  Transmission of disease, spread of information and rumors, adoption of new
products, and many other network phenomena can be fruitfully modeled as
cascading processes, where actions chosen by nodes influence the subsequent
behavior of neighbors in the network graph. Current literature on cascades
tends to assume nodes choose myopically based on the state of choices already
taken by other nodes. We examine the possibility of strategic choice, where
agents representing nodes anticipate the choices of others who have not yet
decided, and take into account their own influence on such choices. Our study
employs the framework of Chierichetti et al. [2012], who (under assumption of
myopic node behavior) investigate the scheduling of node decisions to promote
cascades of product adoptions preferred by the scheduler. We show that when
nodes behave strategically, outcomes can be extremely different. We exhibit
cases where in the strategic setting 100% of agents adopt, but in the myopic
setting only an arbitrarily small epsilon % do. Conversely, we present cases
where in the strategic setting 0% of agents adopt, but in the myopic setting
(100-epsilon)% do, for any constant epsilon > 0. Additionally, we prove some
properties of cascade processes with strategic agents, both in general and for
particular classes of graphs.
