{"title":"Social Influence and Evolution of Market Share","authors":"Simla Ceyhan, M. Mousavi, A. Saberi","doi":"10.1080/15427951.2011.579849","DOIUrl":null,"url":null,"abstract":"Abstract We propose a model for the evolution of market share in the presence of social influence. We study a simple market in which the individuals arrive sequentially and choose one of a number of available products. Their choice of product is a stochastic function of the inherent quality of the product and its market share. Using techniques from stochastic approximation theory, we show that market shares converge to an equilibrium. We also derive the market shares at equilibrium in terms of the level of social influence and the inherent quality of the products. In a special case, in which the choice model is a multinomial logit model, we show that inequality in the market increases with social influence and that with strong enough social influence, monopoly occurs. These results support the observations made in the experimental study of cultural markets in [Salganik et al. 06].","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2011.579849","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Internet Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/15427951.2011.579849","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 16
Abstract
Abstract We propose a model for the evolution of market share in the presence of social influence. We study a simple market in which the individuals arrive sequentially and choose one of a number of available products. Their choice of product is a stochastic function of the inherent quality of the product and its market share. Using techniques from stochastic approximation theory, we show that market shares converge to an equilibrium. We also derive the market shares at equilibrium in terms of the level of social influence and the inherent quality of the products. In a special case, in which the choice model is a multinomial logit model, we show that inequality in the market increases with social influence and that with strong enough social influence, monopoly occurs. These results support the observations made in the experimental study of cultural markets in [Salganik et al. 06].
摘要本文提出了一个存在社会影响的市场份额演化模型。我们研究了一个简单的市场,在这个市场中,个人依次到达并从众多可用产品中选择一种。他们对产品的选择是产品内在质量及其市场份额的随机函数。利用随机逼近理论的技术,我们证明了市场份额收敛于一个均衡。我们还根据社会影响水平和产品的内在质量推导出均衡时的市场份额。在选择模型为多项式逻辑模型的特殊情况下,我们证明了市场中的不平等随着社会影响的增加而增加,当社会影响足够强时,就会出现垄断。这些结果支持了[Salganik et al. 06]在文化市场实验研究中的观察结果。