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1、1Backgroundandintroduction1.1GeneralintentionsConsumerproductssuchasshampooortomatosaucearedesignedsothattheyappealtoconsumers,encouragingthemtobuythoseproducts.Tothatend,theindustrialR&Dorganisationtendstofocusonunderstandingandmanipulatingproductattributes.However,buyingbehaviourisnotonlya
2、functionoftheproduct:itisalso,andinsomecasesperhapsmoreso,afunctionoftheconsumer,hissocialenvironmentofotherconsumers,thecompetingproductsinthemarketplace,andthebrandmarketingstrategy.Inordertodesignthebestproduct,itisnecessarytounderstandnotjustthephysicsandchemistryoftheproduct,butalsothep
3、sychologyofconsumersandthesociologyofconsumergroupsornetworks.Thegoalofthisstudyistohaveamodelofthemarketplacethatdescribescertainaspectsofconsumerbuyingbehaviour.Therearetwomainpartstosuchamodel:•Adescriptionofapopulationof‘consumers’,whoeachchoose(buy)repeatedlyoneofanumberofcompeting‘bran
4、ds’(wecanignorethedifferencebetweenproductandbrandforthesepurposes).Thissubdividesintoadescriptionofthebehaviourofasingleconsumer(‘psychology’),andofthecollectivebehaviourofagroup,inotherwordsoftheinteractionsbetweenconsumers(‘sociology’).•Adescriptionof‘brandmanagement’,i.e.thestrategyofbran
5、dmanagerswhenchangingtheattributesofabrandsuchaspriceorqualityinresponsetoeventsinthemarketplace.Traditionalmarketingmodelstendtofocusonthesecondelement,andtreatthelargenumberofconsumersinamacroscopic,averagedway.Alternatively,onecanlookatindividualconsumersandtheirbuyingbehaviour,andtrytode
6、riveobservablelargescaleeffects,likechangesinmarketshare.Ideallyonewouldliketoconnectthe‘microscopic’consumerviewpointtothe‘macroscopic’viewpointofthebrandmanager.1.2FactorsinthemodelsThemainfeatureswhichwereincludedinthevariousmodelsare:A.LoyaltyLoyaltyisthetendencyfor(some)consumerstostickt
7、othesameproducts.Withthisasakeyeffect,deterministic,continuous-timemodelswillbesystemsofordinarydifferentialequations;thestrongertheloyalty,theslowerthechangesinnumbersofpeoplebuyingparticularproducts.Fordiscrete-timemodels,thedegreeofloyaltycorrespo
