Contagion and coordination in random networks

We study the problem of spreading a particular behavior among agents located in a random social network. In each period of time, neighboring agents interact strategically playing a 2 × 2 coordination game. Assuming myopic best-response dynamics, we show that there exists a threshold for the degree of risk dominance of an action such that below that threshold, contagion of the action occurs. This threshold depends on the connectivity distribution of the network. Based on this, we show that the well-known scale-free networks do not always properly support this type of contagion, which is better accomplished by more intermediate variance networks.