A Class of Automata Networks for Diffusion of Innovations Driven by Riccati Equations : Automata Networks for Diffusion of Innovations.

Innovation diffusion processes are generally described at aggregate level with models like the Bass model (1969) and the Generalized Bass Model (1994). However, the recognized importance of communication channels between agents has recently suggested the use of agent-based models, like Cellular Automata. We argue that an adoption process is nested in a communication network that evolves dynamically and implicitly generates a non-constant potential market. Using Cellular Automata we propose a two- phase model of an innovation diffusion process. First we describe the Communication Network necessary for the awareness of an innovation. Then, we model a nested process representing the proper adoption dynamics. Through a "Mean Field Approximation" we propose a continuous representation of the discrete time equations derived by our Automata Network. This constitutes a special non autonomous Riccati equation, not yet described in well-known international catalogues. The main results refer to the closed form solution of this equation and to the corresponding statistical analysis for identification and inference. We discuss an application in the field of bank services

Cellular Automata with Network Incubation in Information Technology Diffusion.

Innovation diffusion of network goods determines direct network externalities that exhibit delayed full benefits, depressing sales for long periods. We model a multiplicative dynamic market potential driven by a latent heterogeneous individual threshold derived from a basic economic theory by Economides and Himmelberg (1995) which is embedded in a special Cellular Automata representation. The corresponding mean field approximation of its aggregate version is a Riccati equation with a closed form solution. This allows the detection of a change-point time separating an incubation period from a subsequent take-off due to a sufficient critical mass acting as a collective threshold. Weighted nonlinear least squares methodology is the main inferential technique. An application is analysed with reference to USA fax machine diffusion

Market potential dynamics in innovation diffusion: modelling the synergy between two driving forces.

The presence of a slowdown in new products' life cycle has recently received notable attention from many innovation diffusion scholars, who have tried to explain and model it on a typical dual-market hypothesis (early market-main market). In this paper we propose an alternative explanation for the slowdown pattern, based on the co-evolutionary model by Guseo and Guidolin, where diffusion results from the synergy between two driving forces: communication and adoption. We test the model on the sales data of six pharmaceutical drugs presenting a slowdown in their life cycle and observe that this is always identified almost perfectly by the model. A deeper analysis of the synergistic interaction between communication and adoption, based on the likelihood ratio order and on the usual stochastic order, shows that location indexes of each component (communication and adoption), such as mode, median and mean, can inform which of the two had a driving role in early diffusion. Contrary to the general expectation, according to which communication should precede adoptions, our findings show that in two cases adoptions were the main driver in early life cycle. We argue that this different behaviour may be due to the nature of the drug considered; new drugs developed for severe pathologies will be likely to have an accumulated demand at the time of launch, while drugs for minor ailments will present a normal behaviour, "first communication, then adoption"

Modelling seasonality in innovation diffusion. A regressive approach

Although the literature on innovation diffusion is very wide, up to now not much attention has been paid on modelling the seasonal component often present in sales data. In this paper we develop two innovation diffusion models that take into account not only the evolutionary trend of sales but also their intra-year oscillations, that are due to seasonal effects. In particular, we treat seasonality as a deterministic component to be estimated with conventional NLS techniques jointly with the trend. The results obtained by applying these models to the life-cycle of a pharmaceutical drug show a clearly better performance in providing short-term forecasts. Moreover, this methodology proves more parsimonious with respect to the autoregressive method, based on SARMA models

A nuclear power renaissance?

Nuclear energy has been experiencing a revival in many countries, since it is considered to be a possible substitute for fossil fuels for electricity generation. This calls for a focused analysis, in order to evaluate whether conditions exist for its wide employment. While typical aspects against this option have to do with waste management, security of power plants and related health concerns, other issues less frequently considered by politics, mass media, and public opinion seem particularly crucial to understand if we are really going to face a nuclear energy renaissance. In particular, nuclear energy is well known to depend on parallel dynamics of uranium extraction and reactor startup. In this paper we apply an innovation diffusion framework to model co-evolutionary processes of uranium extraction, reactor startup and nuclear energy consumption at a world level. We also perform an analysis of nuclear consumption dynamics in France, Japan, and the USA, which are the three countries that are mostly invested in it. The results obtained by analyzing all of these processes do not seem to support the idea of a new era for nuclear energy

Heterogeneity in Diffusion of Innovations Modelling: A Few Fundamental Types

Heterogeneity of agents in aggregate systems is an important issue in the study of innovation diffusion. In this paper, we propose a modelling approach to latent heterogeneity, based on a few fundamental types, which avoids cumbersome integrations with not easy to motivate a priori distributions. This approach gives rise to a discrete non-parametric Bayesian mixture model with a possibly multimodal distributional behaviour. The result is inspired by two alternative theories: the first is based on the Rosenblueth two-point distributions (TPD), and the second is related to Cellular Automata models. From a statistical point of view, the proposed reduction allows for the recognition of discrete heterogeneous sub-populations by assessing their significance within a realistic diffusion process. An illustrative application is discussed with reference to Compact Cassettes for pre-recorded music in Italy

Regular and promotional sales in new product life-cycle: A competitive approach

In this paper, we consider the application of the Lotka-Volterra model with churn effects, LVch, (Guidolin and Guseo, 2015) to the case of a confectionary product produced in Italy and recently commercialized in a European country. Weekly time series, referring separately to quantities of regular and promotional sales, are available. Their joint inspection highlighted the presence of compensatory dynamics suggesting the study with the LVch to estimate whether competition between regular and promotional sales exists and how it affects product life-cycle. The study of sales under promotion with respect to regular ones represents a new way of dealing with promotional activities effects, whereas the innovation diffusion literature on new product growth has typically considered the effect of pricing and advertising through the generalized Bass model (Bass et al., 1994). In that model, the total amount of sales, regular plus promotional sales, is analyzed with a univariate approach, while price and advertising expenditures are used as exogenous inputs, without a feedback control. Conversely, exploiting the availability of two distinct time series and studying their interaction, our results show that competition has a symmetric character. Regular sales may access the residual market of those under promotion indicating the beneficial effect of promotional efforts, but the reverse effect is also present. Short-term forecasts on the evolution of the two series are then built with a two stage procedure based on an iterated SARMAX. The predicted values are further validated with observed real data. A comparison with Euler standard predictions is also performed

Online Banking Satisfaction in Italy - OBS project

The datasets provide information from a questionnaire that investigated customer satisfaction of some online banking services in Italy in May and September 2015