Adoption of innovations with contrarian agents and repentance

- Data of adoption of innovations provide evidences of a complex behavior.
- A key factor of the model is the idiosyncratic resistance to change.
- Social influence is included by favoring the adoption or acting against it.
- The inclusion of repentance generates a rich landscape including cycles.

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. Besides, in the real world new adopters may have second thoughts and change their decisions accordingly. In this contribution we include this possibility by means of repentance, a feature which was absent in previous models. The model of adoption of an innovation has all the ingredients of a previous version, in which the agents decision to adopt depends on the appeal of the novelty, the inertia or resistance to adopt it, and the social interactions with other agents, but now 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 repentance can 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.