Percolation of new products

Abstract

In most models of diffusion of new products, every individual in the social network is a potential adopter. When, however, a fraction α of the individuals cannot adopt the product at any time, the new product percolates (rather than diffuses) in the network, similarly to movement through porous materials. We obtain explicit expressions for the fraction of adopters as a function of time, for complete networks, circular networks, D-dimensional Cartesian networks, small-worlds networks, and scale-free networks. These expressions show that the complex effect of percolation can be captured by two simple aggregate effects: Decreasing the market potential by 1−α, and reducing the peers effect by (1−α)k, where k depends on the network type. Hence, percolation of new products is qualitatively similar to diffusion of new products. In particular, there is no threshold value at which a phase transition occurs.