Modeling competition between two pharmaceutical drugs using innovation diffusion models

The study of competition among brands in a common category is an interesting strategic issue for involved firms. Sales monitoring and prediction of competitors' performance represent relevant tools for management. In the pharmaceutical market, the diffusion of product knowledge plays a special role, different from the role it plays in other competing fields. This latent feature naturally affects the evolution of drugs' performances in terms of the number of packages sold. In this paper, we propose an innovation diffusion model that takes the spread of knowledge into account. We are motivated by the need of modeling competition of two antidiabetic drugs in the Italian market.Comment: Published at http://dx.doi.org/10.1214/15-AOAS868 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A new competition model combining Lotka- Volterra model and the Bass model in pharmacological market competition

The diffusion of products that compete in the marketplace is a strategic issue for market analysts. In this paper, we propose a new competition model for two competing products essentially thought as an extension of a Lotka-Volterra competition model. This model was introduced the first time by Guseo (2004) but in that paper the application of the model in a real case was missing. This extension came from the observation that in a standard Bass model (1969) the role of innovators has a great importance because it incorporates the innovative effect due to external action (firms communication, advertising) that is proportional to residual market and consequently it is of great relevance in the initial part of diffusion process even if it progressively reduces. Lotka-Volterra models allow for a definition of the residual market of a product category which is more general with respect to alternative approaches. The residual market is not simply defined as the difference between the initial market potential and the sum of all brands adoptions. Conversely, competing products adoptions contribute to the residual market with different weights. This generates brand specific perceived residual markets. Furthermore, the model overtakes the heavy restriction of synchronicity between the two products giving a simple solution based on the Bass model

Modeling competition among pharmaceutical drugs

Competition between rival brands within the same category gives rise to special competition/substitution effects of great interest to the involved forms. The study of competition in the pharmaceutical market highlights special behavior in the diffusion of knowledge about the products that may differ from other competing arenas. This latent feature naturally affects the evolution of the drugs' performances, in terms of number of packages sold. The aim of this paper is to propose a new model structure within the family of innovation diffusion models that specifically takes the step of knowledge spread into account. We show the application of this model with nonlinear regression methods and a comparison with alternative models to antidiabetic drug sales recorded monthly in the Italian market

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

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

Competition and Substitution in Energy: Old Scenarios and Emerging Technologies

The diffusion of an innovation in a social system is characterised as a dynamic that typically gives rise to a nite lifecycle. The pioneering approach by Bass (1969), called the Bass model (BM), has been widely used because it considers the internal rules of the social system. The model has been extended in several directions. The generalised Bass model (GBM), by Bass et al. (1994), is the most popular extension describing the exogenous interventions acting on the timing of the diusion process. Another important extension is the Guseo and Guidolin (2009) model GGM), which defines the dynamic nature of the latent market potential. However, these univariate time series models do not consider the competitive environment, in which two or more concurrent innovations enter the market, possibly at dierent times, and target the main set of potential adopters or subgroups of potential adopters with possible interaction effects. The model proposed by Guseo and Mortarino (2014) allows a exible behaviour in describing the diffusion of two products under competition, where interaction effects, namely word-of-mouth (WOM), are split into within-product and cross-product effects. This thesis proposes an extended diffusion model for three products in a competitive framework that may be able to improve the description of mutual interactions (either competition or cooperation), along with dening specific features of each product. To examine the improvement of the proposed three-competitor model (3CM) compared with the bivariate model (2CM), both models are applied to energy data to describe competition among energy sources. The intervention functions (e.g. the external shocks) are incorporated in the models when necessary to estimate the effect of incentives and policy measures, which are crucial tools in the expansion of renewables and nonrenewable energy technologies. Without incorporating intervention functions, models based on the assumption of a constant market potential are virtually unable to capture the wide variety of shapes of products in a diusion process. Following the model proposed by Guseo and Mortarino (2015), this thesis further proposes a diusion model for three competing products that are suffciently similar to share a common market potential, where the size increases over time. Models 2CM and 3CM with dynamic market potential (DMP) are also applied to the same energy data studied in the preceding part of this work. The obtained results highlight the ecacy of the models with DMP over similar models with xed market potential. Overall, the proposed models (3CM), either with a xed market potential, m, or DMP, prove to be useful in applied contexts, for example, in describing the lifecycle of products and evaluating predictions

When to Adopt a Service Innovation: Nash Equilibria in a Competitive Diffusion Framework

We study the optimal timing of adoption of a service innovation that a new entrant firm brings to a market populated by two incumbent firms. Our analysis is based on a model of competitive diffusion dynamics that extends the monopolistic Bass model to include customer churn processes, as well as a potential market expansion resulting from the introduction of the innovation. We obtain expressions for the time trajectories of the customer bases, i.e., the numbers of customers that use old and new service processes for the competing firms in a general setting, as well as sharper, closed-form characterizations for the setting with a stable market and homogeneous imitation process. In modeling competitive dynamics we consider settings where incumbents anticipate a potential failure of the innovation. We use the trajectories for the customer bases to model an optimal adoption response problem faced by one of the incumbent firms in the setting in which the adoption time for the other incumbent can be anticipated or is pre-announced, and analyze this problem in the absence of market expansion or intra-generational customer churn. Using the optimal response results, we provide the Nash equilibrium analysis of the adoption decisions by competing incumbent firms and derive sufficient conditions for the ``now-now'', ``now-never'' and ``never-never'' adoption equilibria. We use the trading volume data from the foreign exchange markets to estimate the parameters of the competitive diffusion dynamics for our model and to conduct a numerical investigation of the impact of the uncertainty associated with the success of the innovation on the incumbents' Nash equilibrium adoption times.Non

Prevedere la diffusione di un'innovazione nella fase di pre-lancio

Le innovazioni di successo cambiano il mercato o ne creano di nuovi, sono allo stesso tempo frutto e stimolo dello sviluppo tecnologico. Questo eleborato descrive i principali metodi per la stima della diffusione di prodotti innovativi sul mercato, con particolare attenzione alla fase pre-lanci