  The dynamics of adoption of innovations is an important subject in many
fields and areas, like technological development, industrial processes, social
behavior, fashion or marketing. The number of adopters of a new technology
generally increases following a kind of logistic function. However, empirical
data provide evidences that this behavior may be more complex, as many factors
influence the decision to adopt an innovation. On the one hand, although some
individuals are inclined to adopt an innovation if many people do the same,
there are others who act in the opposite direction, trying to differentiate
from the "herd". People who prefer to behave like the others are called
mimetic, whereas individuals who resist adopting new products, the stronger the
greater the number of adopters, are named contrarians. On the other hand, new
adopters may have second thoughts and change their decisions accordingly.
Agents who regret and abandon their decision will be denominated repentant. In
this paper we investigate a simple model for the adoption of an innovation for
a society composed by mimetic and contrarian individuals whose decisions depend
mainly on three elements: the appeal of the novelty, the inertia or resistance
to adopt it, and the social interactions with other agents. In the process,
agents can repent and turn back to the old technology. We present analytic
calculations and numerical simulations to determine the conditions for the
establishment of the new technology. The inclusion of repentant agents modify
the balance between the global incentive to adopt and the number of contrarians
who prevent full adoption, generating a rich landscape of temporal evolution
that includes cycles of adoption.
