenceoftheexternalshocksmaycausethedifferenceinthemarketsharepathsofProduct1andProduct2aftert=3.

Figure5.Marketsharepaths:(a)realonesand(b)simulationresultswithascaleparameterof0.4,ashapeparameterof0.01,arewiringprobabilityof0.05,andadegreeofconnectivityof4

Sensitivityanalysis

6.1 Basedontheexperts'evaluationsoftheproductattributesinTable2,wefindthatProduct2isinferiortobothProduct1andProduct3.TheevaluationsofProduct1andProduct3arethesamewithrespecttoeveryproductattributeexceptforbatterylifeandweight.Product3surpassesProduct1inbatterylife,withadifferenceofthreelinguisticlevels.However,Product1beatsProduct3inweightbyadifferenceofonelevel.Product3isthusjudgedtobeslightlybetterthanProduct1intheoverallevaluation,buttheyarecompetitive.

6.2 Inthissituation,weanalysedthelocalnetworkeffectcausedbyneighbours,theglobalnetworkeffectcausedbyshortcutsamongconsumers,andthepurchasetimeeffect(i.e.,theeffectcausedbydifferentindividualpurchasetimedistributions).Here,weusedtwometricsfortheanalysis:themeanmarketsharepathandthemarketsharevariance.First,wedefinethemeanmarketsharepathofproductibyequation(11):

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(11)

ThisequationyieldsthemeanofRsimulationreplicationsandrepresentstheexpectationforthemarketshareofaproductovertime.Withthismetric,wecancompareonemarketsharepathwithanotherandtherebydeducethemagnitudeofthenetworkeffect.Second,wedefinethemarketsharevarianceofproductigeneratedfromRreplicationsbyequation(12),representingtheuncertaintyinforecastingmarketshare:

(12)

Thelocalnetworkeffect:Asensitivityanalysisonthedegreeofconnectivityofsocialnetwork

6.3 Weanalysedthelocalnetworkeffectbyrunningourmodelwithdifferentdegreesofconnectivity(0,4,6,8,10,and20).Wefixedtheotherparameterstothesamevaluesastheestimatedconditionfoundinthepreviousexperiment.Thatis,therewiringprobabilityandtheshapeparameterweresetat0.05and0.01,respectively.

6.4 Figure6confirmsthatthedegreeofconnectivitygreatlyaffectsthediffusionofproducts.Thedifferencebetweenthemeanmarketsharepathofaproductwithoutanetworkeffect(i.e.,whenthedegreeofconnectivity=0)andthatofaproductwithapositivedegreeofconnectivityrevealsthemagnitudeofthelocalnetworkeffect.Whentherewasnonetworkeffect,consumer-agentsarrivedatmutuallydifferentevaluationsofthethreeproductsbyfilteringtheexperts'opinionsinTable2basedontheirownweights.Asaresult,theproductsgaineddifferentbutstablemarketshares.However,asthedegreeofconnectivityincreased,themarketshareofminorproductssuchasProduct1andProduct2fell,butthatofmajorproductssuchasProduct3rose.

6.5 BasedonourjudgementthatProduct3issuperiortotheothersinalmostallattributes(Table2),thelocalnetworkeffectappearstoenableamajorproducttoclaimasuperiormarketpositionbutrelegatesaminorproducttoaninferiorposition.ThisobservationsuggeststhattheriseofProduct3totakethelargestmarketshareresultednotonlyfromitshigherqualitybutalsofromnetworkeffectspromotingconsumer-agentstobuyProduct3morequickly.ExactlythesameexplanationisofferedbyTellisetal.(2009):"Consequently,theentiremarketsettlesonthebetterproductsmorequicklyandatahigherlevelthanitwouldhaveintheabsenceofnetworkeffects".

6.6 Themajorproduct(Product3)hadtheadvantageofgainingmarketsharefromthelocalnetworkeffect—itsmarketsharewasabruptlyincreasedatthebeginningofproductdiffusion.Wesuggestthatthelocalnetworkeffectultimatelybiasedtheevaluationsofmanyconsumer-agentstowardstheexperts'opinionsfortworeasons.First,atthestartofproductdiffusion,consumer-agentshadtheexperts'opinionsasareferencefortheirevaluations.Evenwhentheirweightswereinitiallydifferent,Product3becamethemostfavourableproductamongtheconsumer-agentsbecausetheexpertsratedProduct3asthebestintheiroverallevaluationofproductattributes.Second,therewasinsufficienttimefortheconsumer-agentstosharetheinformationthatProduct1wasalsoacompetitiveproductbecausetheindividualproductpurchasetimedistributionresemblesanexponentialdistribution.Consequently,ifwedefinereliableknowledgeastheexperts'opinions,thenthereliableknowledgepropagatedbythelocalnetworkeffectwithinthesocialnetworkseemedtoleadtheconsumer-agentstothemajorproduct.

6.7 Althoughtheminorproducts(Product1and2)lostmarketshareduetothelocalnetworkeffect,thereremainedsomemarketsharefortheseproducts.Thisphenomenonindicatesthatthelocalnetworkeffectmayencroachonthemarketshareoftheminorproductbutthattherestillaresomepeoplelockedintotheminorproduct.WeknowthatthestructureofthesocialnetworkofKoreannetbookconsumershasmanysmallclustersduetothelargerewiringprobabilityandsmalldegreeofconnectivity.Additionally,wesurmisethatthenetworkeffectmayoccuronlyintheearlystageofproductdiffusionbecausetheshapeoftheindividualpurchasetimedistributionresemblesanexponentialdistribution.AccordingtoourfindingsonthesocialnetworkstructureandthepurchasetimeofKoreannetbookconsumers,wecanstatethatsomeclustersmaynothavesufficienttimeandinformationtoshifttheirpurchasedecisionstobuyproductsotherthanthebestproductsasinitiallyevaluatedbytheconsumersthemselves.

Figure6.Themeansofthemarketsharepathswithrespecttochangesinthedegreeofconnectivity:(a)Product1,(b)Product2,and(c)Product3

6.8 Ourdiscoveryisthatthelocalnetworkeffectdiminishesdiversityinpurchasingandpromotesstandardisationinpurchasingwhenconsumerstendtobuyproductsearlyafterlaunch,asisthecaseforfashionableproducts.However,whentheconsumers'socialnetworkconsistsofmanysmallclusterscharacterisedbyahighrewiringprobabilityandalowdegreeofconnectivity,quickproductpurchasetendenciesdecreasethelocalnetworkeffectandleavesomemarketsharefortheminorproducts.

6.9 Ourresultsalsoshowthatanincreaseinthedegreeofconnectivitydidnotincreasethemagnitudeofthelocalnetworkeffectcritically.Thedegreeofconnectivityreferstothenumberofcommunicationchannelsandthenumberofneighboursinfluencingproduct-purchasingdecisions.WecaneasilyconfirmthattheranksoftheproductratingsbytheexpertsarestraightforwardinTable2;thus,consistent(orreliable)informationonproductevaluationmayflowthroughthesocialnetworkevenwhenfewneighbourssharethisinformation.Therefore,theinitialevaluationofproductsbytheexpertsisthemostdecisivefactorwhenconsumersbuyproductsearly.

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Figure7.Variancesofthemarketshareswithrespecttochangesinthedegreeofconnectivity

6.10 Figure7illustratesthemarketsharevariancesofthethreeproductswithrespecttothedegreeofconnectivity.Marketsharevarianceisimportanttoafirmbecauseuncertaintythereinisdirectlyrelatedtotheriskofinvestmentinanewproduct.Weobservedthatthemajorproduct(Product3)hadagreatervariancecomparedwiththeminorproducts(Product1andProduct2).Figure6showsthatthemeanmarketsharepathofProduct3risesastheothersfall,indicatingthattheevaluationofProduct3diffusedwellcomparedwiththeevaluationsoftheotherproducts,andthenumberofconsumerswhoconsideredbuyingProduct3increased.Thus,thechanceofProduct3todiffuseroseduetothediffusionoftheproductevaluation,butthisincreasedchancealsoincreasedthevarianceofthemarketsharepathofthisproduct.

6.11 Wealsoobservedthatthemarketsharevariancesofthethreeproductsapproachthevariancesgeneratedwithnonetworkeffectasthedegreeofconnectivityincreases.Consumerstendtobuyaproductbyusingtheirownevaluationsoftheproductswhenthereisnolocalnetworkeffect.However,asthedegreeofconnectivityincreases,consumersareinfluencedbyneighbours,anditbecomesmorelikelythataconsumerwillchooseoneofthethreeproducts.Thus,thevarianceincreases.However,afteracertainpoint,thevariancebecomessmaller,anditappearsthatitapproachesthevariancewhenthereisnonetworkeffect.Wecanexplainthisphenomenonastheresultofanaveragingeffect.Withasmallnumberofneighbours,aconsumer'spurchasemaybebiasedtowardsthoseneighbours'tastes.However,whenthenumberofneighboursissufficientlylarge,theconsumerwillbeexposedtoalmostalltheopinionsofotherpeople.Thissituationmayleadtheconsumertoobtainasomewhatless-biasedevaluationfromneighboursbyaveragingalltheiropinions.Althoughwedonotknowwhatproducteachconsumerpurchases,wecanconcludethatasthedegreeofconnectivityincreases,theuncertaintyinachievingthemeanmarketsharepathsofthethreeproductsreturnstothepointatwhichwherethereisnonetworkeffect.

6.12 Whentheindividualpurchasetimedistributionresemblesanormaldistribution,consumer-agentsthenhavesufficienttimetoconsiderpurchasingaproduct,andthedegreeofconnectivitywillaffectthemagnitudeofthelocalnetworkeffectcrucially,andthemarketsharepathsoftheproductsshoulddisplayvariouspatterns.Ifthissimilarityholdstrue,thisimpliesthatafirmdesiringtoincreasethemarketsharesoftheirproductsshouldinvestconstantlyinsocialnetworkingservicemarketingandprovideconsumerswithmorecommunicationchannelswiththeirfriends.

Theglobalnetworkeffect:Asensitivityanalysisontherewiringprobabilityofasocialnetwork

6.13 Asdiscussedabove,therewiringprobabilitydeterminesthenumberofshortcutsamongconsumer-agents.Asthenumberofshortcutsincreases,itisevidentthatinformationflowswellthroughouttheclustersofthesocialnetworkofconsumers.Thus,wevariedtherewiringprobabilityandobservedtheglobalnetworkeffect.Thedegreeofconnectivityandtheshapeparameterwerefixedat4and0.01,respectively.

Figure8.Themeanmarketshareswithrespecttochangesintherewiringprobability:(a)Product1,(b)Product2,and(c)Product3

6.14 Figure8presentsthemeanmarketsharepathsofthethreeproductswhenwechangedtherewiringprobabilityby0.01,0.05,0.1,and0.25,illustratingthatthemeanmarketsharepathremainsalmostthesameregardlessoftherewiringprobability.Wesuspectthattherapidpurchasesofconsumersdidnotcauseastrongglobalnetworkeffect.Additionally,itisknownthatthenumberofshortcutsbetweendistantconsumersisproportionaltothenumberoflocalneighbours(i.e.,thedegreeofconnectivity)becauseeachshortcutismadebydisconnectingalocallinkandrewiringthelinktoadistantconsumer.Becausethenumberoflocalneighboursinthissocialnetwork(4)wassmall,theabsolutenumberofshortcutsgeneratedevenwhentherewiringprobabilitywasatthemaximumvalueof0.25maynothavebeensufficienttocreateasignificantglobalnetworkeffect.Thus,theglobalnetworkeffectwouldbeinfluencednotonlybytherewiringprobabilitybutalsobythedegreeofconnectivity.Basedontheanalysisoftheresults,wesurmisethattheglobalnetworkeffectmayincreasewiththerewiringprobabilitywhentheindividualpurchasetimedistributionresemblesadistributionandthedegreeofconnectivityishigh.

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Figure9.Variancesofthemarketsharepathswithrespecttochangesintherewiringprobability

6.15 However,inFigure9,adifferenceinthemarketsharevariancesofthethreeproductscanbeobserved.ThisfiguredemonstratesthatthevarianceofProduct3isgreaterthanthoseoftheotherproducts.Forthemajorproduct,Product3,thevariancebecomessmallerwhentherewiringprobabilityis0.05or0.1comparedwith0.01or0.25,meaningthatarewiringprobabilitythatistoosmallortoolargemayincreasetheuncertaintyinreachingthemeanmarketsharepathofthemajorproduct.Thisfindingstandsincontrasttotheprevioussensitivityanalysisrevealingthatatoo-smallortoo-largeconnectivityreducestheuncertainty.

6.16 Forconditionsunderwhichconsumershaveasmallnumberofneighboursandarerapidpurchasers,amoderatenumberofshortcuts(neithertoofewnortoomany)shouldprovidetheproducerofahigh-qualityproduct(e.g.,Product3)withagreaterchancetoachievethemeanmarketsharefortheproduct.Fromtheperspectiveofsocialnetworkservices,itisthusundesirableforafirmthatproducesahigh-qualitynetbooktoprovideonlinecommunicationspacesthatenableKoreannetbookconsumerstotransferproductinformationwithtoomanynewacquaintancesbecausethisconnectivitycouldcausethesocialnetworkofKoreannetbookconsumerstoclustersufficientlytoincreasetheuncertaintyinachievingthemeanmarketshare.

Thepurchasetimeeffect:Asensitivityanalysisontheshapeparameterofindividualpurchasetimedistribution

6.17 Theprevioustwoexperimentsexaminedasensitivityanalysisforthesocialnetwork;wenowexaminepurchasetime.Figure10illustratesthemeanmarketsharepathsofthethreeproductswithrespecttochangesintheshapeparameteroftheindividualpurchasetimedistribution.Wevariedtheshapeparameter,settingitat0.01,0.1,1,or10.However,wefixedthedegreeofconnectivityat0.01andtherewiringprobabilityat0.05.AsillustratedinFigure2,thelargershapeparametercausesashiftofpeakintheindividualpurchasetimedistribution.Forexample,whentheshapeparameteris10,theindividualpurchasetimedistributionresemblesanormaldistribution,anditspeakisformedatTimeStep8inthesimulation.

6.18 Figure10showsthatashapeparametergreaterthan1resultsindifferentmarketsharepatternsforthethreeproducts.Astheshapeparameterwasincreasedfrom0.01to1,themarketsharepathsofProduct1andProduct2fellslightly,whereasthemarketsharepathofProduct3rose.Whentheshapeparameterbecamegreaterthan1,themarketsharepathofProduct1fellinitiallyandroseagainatTimeStep8.Underthesameconditions,Product2lostmoremarketshareafterTimeStep8(i.e.,Product2lost8%),andProduct3lostlessmarketshare(approximately1%).

Figure10.Themeanmarketsharepathswithrespecttochangesintheshapeparameter:(a)Product1,(b)Product2,and(c)Product3

6.19 ItappearsthatProduct1stolethemarketsharesofProduct2andProduct3afterTimeStep8,whentheshapeparameterwasgreaterthan1.Thesingletimedistributionwiththeshapeparametergreaterthan1representsadecreasingnumberofearlyadopters;potentialconsumershavemoretimetoconsidertheirproductchoices,andlocalandglobalnetworkeffectsmayhavetimetoinfluencethepotentialsales.Hence,themarketsharegainofProduct1indicatesthatpurchasetimeeffectshelpedconsumersfavourProduct1insteadofProduct2.Here,theworstproduct(Product2)lostmoremarketsharethanundertheexponential-likeindividualpurchasetimedistribution.Table2reportsthatProduct1andProduct3havesimilarevaluationsforeachproductattribute,buttherearedifferencesinbatterylifeandweight.TheexpertsevaluatedthebatterylifeofProduct1as"poor"butthatofProduct3as"verygood".TheyalsoevaluatedtheweightofProduct1as"verygood"butthatofProduct3as"good".BecauseTable3tellsusthatbatterylifeisnotasimportantasweight,wemayconcludethatsomeconsumersreceivedinformationthatProduct1isbetterthanProduct3withrespecttothemoreimportantproductattributeofweightastimeprogressedandthatthespreadofthisinformationaffectedthemarketshareofProduct1,causingittoriseagainwhentheshapeparameterwas10.

6.20 Figure11illustratesthattheuncertaintyinreachingthemeanmarketsharepathsrisesabruptlywhentheshapeparameteris10.ThevariancesofProduct1andProduct2areapproximately0.000095whentheshapeparameterislessthan1,andthevarianceofProduct3isapproximately0.00013.However,thevariancesriseabruptlywhentheshapeparameteris10.ThevariancesofProduct1and2are0.0002,andthevarianceofProduct3is0.00026.Thispatternsuggestsagreatercertaintyofreachingtheexpectedmarketsharepathswhentheshapeparameterissufficientlysmall(i.e.,smallerthan1).Thismetricisimportanttoafirmbecauseuncertaintyisdirectlyrelatedtorisk.However,theproducerofProduct1wouldpreferanindividualpurchasetimedistributionsimilartoanormaldistribution,evenwhentheuncertaintyishighandthereisachanceofearningamarketsharethatislessthantheexpectedshare.Thispreferencearisesbecausethemarketshareoftheproductishigherwhenanindividualpurchasetimedistributionfollowsanormaldistributionthanwhentheindividualpurchasetimedistributionfollowsanexponentialdistribution.

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Figure11.Variancesofthemarketsharepathswithrespecttochangesintheshapeparameter

6.21 Figures10and11revealseveralmarketingimplications.Thebestandtheworstproductstakeadvantageofanexponential-likeindividualpurchasetimedistribution,butthesecond-bestproductdoesnotbenefitfromthisdistribution.Thus,whenafirmproducesaproductthatearnsthelargestmarketshareamongcompetingproducts,thefirmhasanadvantageousposition,butthefirmwouldstillpreferpeopletopurchaseitsproductearly.Forafirmthatproducesthesecond-bestproductsuchasProduct1(i.e.,afirmproducesahigh-qualityproductbutfailstobecomethefirstinthemarket),thefirmshouldgivepeopleenoughtimetoconsideritsproductandletthenetworkeffecthelpthefirmdisseminategoodinformationonitsproducteventhoughthefirmmaylosecertaintyinachievingitsmeanmarketshare.Whentheindividualpurchasetimedistributionofconsumersresemblesanormaldistribution,thefirmsthatproducelow-qualityproducts,suchasProduct2,mayneedtosellouttheirproductsearly.

Conclusions

7.1 Inthisstudy,weproposedanagent-basedsimulationmodeltopredictthebrand-leveldiffusionofnewproductsinamarket.Totesttheperformanceofthemodel,weappliedthemodeltothediffusionofnetbookproductscompetingintheonlinemarketinKorea.Wefocusedontheindividualpurchasetimedistributionandsocialnetworkstructurethatinfluenceconsumers'productchoices.Socialinfluenceistransferredvialocalandglobalnetworkeffectsoneachproductattribute,bothfromexpertsandpreviousadopters.Thelocalnetworkeffectrepresentsthenetworkeffectcausedbythedegreeofconnectivity(i.e.,thenumberofneighbours),whereastheglobalnetworkeffectisthenetworkeffectattributedtotherewiringprobability(i.e.,thedeterminantofthenumberofshortcuts).Consumerscollectinformationonproductattributesthroughthesenetworkeffects.Eachconsumerthenapplieshis/herownweightsforproductattributestochoosetheproductwithmaximumutility.Wemodelthisproductchoiceprocessusingafuzzymulti-attributeutilitymodel.Finally,weaddindividualproductpurchasetimedistributions(i.e.,thetimewhenaconsumerconsidersbuyingaproduct)tothemodel.Withthiscompletemodel,wethensimulatetheproductdiffusiondynamics.

7.2 WeconductedanempiricalstudytoestimatetheindividualpurchasetimedistributionandthesocialnetworkstructureofKoreannetbookconsumersbyestimatingtheshapeparameterofthedistributionandthedegreeofconnectivityandtherewiringprobabilityofthesocialnetwork.Weuseddynamictimewarpingtocalculatetheaggregateddistancebetweentheactualmarketsharepathsandthemarketsharepathsgeneratedbythesimulation.Weobservedthatthereal-worldindividualpurchasetimedistributionissimilartoanexponentialdistribution(i.e.,theshapeparameteris0.01),andthesocialnetworkhasasmallnumberofneighboursbutalargernumberofshortcuts(i.e.,therewiringprobabilityis0.05,andthedegreeofconnectivityis5).ThisobservationmeansthattheKoreannetbookconsumerislikelytobuyaproductearly;italsomeansthattheKoreannetbookconsumerhasasmallnumberofcommunicationchannelsthroughwhichtoshareinformationonproductsbuteasytoaccessother,distantconsumers.

7.3 Wesuspectthatconstantexternalshocksandthelackofacoercivesynchronisationofproductreleaseswillnecessitateupgradingourmodel.First,weassumedthateveryconsumer-agentreferstotheexperts'opinionsatthebeginningofproductdiffusion.Wemayhaveneglectedseveralexternalshocks(e.g.,marketingstrategiessuchaspricediscountsandpromotions,changesintheexperts'opinions,andoperationalproblems)thatoccurunevenlyinreallife.Second,wealignedproducts'releasetimesinthesimulationsothatthediffusionoftheproductsbegansimultaneously.Inparticular,wetruncatedthetwoweeksofexistingmarketsharesforProducts1and2,whichwerereleasedtwoweeksbeforeProduct3.Asaresult,wemayhavelostthenetworkeffectonProduct1and2accumulatedduringthesetwoweeks.

7.4 Wevariedthedegreeofconnectivity,therewiringprobability,andtheshapeparametertoperformasensitivityanalysis.Asthedegreeofconnectivitywasincreased,thelocalnetworkeffectincreased.However,themarginaleffectwasthegreatestwhenthelocalnetworkeffectfirstarose(i.e.,whenthedegreeofconnectivitywasincreasedfrom0to4).Ourresultshowsthatthelocalnetworkeffectincreasesthemarketshareofthemajorproduct(Product1)butreducesthemarketshareofminorproducts(Products1and2).Thisresultinformsusthatconsumerstendtofollowthemajority,buttherearesomeconsumerswhoarelockedintominorproducts.Thevariancesofthemarketsharepathstellusthattheuncertaintyinachievingthemeanmarketsharepathsisconcavewithrespecttothedegreeofconnectivity.Theglobalnetworkeffectissimilarregardlessofthevalueoftherewiringprobability.Theinitialevaluationofproductsisbiasedtowardstheexperts'opinions,andthepurchasetimesofKoreannetbookconsumersareearly;thus,theglobalnetworkeffecthaslittletimetoinfluencetheseconsumers.Finally,astheshapeparameteroftheindividualpurchasetimedistributionwasincreaseduptoavalueof1,themarketshareofthemajorproduct(Product3)rose,butthatoftheminorproductsfell.However,astheshapeofthedistributionchangedintoanormal-likedistribution,thepurchasetimeeffectwasabletoshednewlightonProduct1(i.e.,thesecond-bestproduct),andthemarketshareofthisproductroseagainafterthefall.Aminorproduct(inparticular,theworst-evaluatedproduct,Product2)isbenefittedastheindividualpurchasetimedistributionchangesfromanormaldistributionshapetoanexponentialdistributionshape,whenamajorproductisnegativelyaffected.

7.5 Infuturework,weplantoincludethefollowingissues:

1. Itisnecessarytoconductananalysisofvarianceonthedegreeofconnectivity,therewiringprobability,andtheshapeparameteroftheindividualpurchasetimedistributiontodeterminetheinteractioneffectsonthemarketsharepath.

2. WemayoptimiseoursimulationmodeltobetterreflecttheactualKoreannetbookmarketsharesbyobservingappropriateexternalshockeventsoccurringinreallife.ThisconsiderationwillleadustoupgradeourmodeltopredicttheKoreannetbookmarketsharemoreprecisely.

3. Oursimulationmodelassumesthatallconsumer-agentshavewillingnesstobuyproductsfromthebeginningofsimulation.However,itmaybenecessaryforourmodeltoreflectasituationthatsomeconsumer-agentsstarttohavewillingnesstobuyproductsandacceptproductevaluationinformationfromneighboursinthemiddleofsimulation.

4. Inthisstudy,welistedseveralthresholdmodelsandtheirshortcomings.However,acomparativestudyisrequiredtodeterminetheconditionsunderwhicheachmodelisapplicable.5. Producersmaydesiretoknowtheconditionsunderwhichtheirproductscanclaimadditionalmarketshare.Weaimtodevelopanoptimisedstrategythatgeneratesthebestdesignforproductattributesto

maximisethemarketshareoftheproducer.

Pseudocode

Function main Foreach rewiring probability Foreach degree of connectivity Foreach replication setup simulateEnd

Function setup setup-individual-product-purchase-distribution make-consumers setup-globals assign-agent-attribute make-init-neighbors

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rewire-neighbors renew-linksEnd

Function setup-individual-product-purchase-distribution Foreach consumer agent Assign values to parameters (i.e., η=0.01, 0.1, 1, 10 and b=0.4) to initialise individual product purchase distribution Assign product purchase time from individual product purchase distributionEnd

Function make-consumers Create some given number of consumersEnd

Function setup-globals Initialise decision matrix of every consumer agent Assign 0 to time step Assign 0 to adopter number for each product Assign expert's opinion on products' attributes in linguistic form Assign crisp numbers to expert's linguistic opinion Assign crisp numbers to consumer's linguistic weights on product attributes Assign the probability of consumer's sensitivity to social influence in linguistic formEnd

Function assign-agent-attribute Foreach consumer agent Initialise and assign consumer weights on product attributes, purchase time, sensitivity to social influenceEnd

Function make-init-neighbors Foreach consumer agent Assign neighbors as many as the degree of connectivityEnd

Function rewire-neighbors Foreach consumer agent Connect to its own neighbors Rewire the connections in probability of rewiring probabilityEnd

Function renew-links Foreach consumer agent if the number of connections is NOT equal to the degree of connectivity Add/Delete connections until the number of connections is equal to the degree of connectivityEnd

Function simulate init-product-adopt-count make-consumer-weighted-decision-matrix init-early-adopter get-socio-decision-matrix get-alternatives-mnlEnd

Function init-product-adopt-count Initialise adoption count for each productEnd

Function make-consumer-weighted-decision-matrix Foreach consumer agent Retrieve expert's opinion Convert expert's opinion on product attributes into crisp numbers using triangular fuzzy number Retrieve consumer's weights on product attributes Convert consumer's weight on product attributes into crisp numbers using triangular fuzzy number Foreach product attribute Induce consumer's value on a product attribute by multiplying expert's opinion by consumer's weight on the product attribute Update the ideal product attributes in best case and the ideal product attributes in the worst caseEnd

Function init-early-adopter Assign early adopters among consumer agents Foreach early adopter Buy a product according to multi-nomial logit modelEnd

Function get-socio-decision-matrix Foreach consumer agent with no product purchase Retrieve all the neighbors' decision matrix and average them Reassign decision matrix by (1 - sensitivity to social influence) * my decision matrix + (sensitivity to social influence * the averaged decision matrix of all the neighborsEnd

Function get-alternatives-mnl Foreach consumer agent with no product purchase, whose purchase time is equal to or more than the current time step Buy a product according to multi-nomial logit modelEnd

Acknowledgements

ThisresearchwassupportedbytheBasicScienceResearchProgramthroughtheNationalResearchFoundationofKorea(NRF)fundedbytheMinistryofEducation,ScienceandTechnology(2010-0009267).

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