  We study proliferation of an action in binary action network coordination
games that are generalized to include global effects. This captures important
aspects of proliferation of a particular action or narrative in online social
networks, providing a basis to understand their impact on societal outcomes.
Our model naturally captures complementarities among starting sets, network
resilience, and global effects, and highlights interdependence in channels
through which contagion spreads. We present new, natural, and computationally
tractable algorithms to define and compute equilibrium objects that facilitate
the general study of contagion in networks and prove their theoretical
properties. 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 analysis
provides quantitative and qualitative insight into the design of policies to
control or spread contagion in networks. The scope of application is enlarged
given the many other situations across different fields that may be modeled
using this framework.
