Adoption of Innovations with Contrarians and Repentant Agents

Abstract: 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.