پویایی های بازار بالقوه در انتشار نوآوری: مدلسازی هم افزایی بین دو نیروی محرکه

The presence of a slowdown in new product life cycles has recently received notable attention from many innovation diffusion scholars, who have tried to explain and model it on a dual-market hypothesis (early market-main market). In this paper we propose an alternative explanation for the slowdown pattern, a dual-effect hypothesis, based on a recent co-evolutionary model, where diffusion results from the synergy between two driving forces: communication and adoption. An analysis of the synergistic interaction between communication and adoption, based on the likelihood ratio order or on a weak stochastic order, can inform us of which of the two had a driving role in early diffusion. We test the model on the sales data of two pharmaceutical drugs presenting a slowdown in their life cycle and observe that this is identified almost perfectly by the model in both cases. Contrary to the general expectation, according to which communication should precede adoption, our findings show that adoptions may be the main driver in early life cycle; this may be related to the drug's specific nature.

The literature on innovation diffusion and new product life cycle has highlighted that in many situations the diffusion process is not as smooth as one would expect, but rather presents a perturbed pattern. In particular, it has been observed that the growth phase of the process is often characterised by the presence of a slowdown. The slowdown phenomenon – also known, with minor differences, as chasm, saddle or dip – indicates the situation in which, after a rapid takeoff, a product's sales reach an initial peak followed by a decline – whose length and depth may vary – and eventually by a resumption that may exceed the initial peak. While in the past there was no consensus on the concrete existence of such a phenomenon, a recent and increasing stream of literature has empirically verified that this regularity occurs in many product categories. However, the slowdown phenomenon is still posing challenges to innovation diffusion scholars, since it has been neither explained nor modelled in a unique way. Some lines of research have followed the idea that the market for new products needs to be divided into two major segments, usually termed “visionaries and pragmatists” (see [1]), “early market and main market” (see [2], [3], [4], [5]), “influentials and imitators” (see [6]). In particular Moore, building on the well-known categorisation of adopters proposed by [7], suggested that the market for innovations is initially represented just by early adopters and that the main market develops in a second stage of diffusion. Early and main markets are different in their attitudes and expectations towards novelties, and this difference may result in a precise separation between the two, implying a different treatment in terms of marketing strategies (see [8]). Such a separation has been theorized as a possible explanation for the slowdown pattern. Grounding on Moore's intuition, Goldenberg et al. (see [2]) have suggested that the existence of a saddle may be seen as a dual-market symptom. Their analysis has been based, first, on two exploratory studies on artificial markets realized with Cellular Automata models in order to verify the frequency of the saddle phenomenon in simulated situations, and then on an aggregate model to tie the dual-market explanation to saddle phenomena emerging in real situations. Van den Bulte and Joshi's model definitely proposes a mixture of two sub-populations of adopters as a possible explanation for the chasm (or dip) exhibited by several diffusion processes: specifically such a pattern appears when considering Eq. (7), i.e., the weighted sum of two densities. In this paper we propose an alternative explanation for the slowdown pattern that we define as a dual-effect hypothesis, based on a co-evolutionary innovation diffusion model by [10], where diffusion results from the synergy between two forces, communication and adoption. In particular, communication is necessary to create the market potential. By studying the properties of this model in depth, we highlight that a slowdown emerges from the co-evolution of communication and adoption, when these two components are significantly separate over time. This analysis is also very useful to show that communication does not necessarily precede adoption, as one would expect, but in some cases the reverse may occur. To illustrate these opposite situations, we present two paradigmatic cases referring to the life cycle of new drugs, providing a plausible explanation for the different behaviour observed. The paper is organised as follows. In Section 2 we summarise the basic properties of the co-evolutionary model by [10] with a particular specification of a dynamic market potential. A natural decomposition of the model density allows a direct interpretation of the evolutionary drivers due to communication and adoption forces. The Likelihood ratio order explains the different time position of these forces. A further weak ordering, based on simple location indexes, is proposed and compared with the likelihood ratio order or the usual stochastic order. In Section 3 we consider two different pharmaceutical drug diffusions in the Italian market that exhibit slowdowns and saddle effects well-recognised by the previous model. In Section 4 we analyse the time positioning of communication and adoption, and propose a possible interpretation for the obtained results. Final comments and discussion are presented in Section 5. Appendix A examines four other applications in order to confirm the proposed results.

This paper examines theoretical, technical and applied aspects of a well-known diffusion-of-innovations class of effects: slowdown, dip, saddle or chasm. The proposed dual-effect hypothesis emphasises a new interpretation of this systematic depression in the early stages of the diffusion process. This effect may be captured by a binary model for an adoption process nested in an evolving communication network, namely a precursor of the corresponding market potential (see [10]). However, there is incontrovertible evidence concerning the non-uniqueness of the causal forces generating a slowdown. Dual-market interpretations or correlated mixture modelling representations introduce a two-segment partition of adopters assuming a temporal decomposition of adoptions pertaining to rigid segments. Nevertheless, repeated adoptions due to the same adopter may be realised in different contexts and with different awareness levels. In the sequel, we summarise some specific properties and limitations of the dual-effect approach: a) The decomposition of the density related to the co-evolutionary model highlights the presence of a self-reinforcing diffusion governed by two synergistic forces, communication and adoption, that are not ordered in a fixed way during time evolution b) In particular, an interchangeable allocation of the two driving forces is possible. As we have observed by examining two new pharmaceutical drugs introduced in Italy in 2005, for one of them there is an “inversion” in the role of adoption, which may be interpreted as a consequence of the severity of the pathology and the accumulated demand effect in the initial stages of diffusion c) The alternative order is simple to detect with a strong likelihood ratio order between k1(t) and k2(t) or, much more practically, through a simplified weak order between f(t) and g(t) based on easy to compute location indexes, i.e., mode, median, and mean values d) The model only requires time series of adoptions. In particular, the dynamics of market potential, which take into account the evolution of the communication effort and related word-of-mouth, are estimated through the only observable adoption data. Moreover, from a computational and statistical point of view, the proposed framework is easy to implement with common commercial software e) A slowdown may be originated by an external perturbation, which is a totally different context. If we are able to absorb a local depression with a generalised Bass model (GBM) following, e.g., [15] or [16], then we should adequately motivate or support this modelling choice, which may be correct in some circumstances, but not in others.