Diffusion of New Products with Recovering 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.

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.

Mathematics of Operations Research

Does a new product spread faster among heterogeneous or homogeneous consumers? We analyze this question using the stochastic discrete Bass model in which consumers may differ in their individual external influence rates [Formula: see text] and in their individual internal influence rates [Formula: see text]. When the network is complete and the heterogeneity is only manifested in [Formula: see text] or only in [Formula: see text], it always slows down the diffusion, compared with the corresponding homogeneous network. When, however, consumers are heterogeneous in both [Formula: see text] and [Formula: see text], heterogeneity slows down the diffusion in some cases but accelerates it in others. Moreover, the dominance between the heterogeneous and homogeneous adoption levels is global in time in some cases but changes with time in others. Perhaps surprisingly, global dominance between two networks is not always preserved under “additive transformations”, such as adding an identical n...

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.

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.

In Proceedings of the Third International Conference on Intelligent Networking and Collaborative Systems (INCoS-2011), IEEE 2011, Fukuoka Institute of Technology, Fukuoka, Japan, Nov 2011, 2011

We propose a model of the evolution of a market with linear utilities in the presence of both local and global social interactions. In the scenario considered, there is a market consisting of buyers and divisible goods. In consecutive time periods, the decision of a buyer is affected by the consumption plan of his neighbors and by a global signal, the distribution of actions of all agents. Moreover, we assume that the market prices and the allocation of the goods are stabilized by the law of supply and demand. We simulate the model, along with a market equilibria algorithm, and we investigate the long time behavior of the system. Specifically, we analyze the distribution of the prices and the market share of the products, when the configuration of the network is Erdos-Renyi and Scale-free graph. The experimental results show that the long time behavior of the system is not always static. The long time states depict a periodic pattern and are sensitive to a) the initial agents' beliefs, b) the weights that each agent assigns to the local and the global factor respectively and c)the degree distribution of the nodes in the network.

Journal of Economic Interaction and Coordination

We formulate a model in which agents embedded in an exogenous social network decide whether to adopt a new network product or not. In the theoretical part of the paper, we characterize the stochastically stable equilibria for complete networks and cycles. For an arbitrary network structure, we develop a novel graph decomposition method to characterize the set of recurrent communication states, which is a superset of stochastically stable equilibria of the adoption game presented in our model. In the simulation part, we study the contagion process of a network product in small-world networks that systematically represent social networks. We simulate a generalization of the Morris (Rev Econ Stud 67(1):57-78, 2000) Contagion model that can explain the chasm between early adopters and early majority. Our numerical analysis shows that the failure of a new network product is less likely in a highly cliquish network. In addition, the contagion process reaches to steady state faster in random networks than in highly cliquish networks. It turns out that marketers should work with mixed marketing strategies, which will result in a full contagion of a network product and faster contagion rates with a higher probability.

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.

We analyze a model of di¤usion on social networks. Agents are connected according to an undirected graph (the network) and choose one of two actions (e.g., either to adopt a new behavior or technology or not to adopt it). The return to each of the actions depends on how many neighbors an agent has, which actions the agent's neighbors choose, and some agent-speci…c cost and bene…t parameters. At the outset, a small portion of the population is randomly selected to adopt the behavior.

2012

Diffusion of items occurs in social networks due to spreading of items through word of mouth and exogenous factors. These items may be news, products, videos, advertisements or contagious viruses. When a user purchases or consumes one of such items, we say that she adopts the item and she becomes an item adopter. Previous research has studied diffusion process at both the macro and micro levels. The former models the number of item adopters in the diffusion process while the latter determines which individuals adopt item. Both macro and micro level models have their merits and limitations. In this paper, we establish a general probabilistic framework, which can be used to derive macro-level diffusion models, including the well known Bass Model (BM). Using this framework, we develop several other models considering the social network's degree distribution coupled with the assumption of linear influence by neighboring adopters in the diffusion process. Through some evaluation on synthetic data, this paper shows that degree distribution actually changes during the diffusion process. We therefore introduce a multi-stage diffusion model to cope with variable degree distribution. By conducting experiments on both synthetic and real datasets, we show that our proposed diffusion models can recover the diffusion parameters from the observed diffusion data, which allows us to model diffusion with high accuracy.