"Two Is a Crowd" - Optimal Trend Adoption in Social Networks

In this paper, we study how an individual in a social network should decide whether or not to adopt a trend, based on how many people in his/her neighborhood in the social network adopted the trend. In particular we are interested in the question in what adoption policy leads to an optimal trend-adoption in the sense that an individual only adopts a trend if the majority of his/her social network will do so. We use a decision process on a Erdös-Rényi random graph model to model and study this situation. Using this model, we obtain the result that the optimal policy for an individual is to adopt a trend if two people in their neighborhood did. Interestingly, this result/behavior was experimentally observed in real social networks. We hope that this work will help towards building applications that is able to automatically push relevant content to users in online social networks.