Optimal Marketing Policy in a Random Network

Viral marketing takes advantage of preexisting social networks among customers to achieve large changes in behavior. Models of influence spread have been studied in a number of domains, including the effect of ’word of mouth’ in the promotion of new products or the diffusion of technologies. A social network can be represented by a graph where the nodes are individuals and the edges indicate a form of social relationship. The flow of influence through this network can be thought of as an increasing process of active nodes: as individuals become aware of new technologies, they have the potential to pass them on to their neighbors. The goal of marketing is to trigger a large cascade of adoptions. In this paper, we present and solve an analytical model where the individuals are connected according to a large sparse random graph. Borrowing ideas and techniques from Markov random fields, we derive analytical results for various threshold models. The parameters of the model (like the initial fraction of active individuals) are tuned by the marketer at a cost. We optimize the amount of marketing funds spent and compare marketing strategies like targeting nodes or edges. Our model allows to compute the advertising effectiveness as a function of the level of advertising spending and it shows that there is a sharp threshold phenomenon which marketing strategies should take advantage of.