  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.
