Competing Diffusions in a Social Network

We develop a model of competing diffusions of goods on a social network. There are two types of goods and individuals: mass-market (more prevalent) and niche-market. We start with a general threshold rule and show that multiple equilibria prevail. Then, when everyone uses a single friend threshold, we find that there is a unique stable steady state and show that the adoption of a mass-market good is greater than its population share. Furthermore, greater connectivity and homophily in the social network will concurrently increase the prevalence of niche-market goods. If there is a strategic agent who wants to promote a niche good, she will invest more in influencing activities than one promoting mass-market goods. When individuals choose their degree of homophily, we show that niche-market individuals exhibit greater homophily than mass-market ones. Finally, we address the issue of political polarization by extending our model to competition on a line with three different political ideologies (left, middle, and right). We show that the pairwise advantage of the middle ideology can enforce amplification of the middle type when it is the more prevalent type or counteract the amplification of the extremes when these are more prevalent.