A SIMPLE GROWTH MODEL FOR THE DIFFUSION OF A NEW COMMUNICATION SERVICE.

The diffusion of an innovation such as a new communication system is modeled using a randomly generated network of interpersonal influence between members of a social system. Each member decides to adopt the innovation when K out of this particular set of L influencers have already become adopters. A discrete-time recursion is obtained which describes the evolution in time of the fraction of adopters. The model exhibits a critical mass effect where the number of initial adopters must exceed a critical value for the diffusion to saturate the population, otherwise the diffusion ends prematurely without substantial growth. Also exhibited is a bandwagon effect which explains a sudden upsurge in growth followng an initial period of slow diffusion. Both phenomena are amply corroborated by Monte Carlo simulations for a population of 10,000 people.