Control and Spread of Contagion in Networks

We study proliferation of an action in a network coordination game that is generalized to include a tractable, model-based measure of virality to make it more realistic. We present new algorithms to compute contagion thresholds and equilibrium depth of contagion and prove their theoretical properties. These algorithms apply to arbitrary connected networks and starting sets, both with and without virality. Our algorithms are easy to implement and help to quantify relationships previously inaccessible due to computational intractability. Using these algorithms, we study the spread of contagion in scale-free networks with 1,000 players using millions of Monte Carlo simulations. Our results highlight channels through which contagion may spread in networks. Small starting sets lead to greater depth of contagion in less connected networks. Virality amplifies the effect of a larger starting set and may make full network contagion inevitable in cases where it would not occur otherwise. It also brings contagion dynamics closer to a type of singularity. Our model and analysis can be used to understand potential consequences of policies designed to control or spread contagion in networks.