Diffusion of New Products with Heterogeneous Consumers

2016

We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but rather by a novel model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from non-adopters to adopters is described by a non-standard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.

SIAM Journal on Applied Mathematics, 2017

We consider the diffusion of new products in the discrete Bass-SIR model, in which consumers who adopt the product can later "recover" and stop influencing their peers to adopt the product. To gain insight into the effect of the social network structure on the diffusion, we focus on two extreme cases. In the "most-connected" configuration where all consumers are interconnected (complete network), averaging over all consumers leads to an aggregate model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. In the "least-connected" configuration where consumers are arranged on a circle and each consumer can only be influenced by his left neighbor (one-sided 1D network), averaging over all consumers leads to a different aggregate model which is linear, and can be solved explicitly. We conjecture that for any other network, the diffusion is bounded from below and from above by that on a one-sided 1D network and on a complete network, respectively. When consumers are arranged on a circle and each consumer can be influenced by his left and right neighbors (two-sided 1D network), the diffusion is strictly faster than on a one-sided 1D network. This is different from the case of non-recovering adopters, where the diffusion on one-sided and on two-sided 1D networks is identical. We also propose a nonlinear model for recoveries, and show that consumers' heterogeneity has a negligible effect on the aggregate diffusion.

Computational & Mathematical …, 2007

Diffusions of new products and technologies through social networks can be formalized as spreading of infectious diseases. However, while epidemiological models describe infection in terms of transmissibility, we propose a diffusion model that explicitly includes consumer decision-making affected by social influences and word-of-mouth processes. In our agent-based model consumers' probability of adoption depends on the external marketing effort and on the internal influence that each consumer perceives in his/her personal networks. Maintaining a given marketing effort and assuming its effect on the probability of adoption as linear, we can study how social processes affect diffusion dynamics and how the speed of the diffusion depends on the network structure and on consumer heterogeneity. First, we show that the speed of diffusion changes with the degree of randomness in the network. In markets with high social influence and in which consumers have a sufficiently large local network, the speed is low in regular networks, it increases in small-world networks and, contrarily to what epidemic models suggest, it becomes very low again in random networks. Second, we show that heterogeneity helps the diffusion. Ceteris paribus and varying the degree of heterogeneity in the population of agents simulation results show that the Springer 186 S. A. Delre, W. Jager et al. more heterogeneous the population, the faster the speed of the diffusion. These results can contribute to the development of marketing strategies for the launch and the dissemination of new products and technologies, especially in turbulent and fashionable markets.

We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.

Physical Review E

We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but rather by a novel model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from non-adopters to adopters is described by a non-standard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a smallworlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.

Often new products, especially high technology products, exhibit a distinct spike in sells at the beginning before settling into a smooth parabolic shape. Apart from the pronounced early spike, sales of new products follow the traditional pattern described by traditional equation based diffusion of innovation models. This paper attributes these spikes to indirect network effects. To explain indirect network effects in diffusion models, the authors extend the Bass (1969) framework by proposing two categories of adopters – thus a third group of customers – and by doing so improves prediction. The first category of adopters – traditional innovators and imitators – see enough value in the new product and adopt it as they become aware of it, through either mass media or word of mouth. These adopters give rise to the initial spike often observed in diffusion of innovation models. The second category of adopters assign a value to products, depending upon the indirect network externality associated with each product. They adopt products only when the value exceeds a threshold.

2009

Within the very broad scientific debate on the role of heterogeneities in models of innovation diffusion, there seems to exist a delay of marketing science in absorbing the fecund developments that took place, in the field of epidemiology of infectious diseases in very recent times. This paper, which constitutes the basis for a future research project, aims to fill this gap. This is done along three main directions. First, the paper discusses in general terms the role of the concept of heterogeneity in innovation diffusion. Second it reviews those recent epidemiological results which are of crucial interest for marketing models. Finally it offers a sample of results which are suggestive of the critical role played by heterogeneities within deterministic models for the diffusion of new products.

Technological Forecasting and Social Change, 1994

A model of innovation diffusion which gives unequal weightage to the adopters of different temporal stages and captures commonly observed ups and downs in new product diffusion is proposed. It is shown that our model possesses features of the existing flexible diffusion models and shows better fit which is indicated by the values of Rid,, mean absolute deviation, and mean percentage error and estimates a larger market potential, M. It has an interesting feature of conversion factors, first increasing then vanishing, much before we approach market saturation, implying that there is a scope of new thrust in converting remaining potential adopters.

The Bass model, which is an effective forecasting tool for innovation diffusion based on large collections of empirical data, assumes an homogeneous diffusion process. We introduce a network structure into this model and we investigate numerically the dynamics in the case of networks with link density P(k) = c/k γ , where k = 1 ,. .. , N. The resulting curve of the total adoptions in time is qualitatively similar to the homogeneous Bass curve corresponding to a case with the same average number of connections. The peak of the adoptions, however, tends to occur earlier, particularly when γ and N are large (i.e., when there are few hubs with a large maximum number of connections). Most interestingly, the adoption curve of the hubs anticipates the total adoption curve in a predictable way, with peak times which can be, for instance when N = 100 , between 10% and 60% of the total adoptions peak. This may allow to monitor the hubs for forecasting purposes. We also consider the case of networks with assortative and disassortative correlations and a case of inhomogeneous advertising where the publicity terms are " targeted " on the hubs while maintaining their total cost constant.

for constructive comments on earlier drafts. Jon Parker assisted with the simulations.