Facilitating adoption of Internet technologies and services with externalities via cost subsidization

This paper models the temporal adoption dynamics of an abstracted Internet technology or service, where the instantaneous net value of the service perceived by each (current or potential) user / customer incorporates three key features: i) user service affinity heterogeneity, ii) a network externality, and iii) a subscription cost. Internet technologies and services with network externalities face a "chicken and egg" adoption problem in that the service requires an established customer base in order to attract new customers. In this paper we study cost subsidization as a means to "reach the knee", at which point the externality drives rapid service adoption, and thereby change the equilibrium service fractional adoption level from an initial near-zero level to a final near-one level (full adoption). We present three simple subsidy models and evaluate them under two natural performance metrics: i) the duration required for the subsidized service to reach a given target adoption level, and ii) the aggregate cost of the subsidy born by the service provide. First, we present a "two target adoption subsidy" (TTAS) that subsidizes the cost so as to keep the fraction of users with positive net utility at a (constant) target level until the actual adoption target is reached. Second, we study a special case of the above where the target ensures all users have positive net utility, corresponding to a "quickest adoption" subsidy (QAS). Third, we introduce an approximation of QAS, called AQAS, that only requires the service provider adjust the subsidy level a prescribed number of times. Fourth, we study equilibria and their stability under uniformly and normally distributed user service affinities, highlighting the unstable equilibrium in each case as the natural target adoption level for the provider. Finally, we provide a fictional case study to illustrate the results.Comment: 29 pages, 15 figures. Accepted for publication by ACM Transactions on Internet Technologies on April 30, 2017. Preliminary version presented at June, 2014 W-PIN + NetEcon workshop in Austin, T